Fdo.: …………………… Fecha: - IIT · finalidad de monitorizar y mapear los cultivos...

Proyecto realizado por la alumna:

María del Pilar Romón Peris

Fdo.: …………………… Fecha: ……/ ……/ ……

Autorizada la entrega del proyecto cuya información no es de carácter confidencial

EL DIRECTOR DEL PROYECTO

Henning Skriver

Fdo.: …………………… Fecha: ……/ ……/ ……

Vº Bº del Coordinador de Proyectos

Álvaro Sánchez Miralles

Fdo.: …………………… Fecha: ……/ ……/ ……

RESUMEN

I

UNIVERSIDAD PONTIFICIA COMILLAS

ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

INGENIERO INDUSTRIAL

RESUMEN

Debido al crecimiento de la población mundial, el sector agrícola se ha convertido

en un factor social y económico muy importante. Este factor hace que el uso de la

tierra y la conservación de recursos naturales sea uno de los grandes retos de la

humanidad. Por esta razón, y para estimar las producciones agrícolas, es necesario

desarrollar métodos para monotorizar el estado de los campos de cultivo y su

estado de desarrollo.

Percepción remota es una técnica que permite analizar la clasificación de los

cultivos agrícolas y monotorizarlos. Se basa en la reflexión de la energía emitida

por una antena sobre la superficie de la Tierra. Los tipos más comunes de

reflexión se muestran en la Figura 1. El instrumento que mide esta energía emitida

y reflejada se llama radar de imagen. SAR (Radar de Apertura Sintética) es un

tipo de radar de imagen que posee una gran resolución y que es operado a través

de una plataforma móvil, como un satélite o un avión, para mantener su alta

resolución. En particular, SAR ofrece grandes ventajas sobre los sensores ópticos

e infrarrojos para aplicaciones en el sector agrícola. Su habilidad para mapear el

terreno en diferentes situaciones ambientales y su sensibilidad para reconocer el

tamaño y la forma de la vegetación, le hace una herramienta idónea para la

monitorización de los campos de cultivo.

Figura 1. Tipos comunes de reflexión de superficies

RESUMEN

II




El objetivo principal de este proyecto es desarrollar e implementar dos métodos

estadísticos basados en la interpretación de imágenes SAR polarimétricas, con la

finalidad de monitorizar y mapear los cultivos agrícolas mostrados en la Figura 2.

Los datos adquiridos de diferentes campos de cultivo provienen de The Foulum,

un área de evaluación de cultivos que se encuentra en el Centro de Investigaciones

Foulum del Instituto Danés de Ciencias Agrícolas, en Jutlandia, Dinamarca. Esta

área es idónea para la evaluación de diferentes algoritmos de mapeo de campos

agrícolas, porque además de constar de un gran número de campos con diferentes

cultivos, lagos, bosques, áreas de vegetación natural, áreas de hierba y urbanas,

fue fotografiado mensualmente por el satélite EMISAR durante la temporada de

crecimiento de cultivos en 1997.

Figura 2. El área de cultivos: The Foulum

De acuerdo con la principal finalidad de este proyecto, los objetivos pueden

dividirse en:

Implementación en MATLAB de dos métodos de descomposición

estadística para analizar las imágenes SAR.

Análisis and comparación de estos dos métodos

RESUMEN

III




Clasificación de los cultivos de las imágenes SAR del área agrícola

Análisis y evaluación del desarrollo de estos cultivos

Los métodos utilizados en este proyecto son: el modelo de Reflexión de Tres

Componentes y el modelo de Reflexión Basado en Entropía. Después de haber

implementado ambos modelos, las principales conclusiones son que es posible

implementar los dos modelos mencionados y cada uno ofrece resultados

significativos para clasificar diferentes tipos de superficies, incluyendo cultivos

agrícolas. El desarrollo de ciertos tipos de cultivos es apreciable usando el modelo

de Reflexión de Tres Componentes, especialmente entre los llamados cultivos de

primavera y de invierno. Algunos de estos resultados se muestran en la Figura 3.

Figura 3. Imagen resultante después de haber usado el modelo de Reflexión de Tres Componentes

(izquierda) y usando el modelo de Reflexión Basado en Entropía (derecha)

La memoria de este proyecto ha sido escrita de manera que ayuda al lector a

entender la teoría aplicada y a seguir cada paso dado durante el desarrollo del

proyecto. Además, la memoria está acompañada de figuras, bibliografía, páginas

consultadas y el código de programación creado en MATLAB.

Por otra parte, los resultados de este trabajo pueden ser usados y combinados con

técnicas de clasificación y modelos de crecimiento de cultivos, para mejorar la

clasificación individual de cada campo y su predicción.

ABSTRACT

I




ABSTRACT

Due to global population growth, the agricultural sector is a social and economic

factor very essential. This social and economic factor reflects that land use and the

conservation of natural resources are one of the biggest challenges of humanity.

Therefore, in order to estimate agricultural productions, it is necessary to develop

methods to monitor the status of crops and its stage of development.

Remote sensing is a technique that can analyze the classification of agricultural

crops and monitor the crops. It depends upon measuring the reflection or

scattering of incident energy from earth surface features emitted by an antenna.

Figure 1 shows the three most common scattering mechanisms. The instrument,

that measures this energy emitted by an antenna and reflected by a distant surface,

is an imaging radar. SAR (Synthetic Aperture Radar) is a form of imaging radars

that has a high resolution and it is operated from a moving platform, such a

satellite or aircraft, to achieve its high resolution. In particular, SAR offers great

advantages over the optical and infrared sensors for agricultural applications. Its

ability to map the terrain in different weather situations and it is sensitive to the

size, shape and form of vegetation, makes SAR an adequate tool to monitor

agricultural crops.

Figure 1. Common scattering mechanisms

ABSTRACT

II




The main aim of this thesis is to develop and implement two statistical methods

based on image interpretation of polarimetric SAR data, in order to monitor the

development and the mappping of crops shown on Figure 2. The data collected

from different crops are from a test site called The Foulum and located at the

Research Centre Foulum of the Danish Institute of Agricultural Sciences, in

Jutland, Denmark. It was ideally suited for evaluation of the performance of

different algorithms for agriculture and land-cover mapping, because it contains a

large number of agricultural fields with different crops, as well as several lakes,

forests, areas with natural vegetation, grasslands, and urban areas; and it was

monthly covered by EMISAR satellite during the growing season in 1997.

Figure 2. The Foulum test site

According to the main aim, the goals established for the thesis were:

Implementation in MATLAB of two decomposition statistical methods to

analyze SAR data

Analysis and comparison of these two methods

Classification of the crops or seeds from SAR data of the test site used in

the study

ABSTRACT

III




Analysis and evaluation of the development of these crops

The models used in this study were: Three Component Scattering model and

Entropy Based Scattering model. After implemented both models, the main

conclusions are, as it has been demonstrated, that it is possible to implement the

two mentioned models and each of them obtains significant results to classify

different kinds of surfaces, including different seeds or crops. Moreover, the

development of certain types of crops, especially between those named spring

crops and winter crops, is visible with Three Component Scattering model. Some

of the results are shown on Figure 3.

Figure 3. The image result of the test site using Three-Component Scattering model (left) and

using Entropy Based Scattering model (right)

The report has been written in a way that helps the reader to understand the theory

used and to follow each step that have been done during the thesis. Besides, it is

complemented with figures, bibliography, the consulted pages that have been used

and the programming codes created in MATLAB.

Furthermore, the results of this work can be used to be combined with

classification techniques and with the models of crop growth, to improve the

individual classification of crops and their prediction.

CONTENTS OF THE REPORT

I




Contents of the report

Part I Report .............................................................................................. 1

Chapter 1 Introduction .................................................................................... 2

1.1 Theory............................................................................................................... 2

1.1.1 Synthetic Aperture Radar (SAR) .................................................................................... 2

1.1.2 Common Scattering Mechanisms ................................................................................... 3

1.1.3 SAR Data ....................................................................................................................... 4

1.1.4 Three Component Scattering Model .............................................................................. 5

1.1.5 Entropy Based Scattering Model.................................................................................... 7

1.1.6 Speckle in SAR images ................................................................................................ 10

1.1.6.1 Speckle filter ........................................................................................................ 11

1.2 Motivation ...................................................................................................... 13

1.3 Objectives ....................................................................................................... 14

1.4 Methodology ................................................................................................... 15

1.5 Sources used and Supporting tools .............................................................. 16

1.5.1 Test site ........................................................................................................................ 16

1.5.2 Data .............................................................................................................................. 18

1.5.3 Programming language: MATLAB ............................................................................. 19

Chapter 2 Implementation ............................................................................. 20

2.1 Speckle filter .................................................................................................. 20

2.2 Three Component Scattering Model ........................................................... 22

2.3 Entropy Based Scattering Model ................................................................. 28

Chapter 3 Results ........................................................................................... 30

3.1 Speckle Filter ................................................................................................. 30

3.2 Three Component Scattering Model ........................................................... 32

3.3 Entropy Based Scattering Model ................................................................. 36


II




3.3.1 Entropy-alpha planes .................................................................................................... 36

3.3.2 Classification of crops .................................................................................................. 38

3.4 Comparison of models ................................................................................... 41

3.4.1 L-band .......................................................................................................................... 41

3.4.2 C-band .......................................................................................................................... 44

3.5 Development of Crops ................................................................................... 46

3.5.1 Beets ............................................................................................................................. 47

3.5.2 Cereals .......................................................................................................................... 50

3.5.2.1 Spring barley ........................................................................................................ 51

3.5.2.2 Winter Wheat ....................................................................................................... 53

3.5.2.3 Rye ....................................................................................................................... 55

3.5.3 Peas .............................................................................................................................. 57

Chapter 4 Conclusions ................................................................................... 60

4.1 Implementation .............................................................................................. 60

4.2 Results............................................................................................................. 61

Chapter 5 Future Work ................................................................................. 62

Bibliography 63

Part II User guide ..................................................................................... 65

Chapter 1 MATLAB Programming .............................................................. 66

Part III Programming code ....................................................................... 69

Chapter 1 Three Component Scattering Model ............................................ 70

Chapter 2 Entropy Based Scattering Model ................................................. 91

Chapter 3 Speckle Filter .............................................................................. 109

Part IV Data results ................................................................................. 120

Chapter 1 Three Component Scattering Model .......................................... 121

1.1 Tables of Powers .......................................................................................... 121

1.1.1 Beets ........................................................................................................................... 121

1.1.2 Grass .......................................................................................................................... 122

1.1.3 Peas ............................................................................................................................ 123


III




1.1.4 Rye ............................................................................................................................. 126

1.1.5 Spring Barley ............................................................................................................. 128

1.1.6 Spring Oats ................................................................................................................. 132

1.1.7 Winter Wheat ............................................................................................................. 133

1.2 Image Result ................................................................................................ 136

1.2.1 April ........................................................................................................................... 136

1.2.2 May ............................................................................................................................ 137

1.2.3 June ............................................................................................................................ 138

1.2.4 July ............................................................................................................................. 139

Chapter 2 Entropy Based Scattering Model ............................................... 140

2.1 Tables of Entropy & Alpha ........................................................................ 140

2.1.1 Beets ........................................................................................................................... 140

2.1.2 Grass .......................................................................................................................... 141

2.1.3 Peas ............................................................................................................................ 142

2.1.4 Rye ............................................................................................................................. 145

2.1.5 Spring Barley ............................................................................................................. 147

2.1.6 Spring Oats ................................................................................................................. 151

2.1.7 Winter Wheat ............................................................................................................. 152

2.2 Entropy Alpha Planes ................................................................................. 155

2.2.1 April ........................................................................................................................... 155

2.2.2 May ............................................................................................................................ 156

2.2.3 June ............................................................................................................................ 157

2.2.4 July ............................................................................................................................. 158

2.3 Image Results ............................................................................................... 159

2.3.1 April ........................................................................................................................... 159

2.3.2 May ............................................................................................................................ 160

2.3.3 June ............................................................................................................................ 161

2.3.4 July ............................................................................................................................. 162

LIST OF FIGURES

IV




List of figures

Figure 1. Common scattering mechanisms ............................................................. 4

Figure 2. Entropy-alpha plane ................................................................................. 9

Figure 3. SAR image with speckle at the left and the same image filtered reducing

the speckle [7] ....................................................................................................... 11

Figure 4. Eight edge-aligned windows. Depending on the edge direction, one of

the eight windows is to be selected ....................................................................... 12

Figure 5. Methodology of the project .................................................................... 15

Figure 6. The Foulum test site ............................................................................... 17

Figure 7. Equivalent number of looks for 8 20x20 homogeneous areas ............... 20

Figure 8. The areas of where var(x) in the SAR image was negative colored in

white ...................................................................................................................... 21

Figure 9. On the right half plane of the plots, the number of pixels for which

surface scatter is assumed to be dominant. All other pixels are assumed to have

double-bounce scatter as a dominant ..................................................................... 22

Figure 10. The histograms represent the amount of pixels corresponding to the

values of in deg when surface is dominant (up) and when

double bounce is dominant (down) ....................................................................... 23

Figure 11. 50 largest values of according to their allocations . 24

Figure 12. 100 largest values of as they are located on the

image ..................................................................................................................... 25

Figure 13. 50 largest values of powers for pixels that correspond to volume and

surface scattering mechanism according to their allocations on the image .......... 26

Figure 14. Histograms of powers of April data at L-band .................................... 27

Figure 15. Entropy-alpha planes in April at C-band ............................................. 28

LIST OF FIGURES

V




Figure 16. Image result in April at C-band, using Entropy Based Scattering model

with uncommon pixels in color white ................................................................... 29

Figure 17. Comparison of HH and VV phase differences from the original data

(up) and filtered data (down). The phase differences were coded by the gray scale

shown above these two images ............................................................................. 31

Figure 18. Powers according to each relevant type of crop in April at C-band (up)

and at L-band (down) ........................................................................................... 32

Figure 19. Image of the test site based on Three Component Scattering model in

April at C-band (up) and at L-band (down) .......................................................... 33

Figure 20. Image result using Three Component Scattering model in May at L-

band. Using only 3 clusters (up) and using 15 clusters (down) ............................ 35

Figure 21. Entropy-alpha planes in May at C-band (up) and at L-band (down) ... 37

Figure 22. Entropy and Alpha according to type of crop in May at C-band (up)

and L-band (down) ................................................................................................ 39

Figure 23. Image based on Entropy Based Scattering model in May, at C-band

(up) and at L-band (down) ..................................................................................... 40

Figure 24. (a) The image result using Three Component Scattering model. (b) The

image result using Entropy Based Scattering model. (c) Areal image with

numbered fields ..................................................................................................... 42

Figure 25. (a) The image result using Three Component Scattering model

(Filtering). (b) The image result using Entropy Based Scattering model (Filtering).

(c) Areal real image with numbered fields ............................................................ 43

Figure 26. C-Band images of the data not filtered and acquired in April with

Three Component Scattering Model (left) and with Entropy Based Scattering

model (right) .......................................................................................................... 45

Figure 27. C-Band image results of filtered data and acquired in April with Three

Component Scattering model (left) with Entropy Based Scattering model (right) 45

Figure 28. Growth stages of beet plants [12] ........................................................ 47

LIST OF FIGURES

VI




Figure 29. Double bounce power of beet crops at C-band: left and, at L-band:

right ....................................................................................................................... 49

Figure 30. Volume power of beet crops at C-band: left, and at L-band: right ...... 49

Figure 31. Surface power of beet crops at C-band: left, and at L-band: right ....... 49

Figure 32. Growth stages of cereal plants [12] ..................................................... 50

Figure 33. Double bounce power of spring barley crops at C-band: left and, at L-

band: right .............................................................................................................. 52

Figure 34. Volume power of spring barley crops at C-band: left and at L-band:

right ....................................................................................................................... 52

Figure 35. Surface power of spring barley crops at C-band: left, and at L-band:

right ....................................................................................................................... 52

Figure 36. Double bounce power of winter wheat crops at C-band: left, and at L-

band: right .............................................................................................................. 54

Figure 37. Volume power of winter wheat crops at C-band: left, and at L-band:

right ....................................................................................................................... 54

Figure 38. Surface power of winter wheat crops at C-band: left, and at L-band:

right ....................................................................................................................... 54

Figure 39. Double bounce power of rye crops at C-band: left, and at L-band: right

............................................................................................................................... 56

Figure 40. Volume power of rye crops at C-band: left and at L-band: right ........ 56

Figure 41. Surface power of rye crops at C-band: left, and at L-band: right ....... 56

Figure 42. Growth stages of pea plants [12] ......................................................... 57

Figure 43. Double bounce power of pea crops at C-band: left, and at L-band: right

............................................................................................................................... 59

Figure 44. Volume power of pea crops at C-band: left, and at L-band: right ....... 59

Figure 45. Surface power of pea crops at C-band: left and at L-band: right ......... 59

Figure 46. C-band of the April acquisition applying Three Component Scattering

model ................................................................................................................... 136

LIST OF FIGURES

VII




Figure 47. L-band of the April acquisition applying Three Component Scattering

model ................................................................................................................... 136

Figure 48. C-band of the May acquisition applying Three Component Scattering

model ................................................................................................................... 137

Figure 49. L-band of the May acquisition applying Three Component Scattering

model ................................................................................................................... 137

Figure 50. C-band of the June acquisition applying Three Component Scattering

model ................................................................................................................... 138

Figure 51. L-band of the June acquisition applying Three Component Scattering

model ................................................................................................................... 138

Figure 52. C-band of the July acquisition applying Three Component Scattering

model ................................................................................................................... 139

Figure 53. L-band of the July acquisition applying Three Component Scattering

model ................................................................................................................... 139

Figure 54. Entropy-alpha planes of the April acquisition at C-band ................... 155

Figure 55. Entropy-alpha planes of the April acquisition at L-band ................... 155

Figure 56. Entropy-alpha planes of the May acquisition at C-band .................... 156

Figure 57. Entropy-alpha planes of the May acquisition at L-band .................... 156

Figure 58. Entropy-alpha planes of the June acquisition at C-band .................... 157

Figure 59. Entropy-alpha planes of the June acquisition at L-band .................... 157

Figure 60. Entropy-alpha planes of the July acquisition at C-band .................... 158

Figure 61. Entropy-alpha planes of the July acquisition at L-band ..................... 158

Figure 62. C-band of the April acquisition applying Entropy Based Scattering

model ................................................................................................................... 159

Figure 63. L-band of the April acquisition applying Entropy Based Scattering

model ................................................................................................................... 159

Figure 64. C-band of the May acquisition applying Entropy Based Scattering

model ................................................................................................................... 160

LIST OF FIGURES

VIII




Figure 65. L-band of the May acquisition applying Entropy Based Scattering

model ................................................................................................................... 160

Figure 66. C-band of the June acquisition applying Entropy Based Scattering

model ................................................................................................................... 161

Figure 67. L-band of the June acquisition applying Entropy Based Scattering

model ................................................................................................................... 161

Figure 68. C-band of the July acquisition applying Entropy Based Scattering

model ................................................................................................................... 162

Figure 69. L-band of the July acquisition applying Entropy Based Scattering

model ................................................................................................................... 162

LIST OF TABLES

IX




List of tables

Table 1: Types of crop and their field number according to Figure 5 ................... 17

Table 2: BBCH scale ............................................................................................. 46

Table 3: Height and BBCH of beet field from April to July ................................. 48

Table 4. Height and BBCH of spring barley field from April to July ................... 51

Table 5: Height and BBCH of winter wheat fields from April to July ................. 53

Table 6: Height and BBCH of rye fields from April to July ................................. 55

Table 7: Height and BBCH of pea fields from April to July ................................ 58

LIST OF SYMBOLS

X




List of symbols

α Complex parameter (Freeman-Durden decomposition)

Average angle (Cloude-Pottier decomposition)

Complex parameter (Freeman-Durden decomposition)


Eigenvalue

Measure of speckle level


b Weighting function

Polarimetric covariance matrix

C1 Function of the first curve of Entropy-alpha plane

C2 Function of the second curve of Entropy-alpha plane

Eigenvector

E {·} Mean operator

Eh Electric field component for polarization h

Ei Incident electric field

Es Scattered electric field

Equivalent number of looks

Ev Electric field component for polarization v

Surface scatter contributions

Double-bounce scatter contributions

Volume scatter contributions

H Entropy (Cloude-Pottier decomposition)

m Multi-look image

LIST OF SYMBOLS

XI




Linear Matrix Transform

N Number of looks

Probability associated to eigenvalue . Called also power

Pd, Pdb Power associated to double bounce scattering

Ps Power associated to surface scattering

Pv Power associated to volume scattering

Scattered Matrix

Shh Complex scattering amplitudes for receive polarization h and transmit

polarization h

Shv Complex scattering amplitudes for receive polarization h and transmit

polarization v

Svh Complex scattering amplitudes for receive polarization v and transmit

polarization h

Svv Complex scattering amplitudes for receive polarization v and transmit

polarization v

Polarimetric coherency matrix

V {·} Variance operator

Variance of the reflectance without speckle noise

Local variance

x Noise-free pixel value

Filtered pixel value

y Center pixel value

Local mean

Z Hermitian matrix

Filtered covariance matrix

LIST OF ACRONYMS

XII




List of acronyms

BBCH Bundesanstalt, Bundessortenamt and CHemical industry

EMISAR Polarimetric Danish airborne SAR system

ENL Equivalent Number of Looks

HH Horizontal Transmit, Horizontal Receive

HV Horizontal Transmit, Vertical Receive

VH Vertical Transmit, Horizontal Receive

SAR Synthetic Aperture Radar

VV Vertical Transmit, Vertical Receive

GLOSSARY

XIII




Glossary

Backscattering: In a scattering problem, backscattering direction refers to the

opposite direction of the incident wave. A backscattering configuration refers to

those situations in which the transmitting and receiving systems are collocated. Booting: It occurs when vegetative plant parts appear in the seed.

Boxcar filter: Spatial filtering consisting of the average of a certain quantity over

a given number of pixels.

Classification: Signal processing technique aiming to cluster the image pixels

which present common characteristics.

Cluster: Group of pixels with the same feature or scattering mechanism.

Coherent decomposition: Any decomposition of the scattering matrix into

simpler scattering mechanisms.

Complex scattering amplitude: Without considering the propagation effects, the

complex scattering amplitude refers to the quotient between the scattered and the

incident fields.

Complex scattering coefficient: The same as complex scattering amplitude.

Correlation coefficient: Magnitude of the complex correlation coefficient of a

pair of complex SAR images.

C-band: Name given to a certain portion of the electromagnetic spectrum,

between 4 to 8 GHz.

Double bounce scattering: It occurs when the wave is reflected in a horizontal

and then in a vertical direction.

GLOSSARY

XIV




Eigen decomposition: It also receives the name of “matrix diagonalization”. For

a square matrix, it consists of the transformation giving as a result a diagonal

matrix. The elements of the resulting diagonal matrix are called eigenvalues,

whereas the columns of the matrix performing the transformation are called

eigenvectors.

Equivalent number of looks (ENL): A quantity employed to describe the

statistics of the speckle noise. The higher its value, the lower the variance of

speckle noise.

Flowering: The process from first flowers open to fruit set is visible.

Germination: The beginning of growth of a seed or crop. The germination of

most crops occurs in response to warmth and water.

Heading: Inflorescence emergence. The process before flowering.

Jones vector: Complex bidimensional vector employed to describe the

polarization of an electromagnetic wave. It contains all the polarization

information except the polarization handedness as it does not contain propagation

information.

L-band: Name given to a certain portion of the electromagnetic spectrum,

between 1 to 2 GHz.

Orthogonality: In elementary geometry, the same as perpendicular. In the case of

a space vector, two elements v and w are said orthogonal if their inner product

equals zero.

Ripening: Maturity of fruit and seed.

Senescence: Deterioration of a seed.

Segmentation: Signal processing technique aiming to divide the image pixels

which present common characteristics.

GLOSSARY

XV




Span: Power received by a fully polarimetric systems. It consists of the addition

of the intensity of the four elements of the scattering matrix.

Speckle: Statistical variation associated with SAR imagery and caused by the

coherent nature of the imaging process.

Stokes vector: Four dimensional real vector able to represent the polarization

state of an electromagnetic wave.

Supervised classification: Classification based on the external help of the user.

This classification scheme is not automatic.

Surface scattering: Scattering mechanism produced by a surface (smooth or

rough).

Synthetic Aperture Radar (SAR): It is a type of radar whose main characteristic

is the use of relative motion between an antenna and its target region to provide

consistent long-term distinctive signal and to obtain a good spatial resolution of

the target.

Tillering: It refers to the production of tillers. This process occurs when multiple

stems (tillers) are produced starting from the initial single tiller.

Unsupervised classification: Classification without any external help of the user.

This classification scheme is considered fully automatic.

Volume scattering: Scattering mechanism produced in a cloud of particles, it is

generally due to trees or vegetation.

REPORT

1




Part I REPORT

REPORT - Introduction

2




Chapter 1 INTRODUCTION

Remote sensing depends upon measuring the reflection or scattering of incident

energy from earth surface features. If the incident energy is in the optical range of

wavelengths – i.e. in the visible or near infrared – it is scattered largely by the

surface of the material being imaged. Sometimes there is penetration into a

medium, such as short wavelengths into water.

Because the wavelength of the microwave energy used in radar remote sensing is

so long by comparison to that used in optical sensors, the energy incident on earth

surface materials can often penetrate so that scattering can occur from within the

medium itself as well as from the surface. Indeed, there are several mechanisms

by which energy can scatter to the sensor, and they can be quite complex. In order

to be able to interpret radar imagery it is necessary to have an understanding of

the principal mechanisms so that received energy can be related to the underlying

biophysical characteristics of the medium, for example an area with crops. [1]

1.1 THEORY

1.1.1 SYNTHETIC APERTURE RADAR (SAR)

A typical radar (RAdio Detection and Ranging) measures the strength and round-

trip time of the microwave signals that are emitted by a radar antenna and

reflected off a distant surface or object. Then, the radar antenna alternately

transmits and receives pulses at particular microwave wavelengths and

polarizations (vertical or horizontal polarization). At the Earth's surface, the

energy in the radar pulse is scattered in all directions, with some reflected back

toward the antenna. This backscatter returns to the radar as a weaker radar echo


3




and is received by the antenna in a specific polarization. This echo is converted to

digital data and passed to a data recorder for later processing and display as an

image.

SAR is a form of imaging radars and is an abbreviation for Synthetic Aperture

Radar. It has a high resolution and it has to be operated from a moving platform,

typically an aircraft or a satellite, in order to achieve its high resolution. If used

for mapping a moving platform is also desirable in order to cover a large terrain

area with the antenna beam. A key characteristic of a SAR is that it is a coherent

radar. It needs a very stable oscillator so that phase between transmitted pulses

and received echoes can be measured.

1.1.2 COMMON SCATTERING MECHANISMS

Figure 1 shows the three most common scattering mechanisms that occur in radar

remote sensing of the land surface.

The first mechanism is surface scattering in which the energy can be seen to

scatter or reflect from a well-defined interface.

The second is volume scattering, for which there is no identifiable single or

countable number of scattering sites; instead, the reflections are seen to come

from a myriad of scattering elements, such as the components of a tree canopy.

The third is called strong or hard target scattering and can come in a variety of

forms. The relevant one in this study is shown on Figure 1 as double bounce

scattering. [1]


4




Figure 1. Common scattering mechanisms

1.1.3 SAR DATA

The polarimetric SAR measures the amplitude and the phase of the backscattered

signals in the four combinations of the linear receive and transmit polarizations

HH, HV, VH and VV [2]. These signals form the complex scattering matrix S [2]

and they relates the incident electric field Ei and the scattered electric field Es, by:

i

v

i

h

vvvh

hvhhrik

s

v

s

h

E

E

SS

SS

r

e

E

E 0

(1)

where Eh is the electric field component for polarization h, Ev is the electric field

component for polarization v; and Shh is the complex scattering amplitudes for

receive polarization h and transmit polarization h, Shv for receive polarization h

and transmit polarization v, Svh for receive polarization v and transmit

polarization h and Svv for receive polarization v and transmit polarization v.

Normally, reciprocity is considered for natural targets, i.e.

As each pixel of a SAR image is composed of many scatterers, the polarimetric

scattering information is presented by a complex vector with three unique

elements of the scattering matrix:


5




(2)

The backscatter of the polarimetric covariance matrix can be considered as the

average of the covariance matrices of individual scatterers in each pixel. This

polarimetric covariance matrix for each pixel is defined as:

(3)

The decomposition of the covariance matrix in different types of reflection

simplifies the data, thus the surface features can be identified readily.

1.1.4 THREE COMPONENT SCATTERING MODEL

Three Component Scattering model is also called Freeman and Durden

decomposition [3] and it represents the three common scattering mechanisms are:

Surface scattering: Scattering mechanism produced by a surface

Double-bounce scattering : Double-bounce scattering mechanism

Volume scattering : Canopy scatter from randomly oriented dipoles

The total power that is considered the span of the covariance matrix is:

(4)

where Ps, Pd and Pv correspond to the part of the power due to surface, double

bounce and volume, respectively.

As each pixel has associated a polarimetric covariance matrix, each pixel also has

three elements of the total backscattering that need to be estimated in order to

determine which scattering mechanism is presented in the pixel.

The surface model used in the Freeman-Durden decomposition is:


6




10

000

0

10

000

0

103

1

03

20

3101

**

2

vdv fffC (5)

where , and are the surface, double-bounce, and volume scatter

contributions.

Then, the model for the total backscatter used to obtain the values of powers is:

(6)

For the pixels that correspond to the surface scattering mechanism:

(7)

For double-bounce scattering:

(8)

And for volume scattering:

(9)

Finally, each of three powers can be calculated as follows:

(10)

It is important to recognize that this decomposition is neither unique nor

theoretically determined. For this reason, an assumption is considered depending

on the predominance of two scattering mechanisms: surface or double bounce.


7




If surface scattering mechanism is dominant, it is assumed that

and , and in order to solve the equation system, the parameter

“α” is set to -1. On the other hand, if , the double-bounce

scattering mechanism is dominant and the parameter “β” is set to 1.

1.1.5 ENTROPY BASED SCATTERING MODEL

Entropy based model, also called Cloude and Pottier decomposition, propose an

algorithm [4] [5] composed of an unsupervised target decomposition classifier.

In this model, the covariance matrix is converted to a coherency matrix by a linear

transform:

(11)

where:

(12)

Then, applying eigenvalue analysis, the multilook coherency matrix is

decomposed as:

(13)

where λ1, λ2 and λ3 are the eigenvalues of the coherency matrix and e1, e2 and e3

their eigenvectors. Furthermore, the eigenvectors can be written as:

(14)

The average of angle that corresponds to the type of scatterers and varies from 0

to 90 degrees:

(15)

TTTeeeeeeT

*

333

*

222

*

111

Ti

ii

i

iii

i

iiii eeee sinsincossincos


8




The measure of the distribution of probabilities, called Cloude and Pottier’s

entropy may be interpreted as a measure of the randomness of the scattering

process and it may show the mixture of scattering types in a region. For example

for pure smooth surfaces, the entropy H is zero and increases with rougher

surface.

3

1

3logi

ii PPH

j

j

iiP

The combination of these two parameters provides the classification plane H-α,

illustrated on Figure 2. The plane H-α is divided into nine zones but only eight

zones are usable and each zone denotes a different type of scattering mechanism.

The region outside the curve on Figure 2 represents mathematically infeasible

combinations of H and values and no pixel can belong to that region.

Curve 1 is defined as following:

(17)

And curve 2 as:

(18)

(19)


9




Figure 2. Entropy-alpha plane

The zones on Figure 2 means:

Zone 1 (Z1) refers to the high entropy and double bounce scattering, and it

is located in: 55 < α < 90 ; 0.9 < H < 1 and curve 1

Zone 2 (Z2) indicates high entropy and volume scattering, and it is

located in: 40 < α < 55 ; 0.9 < H < 1 and curve 2

Zone 3 (Z3) is not a feasible region, and it is located in: 0 < α < 40 ; 0.9

< H < 1 and curve 2

Zone 4 (Z4) designates a medium entropy and double bounce scattering,

and it is located in: 50 < α < 90 ; 0.5 < H < 0.9 and curve 1

Zone 5 (Z5) indicates medium entropy and volume scattering and it is

located in: 40 < α < 50 ; 0.5 < H < 0.9 and curve 2

Zone 6 (Z6), located in: 0 < α < 50 ; 0.5 < H < 0.9 and curve 2, shows a

medium entropy and surface scattering


10




Zone 7 (Z7) designates a low entropy and double bounce scattering, and it

is located in: 47.5 < α < 90 and 0 < H < 0.5

Zone 8 (Z8) indicates low entropy and volume scattering, and it is located

in: 42.5 < α < 47.5 and 0 < H < 0.5

Zone 9 (Z9) is located in: 0 < α < 42.5 ; 0 < H < 0.5 and curve 2

1.1.6 SPECKLE IN SAR IMAGES

Speckle is one of the most serious disadvantages of SAR images. It is a coherent

interference of waves scattered from terrain elements observed in each resolution

cell (set of pixels).

The process of the coherent interference is the following; an incident radar wave

interacts with each element of the surface and surface cover to generate scattered

waves propagating in all directions. Those scattered waves that reach the

receiving antenna are summed in direction and phase to make the received signal.

The relative phase components contain the differential propagation paths.

The SAR focusing operation coherently combines the received signals to form the

image. Then, the scattered wave phase addition results in both constructive and

destructive interference of individual scattered returns and randomly modulates

the strength of the signal in each resolution cell. The constructive interference is

an increase from the mean intensity and produces bright pixels, and the

destructive interference is a decrease from the mean intensity and produces dark

pixels. Finally, these random fluctuations give rise to speckle. [6]

This interference can appreciated on Figure 3, showing two images, one with

speckle and another one with a speckle reduction.


11




Figure 3. SAR image with speckle at the left and the same image filtered reducing the speckle [7]

1.1.6.1 Speckle filter

Lee filter [8] was applied to reduce the speckle. It is a boxcar filter characterized

by avoiding the two main limitations of general boxcar filters:

sharp edges are generally blurred

point scatterers are over filtered and transformed to spread targets

The measure of speckle noise is determined as follows:

where N is a number of looks that can be estimated according to the variance to

ratio taken for several homogeneous areas. The equivalent number of looks can be

calculated as following:

(20)


12




where VMR denotes variance-to-mean-squared ratio and m is the multilook

image.

Before applying the filter, it is necessary to determine the edge direction within

the window. There could be eight possible edge directions as it is shown on

Figure 4.

Figure 4. Eight edge-aligned windows. Depending on the edge direction, one of the eight windows

is to be selected

The appropriate edge-aligned window is determined based on the closeness of the

center sub mean to the two sub means in the edge-direction. While choosing the

size of the window, it is important to take into consideration that the larger is the

window the better speckle reduction can be obtained. However in this case the

image can be much blurred and over filtering can occur. 7x7 moving window is

applied for edge detecting and filtering.

The local statistic filter is:

(22)

where the result is the weighting function b, having a value between 0 and 1 and

can be calculated as follows:

(21)


13




where is the local variance and is the variance of the reflectance

without speckle noise. For inhomogeneous areas is high. For

homogeneous are and .

The span image is used to compute the weight in a selected edge-aligned window.

Then, the weighting function and one of the eight edge aligned windows are used

to filter the whole covariance matrix, including the off-diagonal terms. The

filtered covariance matrix is:

(24)

where each element of is the local mean, computed with pixels in the same

edge-aligned window. It should be noted when applying the filter to a window,

may be negative due to insufficient samples or due to using larger than the

correct value of . If so, should be set to zero to ensure that the weight is

between zero and one.

1.2 MOTIVATION

One of the biggest challenges facing humanity is the understanding of the

environment, particularly with respect to land use and the conservation of natural

resources. Besides, due to global population growth makes the agricultural sector

a social and economic factor very essential. In recent decades, several and

significant changes in agricultural techniques have been generated primarily by

the need to increase crop production. Therefore, in order to make estimates of

agricultural production is also necessary to develop methods to monitor the status

of crops and its stage of development.

Remote sensing is a technique that has analyzed the classification of agricultural

crops and their monitorization for a long time. In particular, Synthetic Aperture

(23)


14




Radar (SAR) offers great advantages over the optical and infrared sensors for

agricultural applications. The ability to map the terrain is higher in different

weather situations, such as cloud cover. Moreover, the radar backscatter is

sensitive to the size, shape and form of vegetation, as well as its orientation and

surface roughness [9].

The test site used in this study is ideally suited for evaluation of the performance

of different algorithms for agriculture and land-cover mapping. Especially, the

1998 data set, with its monthly coverage of the area during the growing season is

well-suited for simulating the performance of satellite systems.

1.3 OBJECTIVES

The main aim of this report is to develop and implement two statistical methods

based on image interpretation of polarimetric SAR data, in order to monitor the

development and the mappping of crops.

The results can be combined with classification techniques and with models of

crop growth, to improve the individual classification of crops and their prediction.

According to this main aim, the objectives can resume as following:

Implementation in MATLAB of two decomposition statistical methods to

analyze SAR data:

o Three Component Scattering model

o Entropy Based Scattering model

Analysis and comparison of these two methods

Classification of the crops or seeds from SAR data of the test site used in

the study

Analysis and evaluation of the development of these crops


15




1.4 METHODOLOGY

The methodology of this Project is illustrated on Figure 5. Methodology of the

project. The first step was obtained appropriate SAR data to work with. Secondly,

a study and selection of statistical methods was necessary. The third step was the

implementation of two scattering models in MATLAB to analyze the SAR data.

Then, the analysis of the results was essential to decide if the quality of the image

result was enough. After that, and optimization was done applying a speckle filter

with the original SAR data. Finally, the process is redone until the quality of the

image result was acceptable to draw the final conclusions.

Figure 5. Methodology of the project


16




1.5 SOURCES USED AND SUPPORTING TOOLS

1.5.1 TEST SITE

The Foulum test site is located at the Research Centre Foulum of the Danish

Institute of Agricultural Sciences, and it contains a large number of agricultural

fields with different crops, as well as several lakes, forests, areas with natural

vegetation, grasslands, and urban areas.

The area of plant production includes facilities for experimental cultivation as

well as research in applied cropping systems and specialized facilities. Research

Centre Foulum disposes of a built up area of approx. 100,000 m2 and 550 hectares

of land. The forest areas consist of deciduous forest and coniferous forest:

Norway spruce and Caucasian fir.

The crop types present in the area are 10, for spring crops: beets, peas, potatoes,

maize, spring barley, and oats, and for winter crops: rye, winter barley, winter

wheat, winter rape, and grass. However, the land area has 7 relevant types of

crops for this study and in total 37 fields of them, this is shown on Figure 6. This

area is relatively flat, and corrections of the local incidence angle due to terrain

slope are therefore as a first approximation not necessary.

The types of crops analyzed are for spring crops: beets, peas, spring barley, and

spring oats; and for winter crops: grass, rye and winter wheat. Table 1 shows the

type of crop corresponding to the field number on Figure 6.


17




Figure 6. The Foulum test site

Type of crop Field number

Beets 30

Grass 2,4,10,16,26,32

Peas 7,15, 17,18,19,21,24,28 ,37

Rye 1,8,12,23

Spring barley 6,13,14,29,31,34,36

Spring oats 9

Winter barley 17,25

Winter wheat 3,5,11,20,27,33

Table 1: Types of crop and their field number according to Figure 6. The Foulum test site


18




1.5.2 DATA

The ability of SAR to penetrate cloud cover makes it particularly valuable in

frequently cloudy areas. Image data serve to map and monitor the use of the land,

and these data are of gaining importance for forestry and agriculture .

In this study, the SAR data were acquired by the fully polarimetric Danish

airborne SAR system, EMISAR, which operates at two frequencies, C-band (5.3

GHz/5.7 cm wavelength) and L-band (1.25 GHz/24 cm wavelength). The

nominal one-look spatial resolution is 2 m by 2 m (one-look); the ground range

swath is approximately 12 km and typical incidence angles range from 35º to 60º.

The processed data from this system are fully calibrated by using an advanced

internal calibration system. In the period from 1993 to 1999 the Foulum test site

has been covered by the EMISAR many times, because the test site has acted as

calibration site for the system. In 1998 simultaneous L-band and C-band data

were acquired over the Foulum agricultural test site in Jutland, Denmark, on 21

March, 17 April, 20 May, 16 June, 15 July and 16 August. On 17 April, 20 May,

16 June, and 15 July four parallel acquisitions were made with different incidence

angles. Each field was therefore measured with four different incidence angles,

with values ranging from about 20° to 65°.

All acquisitions were co-registered by identifying ground control points in the

images and using an interferometric DEM acquired by the EMISAR system.

Before resampling, the original one-look scattering matrix data were transformed

to covariance matrix data, and these data were averaged to reduce the speckle by a

cosine-squared weighted 9 by 9 filter. The new pixel spacing in the images is 5 m

by 5 m, and the effective spatial resolution is approximately 8 m by 8 m at mid-

range. After the averaging the equivalent number of looks is estimated to be 9-11

from homogenous areas in the images. This corresponds to a standard deviation

for the backscatter coefficient of approximately 1.1 – 1.8 dB.

http://earth.esa.int/applications/data_util/landc/index.htm


19




1.5.3 PROGRAMMING LANGUAGE: MATLAB

MATLAB is a matrix processing language and images are represented as

matrices. Thus, instead of representing pixel positions as (x,y), it is common to

use the notation (r,c) indicating the row and column position of a pixel in the

matrix.

MATLAB provides an image input function, “imread()”, that reads an image from

a graphics file. The return value is an array containing the image data. If the file

contains a grayscale image, the return value is an M-by-N array. If the file

contains a truecolor image, the return value is an M-by-N-by-3 array. To display

image data, the function is “imshow()” and displays the image stored in the

graphics file. The file must contain an image that can be read by “imread” or

“dicomread”. “imshow” calls “imread” or “dicomread” to read the image from the

file, but does not store the image data in the MATLAB workspace. If the file

contains multiple images, imshow displays the first image in the file. [10]

In addition, it was necessary to use other MATLAB function in this project. Since

statistic methods are implemented to analyze the SAR data, the MATLAB user

guide about mathematics were used [11]. A basic MATLAB programming guide

can also be found in the section Part II.

REPORT - Implementation

20




Chapter 2 IMPLEMENTATION

2.1 SPECKLE FILTER

Before applying the filter it is important to estimate the number of looks correctly

to obtain the value σ2 for the variance of the noise, σ is a measure of speckle

noise.

Equivalent number of looks can be determined as follows:

Figure 7 shows the values of ENL for 8 areas of 20x20 pixels2

Figure 7. Equivalent number of looks for 8 20x20 homogeneous areas

ENL is determined calculating variance to mean ratio for 8 areas 10x10 with high

backscattering that are assumed to be homogeneous. According to Figure 7 the

1 2 3 4 5 6 7 8

2

4

6

8

10

12

Area 20x20

EN

L

Number of looks HH

Number of looks VV


21




most plausible number of looks is 10 as for the most of the areas ENL is less than

10. Small values of ENL indicates that the variance of the values of and

are very large. This is possible because the image has a lot of speckle or

because the chosen area was not totally homogeneous.

While implementing the filtering for some of the areas calculated values of

was negative due to insufficient samples or due to using larger than the correct

value of .

The areas where was negative are indicated white on the image. Each

pixel on the image on the Figure 8 corresponds to 7x7 pixels window of the

original image.

Figure 8. The areas of where var(x) in the SAR image was negative colored in white


22




2.2 THREE COMPONENT SCATTERING MODEL

The Calculation of powers for each of the pixels is based on the assumption that

is close to zero when the surface scatter is dominant and is around

±π when the double bounce scatter is dominant. However on Figure 9, it is shown

that the values of vary from 0 to ±π.

Figure 9. On the right half plane of the plots, the number of pixels for which surface scatter is

assumed to be dominant. All other pixels are assumed to have double-bounce scatter as a

dominant

Apparently, there are a lot of pixels that do not fit the proposed model. Taking a

closer look for both halves of the plane it is shown on Figure 10. The bulk of the

pixels at the right half plane is close to zero, however values of

on the left half plane are not concentrated at near ±π.


23




Figure 10. The histograms represent the amount of pixels corresponding to the values of

in deg when surface is dominant (up) and when double bounce is dominant

(down)

The amount of pixels with surface scattering dominant is 838628, double bounce

209948.

-100 -80 -60 -40 -20 0 20 40 60 80 1000

2000

4000

6000

8000

10000

12000

14000

am

ou

nt o

f p

ixe

ls

arg(ShhSvv*)

-200 -150 -100 -50 0 50 100 150 2000

1000

2000

3000

4000

5000

6000

7000

8000

9000

am

ou

nt o

f p

ixe

ls

arg(ShhSvv*)


24




According to the Figure 11 polarimetric SAR data has few large deviations of

values. Experimental result shows that pixels with large values of

powers are in most cases clustered around one particular area as shown on Figure

11.

Figure 11. 50 largest values of according to their allocations

The allocation of the 100 hundred largest values of the component

amplitudes on the image are shown on the Figure 12. Some of them randomly

appear on the image, however, there can be determined 5 clusters of largest

deviations.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 105

0

10

20

30

40

ab

s(S

hh

Svv*)

pixel position

Re(ShhSvv*)<0

0 1 2 3 4 5 6 7 8

x 105

0

100

200

300

400

ab

s(S

hh

Svv*)

pixel position

Re(ShhSvv*)>0


25




Figure 12. 100 largest values of as they are located on the image

It can be inferred, that as the clusters of the large values are allocated at the areas

that are covered with some buildings, that deviation should not be considered as

an error.

Apparently, the presence of error in polarimetric SAR data has the influence on

calculated values of powers for pixels as it is shown on Figure 13.


26




Figure 13. 50 largest values of powers for pixels that correspond to volume and surface scattering

mechanism according to their allocations on the image

Furthermore, according to Freeman-Durden decomposition, each pixel has three

powers related to their scattering mechanism: double bounce, volume and surface.

The values of the powers vary incredibly among some pixels and a comparison

between them is difficult, even more the representation of the color image

according to the type of powers.

This problem was solved changing the normal scale to a decibel scale, using as

reference: Pref=1, as follows:

Figure 14 shows the histograms of the three different powers of all pixels in the

SAR image in April and with L-band.

0 2 4 6 8 10 12

x 105

0

100

200

300

400

Po

we

r

Pixel position

Volume

0 1 2 3 4 5 6 7 8 9

x 105

0

500

1000

1500

2000

Po

we

r

Pixel position

Surface

(25)


27




Figure 14. Histograms of powers of April data at L-band

It is interesting to see the large number of pixels that have the value of powers

almost zero. These pixels do not belong to agricultural areas and they are

representing pure scattering mechanism. For example, the highest double bounce

values (Pd) correspond to building areas, the highest volume values (Pv) are

related to the trees of the forest and the highest surface values (Ps) correspond to

the lake.


28




2.3 ENTROPY BASED SCATTERING MODEL

Implementing the Cloude-Pottier decomposition, the SAR image obtained in April

with C-band presents an odd H-α plane (Figure 15). Several pixels have entropy

lower than zero. It is not correct to obtain a negative entropy because entropy

represents the randomness of the eigenvalues of the coherency matrix .

Figure 15. Entropy-alpha planes in April at C-band

In order to determine the origin of this inconsistency, the uncommon pixels have

been represented in color white on the SAR image of May (Figure 16).

Figure 16 shows that the white pixels are spread on the SAR image and no visual

correlation is appreciated. This situation may mean that the polarimetric SAR data

of this image were corrupted before the implementation of the scattering model.


29




Figure 16. Image result in April at C-band, using Entropy Based Scattering model with uncommon

pixels in color white

REPORT - Results

30




Chapter 3 RESULTS

3.1 SPECKLE FILTER

The ideal situation is when the image would be colored just in black and white

after apply the filter, because in this case is close to 0 and ±π

values as it is assumed when applying the classification method.

The results indicate that the speckle is clearly reduced, however the image is still

much noisy. One of the reasons is that, while applying the filter, one of the eight

edge aligned windows was used in a moving 7x7 window, the situation when

there is no edge inside the window was not taken into consideration.

In the case where the window without edges is considered, it would be possible to

observe each field with only one color. Nevertheless, in some fields there are

buildings that produce small zones (very few amount of pixels) inside the fields

and it may be misunderstanding by noise.

After filtering the amount of gray colored areas is reduced that indicates that HH

VV phase difference is more concentrated around the desired values. The results

of division into three categories (black, grey and white) before and after filtering

are shown on the Figure 17. Besides, two relevant fields with buildings areas are

marked with blue circles in the filtered image. The crops of the fields are black

and the buildings are represented by the color white.

REPORT - Results

31




Figure 17. Comparison of HH and VV phase differences from the original data (up) and filtered

data (down). The phase differences were coded by the gray scale shown above these two images

±π 0

REPORT - Results

32




3.2 THREE COMPONENT SCATTERING MODEL

Figure 18 shows the result of the powers of each band and for the relevant types

of crop. On Figure 19, it can be seen the image result of April at L-band, using

this model. On this Figure 19, the intensity of color red is proportional to Pd

(double bounce scattering), the color green to Pv (volume scattering) and the color

blue to Ps (surface scattering).

Figure 18. Powers according to each relevant type of crop in April at C-band (up) and at L-band

(down)

-20-18-16-14-12-10

-8-6-4-20

Spring barley

Beets Peas Spring oats

Grass Rye Winter wheat

Po

we

r (d

B)

C band (April)

mean_Pdb mean_Pv mean_Ps

-20

-15

-10

-5

0

Spring barley



Po

we

r (d

B)

L band (April)

mean_Pdb mean_Pv mean_Ps

REPORT - Results

33




Figure 19. Image of the test site based on Three Component Scattering model in April at C-band

(up) and at L-band (down)

REPORT - Results

34




SAR data corresponding in April was used in this section to analyze the different

types of crops because the height of each crop is significant in April. Grass (field

5) is very appreciable on the graphic of L-band (Figure 18). It has a high Ps and

Pd scattering and low Pv compared to other relevant crops. This is the reason that

grass is shown in color pink on Figure 19 spring barley (field 6, 13 and 14) spring

oats (field 9) and Peas has a higher Ps than Pd and Pv, this is shown in the dark

blue of these fields shown on the L-band of Figure 18. Beets (field 30) has a

higher Ps and Pv than Pd but Pv is higher than Ps, shown greener than other

mentioned fields at the L-band of Figure 19.

On the other hand, rye and winter wheat fields have the three powers very

similar, especially Pd and Pv, this is shown at both L-band and C- band on Figure

18. These both types of crops present the same color due to the similarity of the

crop plant and its development. C-band presents a higher Pv in all of the analyzed

fields due to the penetration of the wavelength.

The classification of crops must start assigning a specific class to each pixel. A

primary classification consists in defining three different classes according to each

power (Pd, Pv, Ps). Then, it is possible to divide each class in clusters in order to

obtain a more precise classification.

The difference between only 3 classes without clusters and the 15 clusters for

each class is shown on Figure 20; now using the May acquisition, because this

acquisition is more adequate to distinguish fields. The result of Figure 20 is

different of Figure 19 because Three Component Scattering model requires giving

the value of the highest power in each pixel, instead the value of the three of them.

Grass and winter wheat fields are clearly different compared to the other fields,

presenting a darker red. Besides, spring oats field shows a color practically

orange, differing from the rest of fields. In addition, peas and beets fields are

represented with dark blue and in this way they can distinguish from other fields

with the same surface scattering, such as rye field which presents a lighter blue.

REPORT - Results

35




Figure 20. Image result using Three Component Scattering model in May at L-band. Using only

3 clusters (up) and using 15 clusters (down)

REPORT - Results

36




3.3 ENTROPY BASED SCATTERING MODEL

3.3.1 ENTROPY-ALPHA PLANES

The Foulum test site has several types of fields, including small buildings areas

forests and crops. The entropy based scattering provides a useful tool to classify

these terrains, H-α plane.

The April acquisition was not appropriate in this model because after the

implementation of the model, some pixels were placed outside the feasible

regions; this indicates inaccuracy in the SAR data used.

On Figure 21, there are two H-α planes corresponding to C and L band in May.

The results of this month are the most interesting because of the growth stage of

some of the crops.

The H-α planes in May shows that L-band has larger number of pixels with

double bounce scattering (zones 1, 4 y 7) and smooth surfaces, this is low entropy

and low alpha (zone 9) at L-band compared to C-band. This difference between

bands is because the penetration of the C-band is shorter than L-band.

REPORT - Results

37




Figure 21. Entropy-alpha planes in May at C-band (up) and at L-band (down)

REPORT - Results

38




3.3.2 CLASSIFICATION OF CROPS

As it was mention in the previous section, the analysis of different types of crops

with this model was using the May acquisition, due to the inadequate SAR data in

April with C-band.

Grass (field 5) can be distinguished in both bands, but especially at C-band, where

its entropy has the lowest value. Spring barley (field 6, 13 and 14) shows the

highest entropy and alpha of the crops, this means that these spring barley fields

are roughness surfaces. Beets (field 30) and Pea fields have a higher value of

entropy when it was measured at L-band but the value of alpha almost remains

constant at L and C-band. rye and winter wheat fields are cereal very similar, that

is the reason because the entropy and alpha almost the same in both bands.

It can be inferred from the results on Figure 22 that cereals (spring barley, spring

oats, rye and winter wheat) have very similar scattering at C-band, both because

of entropy and alpha values, so they can distinguish between no cereal crops.

Moreover, it is possible to distinguish between them using the results of L-band,

but only spring cereals and winter cereals. The winter cereals, rye and winter

wheat, are always crops difficult to distinguish between them because they have

the same growth stage and very similar shape of plants.

REPORT - Results

39




Figure 22. Entropy and Alpha according to type of crop in May at C-band (up) and L-band

(down)

On Figure 23, the implementation of this model is presented at C and L band.

Only 8 zones were implemented, thus an exhaustive classification of crops is

difficult with this limited number of zones. The implementation of a classifier to

increase the number of zones will be necessary to distinguish between crops with

same scattering mechanism. According to Figure 23, C-band has fewer pixels

with surface and especially with double bounce scattering; this is because the

wavelength of C-band is lower than the wavelength of L-band.

10

15

20

25

30

35

40

45

50

0,5

0,6

0,7

0,8

0,9

1,0

Spring barley



Alp

ha

(de

gre

es)

Entr

op

y

C band (May)

mean_H mean_alpha

10

15

20

25

30

35

40

45

50

55

0,5

0,6

0,7

0,8

0,9

1,0

Spring barley



Entr

op

y

L band (May)

mean_H mean_alpha

REPORT - Results

40




Figure 23. Image based on Entropy Based Scattering model in May, at C-band (up) and at L-band

(down)

REPORT - Results

41




3.4 COMPARISON OF MODELS

In this section, both scattering models are compared with and without filtering,

using the SAR data of May acquisition. This month is a crucial stage of all the

fields because spring and winter crops can be distinguished easily.

3.4.1 L-BAND

Figure 24 (a) and (b) show the results without filtering of the two models and they

are very similar. All the fields have speckle and in some of them the speckle is not

acceptable because it is not possible to recognize the field. However, Three

Component Scattering model seems to have more homogenous fields with almost

the same color for them. This occurs in fields 15, 19 and 21, all pea crops. For this

reason, it may infer that pea crops are more homogenous fields than others.

Furthermore, Three Component Scattering model presented on Figure 25 (a) has

better results after filtering, because can show different types of homogenous

fields with the same scattering. For instance, fields 18, 19, 21 and 24 are peas

crops and on Figure 25 (a) these are dark blue (surface), but on Figure 25(b), these

crops are not enough homogenous to consider the same type of crop although they

are measured as surface scattering too.

For double bounce, a similar situation happens. Fields 2, 4, 16 and 26 are grass. A

better displayed image results on Figure 25(a) than on Figure 25 (b). On the other

hand, two much details of surface scattering are gone in the huge area of volume

scattering on Figure 25 (a), this is not the case of Figure 25 (b).

REPORT - Results

42




(a) (b)

(c)

Figure 24. (a) The image result using Three Component Scattering model. (b) The image result

using Entropy Based Scattering model. (c) Areal image with numbered fields

REPORT - Results

43




(a) (b)

(c)

Figure 25. (a) The image result using Three Component Scattering model (Filtering). (b) The

image result using Entropy Based Scattering model (Filtering). (c) Areal real image with

numbered fields

REPORT - Results

44




3.4.2 C-BAND

The models were also applied to the C-band of the data that was taken in different

periods of the year: in April and in May. As the wave length of C-band is smaller

than L-band, the results do not give accurate information about areas that

correspond to three common scattering mechanisms. However, the results at this

band are useful to compare both models.

Volume scattering is coherent to find in more quantity because this C-band cannot

penetrate as well as L-band. Figure 26 shows the results of both models in April.

On this Figure 26 the lake shores are determined as areas with double bounce

scattering as dominant. That is a correct scattering because there are steep vertical

surfaces along the lake shore. These vertical surfaces are more appreciable with

Three Component Scattering model but this model is not as good as Entropy

Based model to distinguish among fields at C-band. In May the vegetation is

larger; that is the reason why there are less surface scatters in May than in April.

Nevertheless, similar results of Figure 26 are on Figure 27: double bounce

scattering is reflected with more intensity using Three Component scattering

model and more fields are distinguished with Entropy Based Scattering model.

REPORT - Results

45




Figure 26. C-Band images of the data not filtered and acquired in April with Three Component

Scattering Model (left) and with Entropy Based Scattering model (right)

Figure 27. C-Band image results of filtered data and acquired in April with Three Component

Scattering model (left) with Entropy Based Scattering model (right)

REPORT - Results

46




3.5 DEVELOPMENT OF CROPS

After the comparison of models, Three Component Scattering model provided the

best results to classify fields, especially at L-band. Therefore, this model was used

in this section to analyze the development of the most relevant crops with growth

data available. These crops are: cereals (spring barley, winter wheat and rye),

beets and peas. Furthermore, additional data were collected from the crops to

evaluate the development. These new data are the mean height of each crop and

their growth stage measured with BBCH scale. Table 2 shows the growth stages

according to BBCH scale [12], the common scale to measure the growth stage of

seeds.

Growth stage BBCH scale

Germination 0-9

Leaf development (second digit is number

of leaves unfolded) 10-19

Tillering (second digit is number of tillers

detectable) 20-29

Stem elongation 30-39

Booting 40-49

Heading 50-59

Flowering 60-69

Development of fruit 70-79

Ripening 80-89

Senescence 90-99

Table 2: BBCH scale

REPORT - Results

47




3.5.1 BEETS

Figure 28 shows the growth of a beet plant and according to BBCH scale and

Table 3 provides the information of height and BBCH of each month. This

information shows that beet fields are a bare field in April and May, with small

plants present in June and with fully developed plants in July.

Figure 28. Growth stages of beet plants [12]

REPORT - Results

48




Table 3: Height and BBCH of beet field from April to July

Figure 29, Figure 30 and Figure 31 illustrate the development of the beet field

from April to July, according to the three scattering powers.

Surface and volume scattering are dominating at L-band. However, a higher

contribution of surface scattering was expected in April and May because of the

bare beet field. This expectation could be not shown as a higher Ps than the other

powers, if the terrain is rough. Therefore, the high and similar powers Pv and Ps

indicate a rough surface of beet crop in April and May.

In addition, for the July acquisition, beet plants are developed with broad leaves,

as it is shown on Table 3. Volume scattering is clearly superior at C-band because

Pv is evidently higher at C-band due to the wavelength of this band, like it occurs

in the other results of this study.

On the other hand, double bounce scattering, shown on Figure 29, is clearly less

predominant due to the shape of beet crops. The first growth stages of beets start

with small and short leaves and it develops to big and large leaves without long

and rigid stems.

Field

April May June July

Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH

30 - - - - - 21 26 35

REPORT - Results

49




Figure 29. Double bounce power of beet crops at C-band: left and, at L-band: right

Figure 30. Volume power of beet crops at C-band: left, and at L-band: right

Figure 31. Surface power of beet crops at C-band: left, and at L-band: right

-15

-10

-5

0

April May June July

Pd

(d

B)

C band (Pdb - Beets)

Field 30

-15

-10

-5

0

April May June July

Pd

(d

B)

L band (Pdb - Beets)

Field 30

-20

-15

-10

-5

0

April May June July

Pv

(dB

)

C band (Pv - Beets)

Field 30

-20

-15

-10

-5

0

April May June July

Pv

(dB

)L band (Pv - Beets)

Field 30

-20

-15

-10

-5

0

April May June July

Ps

(dB

)

C band (Ps - Beets)

Field 30

-20

-15

-10

-5

0

April May June July

Ps

(dB

)

L band (Ps - Beets)

Field 30

REPORT - Results

50




3.5.2 CEREALS

There are three types of cereals in the crops of this study: spring barley, rye and

winter wheat. They have a very similar growth and this growth is shown on

Figure 32.

Figure 32. Growth stages of cereal plants [12]

REPORT - Results

51




3.5.2.1 Spring barley

Table 4 shows the height and the BBCH of spring barley crops. The height and

BBCH in April is zero because the plant has not started to germinate yet.

Field

April May June July

Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH

6 0 0 14 28 54 49 63 63

13 0 0 15 21 46 41 63 79

36 0 0 11 22-26 62 54 67 86

Table 4. Height and BBCH of spring barley field from April to July

Figure 33 shows the mean of surface power Ps of these crops, Figure 34 shows the

volume scattering and Figure 35 shows the surface scattering at C and L band for

each month.

The scattering from spring barley is dominated by surface at L-band, including the

May acquisitions at this band. The development of these crops seems to be

constant during 4 months, except in the July acquisitions where the three powers

increase about 5 dB.

On the other hand, Figure 34 also shows that the dominating scattering

mechanism at C-band is volume scattering for the all acquisitions and Pv becomes

high, especially in July as at L-band. The dominating volume scattering at C-band

may be due of the short penetration of this band.

REPORT - Results

52




Figure 33. Double bounce power of spring barley crops at C-band: left and, at L-band: right

Figure 34. Volume power of spring barley crops at C-band: left and at L-band: right

Figure 35. Surface power of spring barley crops at C-band: left, and at L-band: right

-20

-15

-10

-5

0

April May June July

Pd

(d

B)

C band (Pdb - Spring barley)

Field 6 Field 13 Field 36

-20

-15

-10

-5

0

April May June July

Pd

(d

B)

L band (Pdb - Spring barley)


-15

-10

-5

0

April May June July

Pv

(dB

)

C band (Pv - Spring barley)


-15

-10

-5

0

April May June July

Pv

(dB

)

L band (Pv - Spring barley)


-15

-10

-5

0

April May June July

Ps

(dB

)

C band (Ps - Spring barley)


-15

-10

-5

0

April May June July

Ps

(dB

)

L band (Ps - Spring barley)


REPORT - Results

53




3.5.2.2 Winter Wheat

The results of winter wheat crop are expected different compared to spring barley

crop. This difference is mainly due to the growth stage of both crops. Table 5

presents the values of height and BBCH of winter wheat crops and the value of

BBCH in April.

Field

April May June July

Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH

3 20 48 37 74 59 71 85

5 14 29 42 39 78 58 90 81

11 30 44 39 73 55 78 85

Table 5: Height and BBCH of winter wheat fields from April to July

The results of the model are shown on Figure 36, Figure 37 and Figure 38 for

double bounce, volume and surface scattering respectively. The height and the

growth stage are similar in the three winter wheat crops for each month and this

can be seen on all Figure 36, Figure 37 and Figure 38, especially in fields 3 and 5.

The scattering of winter wheat is dominated by surface at L-band, except the May

results at L-band which shows dominating double-bounce scattering. On the other

hand, the dominating scattering mechanism at C-band is volume scattering for the

all acquisitions, as it is shown on Figure 36 and Pv becomes high, especially in

July. The scattering presented in field 11 shows a lower volume scattering in the

four months at L-band, this may be due to the rough of the terrain. However, the

dominating scattering mechanism at C-band in field 11 is volume scattering; in

this case the reason is because of the wavelength, shorter at C-band than L-band.

The height of field 5 in July is higher than the other winter wheat crops but no

signs of evidence appeared in the graphics. This may means that BBCH, that

reflects the same growth stage in field 3, 5 and 11, is more significant than height.

REPORT - Results

54




Figure 36. Double bounce power of winter wheat crops at C-band: left, and at L-band: right

Figure 37. Volume power of winter wheat crops at C-band: left, and at L-band: right

Figure 38. Surface power of winter wheat crops at C-band: left, and at L-band: right

-20

-15

-10

-5

0

April May June July

Pd

(d

B)

C band (Pdb - Winter wheat)


-20

-15

-10

-5

0

April May June July

Pd

(d

B)

L band (Pdb -Winter wheat)


-15

-10

-5

0

April May June July

Pv

(dB

)

C band (Pv -Winter wheat)


-15

-10

-5

0

April May June July

Pv

(dB

)L band (Pv -Winter wheat)


-15

-10

-5

0

April May June July

Ps

(dB

)

C band (Ps -Winter wheat)


-15

-10

-5

0

April May June July

Ps

(dB

)

L band (Ps -Winter wheat)


REPORT - Results

55




3.5.2.3 Rye

The results of rye crops are expected similar to winter wheat crops, because they

have very similar features. Table 6 shows the values of height and BBCH of rye

fields.

Table 6: Height and BBCH of rye fields from April to July

The height and the growth stage of the three rye crops are similar for each month,

and the graphics presented on Figure 39, Figure 40 and Figure 41 show the three

scattering mechanisms of each rye crop at both bands. As the case of winter wheat

crops, the May acquisition at L-band shows an increase of double-bounce

scattering. Field 1 shows a more different graphic than the rest of rye fields, with

the lowest values of the powers of all months at L-band. This anomaly may occur

because of edge detection during the filtering. In particular, field 1 has very

irregular crop edges compared to the rest of fields. It is also possible that other

features of crops, not considered in this study, as moisture content can be

responsible of this difference.

Anyway, according to Figure 41, the scattering from rye is dominated by surface

because the power Ps shows the highest values at L-band.

On the other hand, volume scattering is still dominating C-band, but in this case

Pv is higher than in other crops. Besides, volume scattering becomes dominant in

July at L-band due to the development of the vegetation.

Field

April May June July

Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH

1 23-24 61 49 110 60 92 86

8 21 21 51 49 98 65 99 80

12 22 55 63 94 61 88 82

REPORT - Results

56




Figure 39. Double bounce power of rye crops at C-band: left, and at L-band: right

Figure 40. Volume power of rye crops at C-band: left and at L-band: right

Figure 41. Surface power of rye crops at C-band: left, and at L-band: right

-25

-20

-15

-10

-5

0

April May June July

Pd

(d

B)

C band (Pdb - Rye)


-25

-20

-15

-10

-5

0

April May June July

Pd

(d

B)

L band (Pdb - Rye)


-20

-15

-10

-5

0

April May June July

Pv

(dB

)

C band (Pv - Rye)


-20

-15

-10

-5

0

April May June July

Pv

(dB

)L band (Pv - Rye)


-20

-15

-10

-5

0

April May June July

Ps

(dB

)

C band (Ps - Rye)


-20

-15

-10

-5

0

April May June July

Ps

(dB

)

L band (Ps - Rye)


REPORT - Results

57




3.5.3 PEAS

The pea fields are bare fields in April. Then, they start the leaf development in

May, heading in June and development of fruit in July. Figure 42 shows the

growth of a pea plant according to BBCH scale and Table 7 has the information of

BBCH and the height for each field April, May and July.

Figure 42. Growth stages of pea plants [12]

REPORT - Results

58




Table 7: Height and BBCH of pea fields from April to July

Figure 43, Figure 44 and Figure 45 illustrates the mean of each power of each pea

field. The height and the growth stage is almost the same in the three pea crops for

each month and it is reflected in all powers at L-band, except in May where field

18 presents a decrease in each power while the other pea crops show an increase.

Unfortunately, this anomaly cannot explain only with the height and BBCH of the

crop, being necessary other data about the feature of these crops, such as moisture

content.

The powers for pea crops follow the increase of the powers for the beet field but

with a difference of 5 to 10 dB. However, for the July acquisition Pd and Ps

decrease while in pea crops these powers are still increasing.

Moreover, it was expected higher values of Pv in the peas compared to beets.

Because, according to the Table 1 and Table 7, pea crops have developed further

than beets, thus volume scattering would occur in the canopy of pea crops.

Therefore, to distinguish between beets and peas, it would be necessary, another

study of both types of crops, because primarily expectations are not accomplished

and data from only one small field of beets was obtained.

Field

April May June July

Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH Height

[cm]

BBCH

7 0 0 12 14 42 54 69 71

15 0 0 12 14 42 52 69 71

18 0 0 13 14 63 59 52 81

REPORT - Results

59




Figure 43. Double bounce power of pea crops at C-band: left, and at L-band: right

Figure 44. Volume power of pea crops at C-band: left, and at L-band: right

Figure 45. Surface power of pea crops at C-band: left and at L-band: right

-30

-25

-20

-15

-10

-5

0

April May June July

Pd

(d

B)

C band (Pdb - Peas)


-30

-25

-20

-15

-10

-5

0

April May June July

Pd

(d

B)

L band (Pdb - Peas)


-30

-25

-20

-15

-10

-5

0

April May June July

Pv

(dB

)

C band (Pv - Peas)


-30

-25

-20

-15

-10

-5

0

April May June July

Pv

(dB

)

L band (Pv - Peas)


-25

-20

-15

-10

-5

0

April May June July

Ps

(dB

)

C band (Ps - Peas)


-25

-20

-15

-10

-5

0

April May June July

Ps

(dB

)

L band (Ps - Peas)


REPORT - Conclusions

60




Chapter 4 CONCLUSIONS

The objectives of this project were fully accomplished, showing that Three

Component Scattering model and Entropy Based Scattering model are two

decomposition models that can be implemented in MATLAB, and they produce

useful results to classify some agricultural areas and monitor their development.

Nevertheless, the presence of speckle and errors in the SAR data used may

produce the misunderstanding of some fields. For this reason, it was necessary to

analyze SAR data before their interpretation and also to apply a filter before the

implementation of the models. Besides, additional data about the crops, apart of

BBCH and height, would be interesting to analyze with the results of these

models.

4.1 IMPLEMENTATION

During the implementation, data analysis shows that polarimetric SAR data do not

totally fit the Three Component Scattering model. However, that does not have

great influence on the accuracy of the obtained results. As the number of

deviations of element amplitudes is not larger than 200 in this particular

image the error is about 0.02%, which indicates that the SAR data accuracy is

very high.

Moreover, Entropy Based Scattering model detected an error in one of the SAR

images. The error appeared in the calculation of entropy and alpha when some

pixels had a value outside the limits (H<0 and α>90º). However, Three-

Component Scattering model could not discover this error during its

implementation or its result.

REPORT - Conclusions

61




4.2 RESULTS

Three Component Scattering model was a useful tool to analyze the development

of crops. The analysis of winter crops, such as winter wheat, rye and grass, shows

a dominant double bounce scattering in May due to the shape of the winter crop

and the growth state at that date, especially at L-band. On the other hand, spring

crops present some differences in scattering among them. The reason of these

differences is that they are different type of crops, with different shape and growth

stages. However, since only data from one beet crop were available, it is possible

that the comparison were not enough accurate. Furthermore, volume scattering

was dominant at C-band in all of the fields because the penetration of this band is

very limited compared to L-band.

The application of a speckle filter improved the image markedly. Speckle was

sufficiently reduced and edges of areas were not blurred that indicates that the

chosen size of the moving window was appropriate for edge directions detection

and the estimation of the value of noise variance was likely accurate.

After the comparison of both models, the results of the SAR images were more

satisfactory in Three Component Scattering model at L-band. However, better

results were found with the other model, Entropy Based Scattering model, at C-

band.

REPORT - Future Work

62




Chapter 5 FUTURE WORK

It is possible to apply statistical classifiers to distinguish in more detail different

types of crops. A good recommendation is to use a classifier called “Wishart

classifier” [13]. It needs some iterations to see significant results and can be used

in both models. However, with Entropy Based Scattering model create wrong

final results because a pixel can change the zone during the iterations and thus, a

pixel can end at a wrong scattering mechanism. This problem does not occur with

Three Component Scattering model because it already has a previous

classification in the three common scattering mechanisms.

In addition, some studies indicate that Entropy Based Scattering model needs

another variable to classify with precision. Thus, this model may be further

improved by explicitly including the anisotropy information during the

segmentation procedure with the Wishart classifier. The anisotropy indicates the

relative importance of secondary mechanisms obtained from the expansion of a

coherency matrix. This polarimetric indicator is particularly useful to discriminate

scattering mechanisms with different eigenvalue distributions but with similar

intermediate entropy values.

Moreover, although a speckle filter was successfully implemented, it is possible to

improve it, reducing the speckle but keeping as much information as possible. In

this way, the edge detection may have more type of windows, including one

without edges. Besides, different sizes of the window may adjust better to edges

of some fields, thus windows with different sizes may be implemented.

USER GUIDE

63




BIBLIOGRAPHY

[1] J. A. Richards, Remote sensing with Radar Imaging, Springer. Verlag, Berlin,

Heidelberg, 2009.

[2] J. J. van Zyl, and F. T. Ulaby, Scattering Matrix Representation for Simple

Targets, in F. T. Ulaby and C. Elachi (editors), Radar Polarimetry for

Geoscience Applications, Norwood, Artech House, Inc. 1990.

[3] A. Freeman, S. L. Durden, A Three-component Scattering Model for

Polarimetric SAR Data. May, 1998.

[4] S. R. Cloude, E. Pottier, An Entropy Based Classification scheme for Land

Applications for Polarimetric SAR. January, 1997.

[5] J. Lee, M. R. Grunes, T. L. Ainsworth, L. Du, D. L. Schuler, S. R. Cloude,

Unsupervised Classification Using Polarimetric Decomposition and the Complex

Wishart Classifier. September, 1999.

[6] A. C. Frery, A. Correia, C. D. Rennó, C. C. Freitas, J. Jacobo-Berlles, K. L. P.

Vasconcellos, M. Mejail, S. J. S. Sant’ann, Models for Synthetic Aperture Radar

Image Analysis. Brazil, Argentina. 2009.

[7] ESA Earthnet Online. Temporal Averaging [Online]

http://earth.esa.int/applications/data_util/SARDOCS/spaceborne/Radar_Courses/

Radar_Course_III/temporal_averaging.htm consulted on 25th January 2011.

[8] J. Lee, M. R. Grunes, G. de Grandi. Polarimetric SAR Speckle Filtering and Its

Implication for Classification. September, 1999.

[9] F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active

and Passive, vol. 3. Dedham, MA: Artech, 1986.

[10] MATLAB® 7. Documentation - Data Analysis. MathWorks. [Online]

http://www.mathworks.com/help/techdoc/data_analysis/ug_intropage.html

consulted on 25th January.

http://www.mathworks.com/help/techdoc/data_analysis/ug_intropage.html

USER GUIDE

64




[11] MATLAB® 7. Documentation - Mathematics. MathWorks. [Online]

http://www.mathworks.com/help/techdoc/math/bqqz59g.html consulted on 25th

January.

[12] U. Meier, Growth stages of mono-and dicotyledonous plants. BBCH Monograph,

2 ed. Federal Biological Research Centre for Agriculture and Forestry, 2001.

[13] J. Lee, M. R. Grunes, R. Kwok, Classification of multi-look polarimetric SAR

imagery based on complex Wishart distribution. November, 1994.

[14] J. Lee, M. R. Grunes, E. Pottier, L. Ferro-Famil, Unsupervised Terrain

Classification Preserving Polarimetric Scattering Characteristics. April, 2004.

http://www.mathworks.com/help/techdoc/math/bqqz59g.html

USER GUIDE

65




Part II USER GUIDE

USER GUIDE - MATLAB Programming

66




Chapter 1 MATLAB PROGRAMMING

MATLAB allows sequences of instructions to be stored in so-called M-files.

An M-file has the following structure:

• The function definition line

• The H1 line

• Help text

• The function body

• Comments

The function definition line looks like:

function [outputs] = function_name(inputs)

For example, a function to split a colour image into its R, G, and B components

would look like:

function [R, G, B] = split_colour_planes(src)

This would be called at the command prompt as:

>> [r, g, b] = split_colour_planes(a_colour_image);

There are restrictions on the form of function names: they must begin with a

letter, can’t contain any spaces and only the first 63 characters are significant. If

the function has no output, the square brackets and equal sign are omitted. If the

function has a single output, the square brackets may be omitted.


67




The H1 line follows the definition line with no blank lines of leading spaces. It is

a comment that Matlab returns first when help is invoked, and is searched for

keywords when look for keyword is used. The format of the H1 line is

% function_name <text description>

The help text must follow with no blank lines. The lines up to the next blank line

are also printed by help. Each line of help text must start with a % symbol.

Other lines stating with the % symbol are treated simply as comments for the

programmer.

The function body can contain any instruction that would be valid at the command

line.

Matlab provides the usual programming constructs, but (naturally) the syntax is

different to other languages.

Conditional execution:

if expression

statement(s)

end

OR

if expression1

statement1

elseif expression2

statement2

else

statement3


68




end

For loop:

for index = start:increment:end

statements

end

PROGRAMMING CODE

69




Part III PROGRAMMING

CODE

PROGRAMMING CODE - Three Component Scattering model

70




Chapter 1 THREE COMPONENT SCATTERING

MODEL

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Unsupervised Classification of Polarimetric SAR Data %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%% 3 COMPONENT SCATTERING MODEL %%%%%%%%%%%%%%%%%%%%%

%%%%%%%%% Open SAR data and Calculation of Covariance matrix %%%%%%%%%%%%

clear all

clc

file_hhhh=fopen('hhhh.dat','r','b');

hhhh=fread(file_hhhh,[1,inf],'float32');

fclose(file_hhhh);

file_hhhv=fopen('hhhv.dat','r','b');

hhhv0=fread(file_hhhv,[2,inf],'float32');

hhhv=hhhv0(1,:)+j*hhhv0(2,:);

fclose(file_hhhv);

file_hvhv=fopen('hvhv.dat','r','b');

hvhv=fread(file_hvhv,[1,inf],'float32');

fclose(file_hvhv);

file_hhvv = fopen('hhvv.dat','r','b');

hhvv0=fread(file_hhvv,[2,inf],'float32');

hhvv=hhvv0(1,:)+j*hhvv0(2,:);

fclose(file_hhvv);

file_hvvv = fopen('hvvv.dat','r','b');

hvvv0=fread(file_hvvv,[2,inf],'float32');

hvvv=hvvv0(1,:)+j*hvvv0(2,:);

fclose(file_hvvv);

file_vvvv = fopen('vvvv.dat','r','b');


71




vvvv=fread(file_vvvv,[1,inf],'float32');

fclose(file_vvvv);

l=length(hhhh);

CM=zeros(3,3,l);

CM(1,1,:)=hhhh;

CM(1,2,:)=sqrt(2)*hhhv;

CM(1,3,:)=hhvv;

CM(2,1,:)=sqrt(2)*conj(hhhv);

CM(2,2,:)=2*hvhv;

CM(2,3,:)=sqrt(2)*hvvv;

CM(3,1,:)=conj(hhhv);

CM(3,2,:)=sqrt(2)*(hvvv);

CM(3,3,:)

else

fd=r(3);

end

fs=b-fd;

alfa=(k-fs)/fd+(m/fd)*1i;

fv=3*CovMat(2,2);

Ps=fs*(1+beta^2);

Pd=fd*(1+alfa^2);

Pv=8*fv/3;

end

% These powers are the real value but it is necessary to convert the

scala into logarithm scala %

% Power_matrix(ii,1)=Pd; %

% Power_matrix(ii,2)=Pv; %

% Power_matrix(ii,3)=Ps; %

Power_matrix(ii,1)=10*log10(abs(Pd));

Power_matrix(ii,2)=10*log10(abs(Pv));

Power_matrix(ii,3)=10*log10(abs(Ps));

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


72




%%%%%%%%%%%%%% HISTOGRAMS (to see the data distribution) %%%%%%%%%%%%%%%%

x = 50;

y = Power_matrix(:,1);

hist(y,x); title('Double Bounce');

figure

hold on

y = Power_matrix(:,2); title('Volume');

hist(y,x)

figure

hold on

y = Power_matrix(:,3); title('Surface');

hist(y,x)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% IMAGE REPRESENTATION %%%%%%%%%%%%%%%%%%%%%%%%%%%

nstd = 2;

image1 = Power_matrix(:,1)-repmat(mean(Power_matrix(:,1)),1024*1024, 1);



stdvar1 = std(image1);



image1 = reshape(image1, 1024, 1024)';



r = image1/(2*nstd*stdvar1)+0.5;

g = image2/(2*nstd*stdvar2)+0.5;

b = image3/(5*nstd*stdvar3)+0.6;

figure

imshow(cat(3,r,g,b))

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


73




%%%%%%%%%%%%% Calculation of MEAN POWERS OF EACH FIELD %%%%%%%%%%%%%%%%%%

mean_P=zeros(26,2);

%%%%%%%%%%%%%%%%%%%%%%% Field 4 (grass) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

pixels_square_grass= zeros(70,70);

y_pixels=260;

image_Pdb = reshape(Power_matrix(:,1), 1024, 1024)';

image_Pv = reshape(Power_matrix(:,2), 1024, 1024)';

image_Ps = reshape(Power_matrix(:,3), 1024, 1024)';

for ysquare_pixels=1:70 % 70 is the number of pixels in y direction %

x_pixels=150;

for xsquare_pixels=1:70 % 70 is the number of pixels in x direction %

pixels_square_Pdb_1(xsquare_pixels,ysquare_pixels) =

image_Pdb(x_pixels,y_pixels);

pixels_square_Pv_1(xsquare_pixels,ysquare_pixels) =

image_Pv(x_pixels,y_pixels);

pixels_square_Ps_1(xsquare_pixels,ysquare_pixels) =

image_Ps(x_pixels,y_pixels);

x_pixels=x_pixels+1;

end

y_pixels=y_pixels+1;

end

pixels_notsquare_Pdb=reshape(pixels_square_Pdb_1,1,4900);

pixels_notsquare_Pv=reshape(pixels_square_Pv_1,1,4900);

pixels_notsquare_Ps=reshape(pixels_square_Ps_1,1,4900);

mean_P(1,1)=mean(pixels_notsquare_Pdb);

mean_P(1,2)=mean(pixels_notsquare_Pv);

mean_P(1,3)=mean(pixels_notsquare_Ps);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 30 (beets)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

pixels_square_beet= zeros(20,15);

y_pixels=70;





x_pixels=260;






74








end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Field 5 (winter wheat) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=340;





x_pixels=220;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%% Field 11 (winter wheat)%%%%%%%%%%%%%%%%%%%%%%%%%%%


75




y_pixels=540;





x_pixels=420;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%% Field 20 (winter wheat) %%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=585;





x_pixels=785;









end



76




end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%% Field 27 (winter wheat) %%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=970;





x_pixels=690;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%% Field 33 (winter wheat)%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=75;





x_pixels=90;


77












end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 6 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=450;





x_pixels=230;









end


end






78






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Field 13 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=728;





x_pixels=428;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Field 14 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=700;





x_pixels=490;







79







end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%% Field 29 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=90;





x_pixels=275;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%% Field 31 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=40;


80








x_pixels=245;









end


end








y_pixels=130;





x_pixels=110;









end


end



81









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


y_pixels=150;





x_pixels=50;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

mean_P=zeros(4,3);

%%%%%%%%%%%%%%%%%%%%%%%%% Field 1 (Rye) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=115;





x_pixels=335;



82











end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%% Field 8 (Rye) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=355;





x_pixels=360;









end


end








83




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%% Field 12 (Rye) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=700;





x_pixels=340;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%% Field 23 (Rye) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=810;





x_pixels=690;









84





end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

mean_P=zeros(6,3);

%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 7 (Peas) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=295;





x_pixels=395;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


85




%%%%%%%%%%%%%%%%%%%%%%%%% Field 15 (Peas) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=730;





x_pixels=575;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 18 (Peas) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=555;





x_pixels=750;










86




end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 24 (Peas) %%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=935;





x_pixels=505;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

mean_P=zeros(4,3);

%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 28 (Peas) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=885;




87





for ysquare_pixels=1:30

x_pixels=835;

for xsquare_pixels=1:30








end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 37 (Peas) %%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=215;





x_pixels=45;









end


end




88








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 9 (Spring oats) %%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=450;





x_pixels=405;









end


end







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%% GRAPHIC WITH THE PIXELS of ONE FIELD %%%%%%%%%%%%%%%%%

figure

plot(1:4900,pixels_notsquare_Pdb,'+r');

figure

plot(1:4900,pixels_notsquare_Pv,'+g');

figure

plot(1:4900,pixels_notsquare_Ps,'+b');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


89




%%%%%%%%%%%%%%%%%%%%%%%% TOO DARK PICTURE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% r=reshape(Power_matrix(:,1)/20,1024, 1024)';

% g=reshape(Power_matrix(:,2)/20,1024, 1024)';

% b=reshape(Power_matrix(:,3)/20,1024, 1024)';

% imshow(cat(3,r,g,b));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%% 3 POWER COMPONENT ASSUMPTIONS %%%%%%%%%%%%%%%%%%%%%

l=length(hhhh);

aa=1;bb=1;cc=1; Power_matrix=zeros(l,3);

for ii=1:l

CovMat = CM(:,:,ii);

b = CovMat(3,3);

a = CovMat(1,1);

c = CovMat(1,3);

k=real(CovMat(1,3));

m=imag(CovMat(1,3));

% Assumption if SURFACE scattering dominant %

if (real(CovMat(1,3))>0)

alfa=-1;

fs=b-(a*b-c^2)/(a+2*c+b);

fd=(a*b-c^2)/(a+2*c+b);

beta=(c+fd)/(b-fd);

fv=3*CovMat(2,2);

Ps=fs*(1+beta^2);

Pd=fd*(1+alfa^2);

Pv=8*fv/3;

% Assumption if DOUBLE BOUNCE dominant %

else

p=[1 -(a-b-2*(k-b)+1) (k-b)^2 -m^2];

r=roots(p);

if imag(r(1))==0

fd=r(1);

elseif imag(r(2))==0

fd=r(2);

end


90




end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

PROGRAMMING CODE - Entropy Based Scattering model

91




Chapter 2 ENTROPY BASED SCATTERING

MODEL

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Unsupervised Classification of Polarimetric SAR Data %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% ENTROPY BASED SCATTERING MODEL %%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Coherency matrix calculation %%%%%%%%%%%%%%%%%%%%%%%

clear all

clc

%%%%%%% Function to read data from file and make the matrices %%%%%%%%%%

% The function takes no arguments so the data must be placed in files

called: hhhh.dat, hhhv.dat, hvhv.dat, hhvv.dat, hvvv.dat, vvvv.dat %

file_hhhh = fopen('hhhh.dat','r','b');

hhhh=fread(file_hhhh,[1,inf],'float32');

fclose(file_hhhh);

file_hhhv = fopen('hhhv.dat','r','b');

hhhv0=fread(file_hhhv,[2,inf],'float32');

hhhv=hhhv0(1,:)+j*hhhv0(2,:);

fclose(file_hhhv);

file_hvhv = fopen('hvhv.dat','r','b');

hvhv=fread(file_hvhv,[1,inf],'float32');

fclose(file_hvhv);

file_hhvv = fopen('hhvv.dat','r','b');

hhvv0=fread(file_hhvv,[2,inf],'float32');

hhvv=hhvv0(1,:)+j*hhvv0(2,:);

fclose(file_hhvv);


92




file_hvvv = fopen('hvvv.dat','r','b');

hvvv0=fread(file_hvvv,[2,inf],'float32');

hvvv=hvvv0(1,:)+j*hvvv0(2,:);

fclose(file_hvvv);

file_vvvv = fopen('vvvv.dat','r','b');

vvvv=fread(file_vvvv,[1,inf],'float32');

fclose(file_vvvv);

l=length(hhhh);

CM=zeros(3,3,l);

CM(1,1,:)=hhhh+2*real(hhvv)+vvvv;

CM(1,2,:)=hhhh-vvvv+conj(hhvv)-hhvv;

CM(1,3,:)=2*(hhhv+conj(hvvv));

CM(2,1,:)=hhhh-vvvv-conj(hhvv)+hhvv;

CM(2,2,:)=hhhh+vvvv-2*real(hhvv);

CM(2,3,:)=2*(hhhv-conj(hvvv));

CM(3,1,:)=2*(conj(hhhv)+hvvv);

CM(3,2,:)=2*(conj(hhhv)-hvvv);

CM(3,3,:)=4*hvhv;

CohMat=0.5*CM;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Calculation ENTROPY and ALPHA %%%%%%%%%%%%%%%%%%%%%%

l=length(hhhh);

V=NaN(3,3,l);

D=NaN(3,3,l);

for ii=1:l

[V(:,:,ii),D(:,:,ii)]= eig(CohMat(:,:,ii));

P1(ii) = D(1,1,ii)/((D(1,1,ii)+D(2,2,ii)+D(3,3,ii)));



alpha1(ii) = acos(abs(V(1,1,ii)));



% Entropy %

H(ii)= -P1(ii)*(log(P1(ii))/log(3))-P2(ii)*(log(P2(ii))/log(3))-


93




P3(ii)*(log(P3(ii))/log(3));

% Average alpha %

alpha_average(ii)=

P1(ii)*(alpha1(ii))+P2(ii)*(alpha2(ii))+P3(ii)*(alpha3(ii));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%% Classification of pixels by zones and color %%%%%%%%%%

% Initial conditions (Several iterations are only used if a statistical

classifier is applied) %

iter = 1;

color_iter = zeros(l,4);

Zone_iter = zeros(l,4);

if alpha_average(ii)<(42.5*pi/180) & H(ii)<0.5

Zone(ii)= 9;

color(ii)=40;

elseif alpha_average(ii)>(42.5*pi/180)& alpha_average(ii)<(47.5*pi/180) &

H(ii)<0.5

Zone(ii)= 8;

color(ii)=25;

elseif alpha_average(ii)>(47.5*pi/180)& H(ii)<0.5

Zone(ii)= 7;

color(ii)=1;

elseif alpha_average(ii)<(40*pi/180)& H(ii)>0.5 & H(ii)<0.9

Zone(ii)= 6;

color(ii)=35;

elseif alpha_average(ii)>(40*pi/180)& alpha_average(ii)<(50*pi/180) &

H(ii)>0.5 & H(ii)<0.9

Zone(ii)= 5;

color(ii)=23;

elseif alpha_average(ii)>(50*pi/180)& H(ii)>0.5 & H(ii)<0.9

Zone(ii)= 4;

color(ii)=3;

elseif alpha_average(ii)<(40*pi/180)& H(ii)>0.9

Zone(ii)= 3;

color(ii)=30;

elseif alpha_average(ii)>(40*pi/180)& alpha_average(ii)<(55*pi/180) &

H(ii)>0.9

Zone(ii)= 2;


94




color(ii)=20;

elseif alpha_average(ii)>(55*pi/180) & H(ii)>0.9

Zone(ii)= 1;

color(ii)=7;

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%% Calculation of H_ALPHA CURVES %%%%%%%%%%%%%%%%%%%%%%%%%

V_T1=NaN(3,3,100);

D_T1=NaN(3,3,100);

V_T2=NaN(3,3,100);

D_T2=NaN(3,3,100);

ll=0;

for mm=0:0.01:1

ll=ll+1;

T1(:,:,ll)= [1 0 0; 0 mm 0; 0 0 mm];

if mm<0.5

T2(:,:,ll)= [0 0 0; 0 1 0; 0 0 2*mm];

else

T2(:,:,ll)= [(2*mm-1) 0 0; 0 1 0; 0 0 1];

end

% Eigenvalues and eigenvectors T1 and T2 %

[V_T1(:,:,ll),D_T1(:,:,ll)]= eig(T1(:,:,ll));

[V_T2(:,:,ll),D_T2(:,:,ll)]= eig(T2(:,:,ll));

% Entropy T1 and average alpha T1 %

P1_T1(ll) = D_T1(1,1,ll)/((D_T1(1,1,ll)+D_T1(2,2,ll)+D_T1(3,3,ll)));



alpha1_T1(ll) = acos(abs(V_T1(1,1,ll)));



H_T1(ll)= -P1_T1(ll)*(log(P1_T1(ll))/log(3))-

P2_T1(ll)*(log(P2_T1(ll))/log(3))-P3_T1(ll)*(log(P3_T1(ll))/log(3));

% Average alpha %

alpha_averageT1(ll)=

P1_T1(ll)*(alpha1_T1(ll))+P2_T1(ll)*(alpha2_T1(ll))+P3_T1(ll)*(alpha3_T1(

ll));

% Entropy T2 %





95







H_T2(ll)= -P1_T2(ll)*(log(P1_T2(ll))/log(3))-

P2_T2(ll)*(log(P2_T2(ll))/log(3))-P3_T2(ll)*(log(P3_T2(ll))/log(3));

% Average alpha %

alpha_averageT2(ll)=

P1_T2(ll)*(alpha1_T2(ll))+P2_T2(ll)*(alpha2_T2(ll))+P3_T2(ll)*(alpha3_T2(

ll));

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%% Calculation of MEAN H and ALPHA FOR EACH FIELD %%%%%%%%%%%%%

mean_P=zeros(26,2);

%%%%%%%%%%%%%%%%%%%%%%%%%% Field 4 (grass)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=260; % first pixel of the field in vertical direction %

image_H = reshape(abs(H(:)), 1024, 1024)';

image_alpha = reshape(alpha_average(:), 1024, 1024)';


x_pixels=150; % first pixel of the field in horizontal direction %


pixels_square_H_1(xsquare_pixels,ysquare_pixels) =

image_H(x_pixels,y_pixels);

pixels_square_alpha_1(xsquare_pixels,ysquare_pixels) =

image_alpha(x_pixels,y_pixels);


end


end

pixels_notsquare_H=reshape(pixels_square_H_1,1,4900);

pixels_notsquare_alpha=reshape(pixels_square_alpha_1,1,4900);

mean_P(1,1)=mean(pixels_notsquare_H);

mean_P(1,2)=mean(pixels_notsquare_alpha);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 30 (beets)% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





96





x_pixels=260; % first pixel of the field in horizontal direction %







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 3 (winter wheat) %%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=250;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 5 (winter wheat)% %%%%%%%%%%%%%%%%%%%%%%%%





97





x_pixels=220;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 11 (winter wheat) %%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=420;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%% Field 20 (winter wheat)%%%%%%%%%%%%%%%%%%%%%%%%%%%




98






x_pixels=785;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 27 (winter wheat)% %%%%%%%%%%%%%%%%%%%%%%%





x_pixels=690;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%% Field 33 (winter wheat)% %%%%%%%%%%%%%%%%%%%%%%%%%




99






x_pixels=90;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%% Field 6 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=230;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%% Field 13 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%%




100






x_pixels=428;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%% Field 14 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=490;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%% Field 29 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=90;



101






x_pixels=275;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 31 (spring barley) %%%%%%%%%%%%%%%%%%%%%%%





x_pixels=245;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Field 34 (spring barley)% %%%%%%%%%%%%%%%%%%%%%%%%%%




102






x_pixels=110;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%% Field 36 (spring barley)% %%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=50;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%% Field 1 (Rye)% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




103






x_pixels=335;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 8 (Rye) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=360;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 12 (Rye)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




104






x_pixels=340;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 23 (Rye)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=690;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 7 (Peas)% %%%%%%%%%%%%%%%%%%%%%%%%%%%%




105






x_pixels=395;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 15 (Peas)% %%%%%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=575;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

&&&&%%%%%%%%%%%%%%%%%%%%%% Field 18 (Peas)% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y_pixels=555;



106






x_pixels=750;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 24 (Peas) %%%%%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=505;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%% Field 28 (Peas)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





107





x_pixels=835;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Field 37 (Peas)%%%%%%%%%%%%%%%%%%%%%%%%%%%%





x_pixels=45;







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%% Field 9 (Spring oats)%%%%%%%%%%%%%%%%%%%%%%%%%%%





108





x_pixels=405; % first pixel of the field in vertical direction %







end


end





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

PROGRAMMING CODE - Speckle Filter

109




Chapter 3 SPECKLE FILTER

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FILTER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

CoM=get_data; % function to read SAR data, included in the models %

L=1024; Cov=zeros(3,3,L+6,L+6); kk=1;

for ii=4:L+3

for jj=4:L+3

Cov(:,:,ii,jj)=CoM(:,:,kk);

kk=kk+1;

end

end

Mat=zeros(((L+5)/7)^2,4); span=zeros(7,7,((L+5)/7)^2);

Loc=zeros(3,3,((L+5)/7)^2);

ffx=1;fx=0;

for kk=1:7:length(Cov)-1

fy=0;

for hh=1:7:length(Cov)-1

format short;

Cent_pix=Cov(:,:,kk+3,hh+3);

cur_x=kk; cur_y=hh;

aa=1;bb=1;

xx=cur_x; zz=cur_y;

mm=1; nn=1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% CALCULATE THE TOTAL POWER(SPAN) %%%%%%%%%%%%%%%%%%%%

for ii=xx1:xx1+6

for jj=zz1:zz1+6

span(mm,nn,ffx)=Cov(1,1,ii,jj)+Cov(2,2,ii,jj)+Cov(3,3,ii,jj);

nn=nn+1;

end


110




mm=mm+1; nn=1;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%% THE AVERAGE FOR EACH OF 3X3 SUBWINDOWS %%%%%%%%%%%%%%%%%%

Av=zeros(3,3);

for xx=1:2:1+4

for zz=1:2:1+4

Sum=0;

for ii=xx:xx+2

for jj=zz:zz+2

Sum=Sum+span(ii,jj,ffx);

end

end

Av(aa,bb)=Sum/9; bb=bb+1;

end

bb=1; aa=aa+1;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%% DIFFERENCE BETWEEN AREA MEANS %%%%%%%%%%%%%%%%%%%%%%%%

dif=zeros(3,3);

for ii=1:3

for jj=1:3

dif(ii,jj)=Av(ii,jj)-Av(2,2);

end

end

dif(2,2)=1000; fl=0; n=0; mm=0;

sum=zeros(3,3); c11=zeros(28,1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%% FIRST WINDOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if min(min(dif))==dif(1,1)

if fl==0


111




% Local mean %

n=0;

for ii=xx:xx+6

for jj=yy:yy+6-n

sum=sum+Cov(:,:,ii,jj);

end

n=n+1;

end

Loc_mean=sum./28;

% Mean of the span %

n=0;

for ii=1:7

for jj=1:7-n

mm=mm+1;

c11(mm,1)=span(ii,jj,ffx);

end

n=n+1;

end

Var=var(c11); Mean=mean(c11);

Varx=(Var-Mean^2*0.31^2)/(1+0.31^2);

if Varx<0

Varx=0;

end

% Weighting function %

b=Varx/Var;

n=0;

for ii=cur_x:cur_x+6

for jj=cur_y:cur_y+6-n

Cov(:,:,ii,jj)=Loc_mean+b*(Cent_pix-Loc_mean);

end

n=n+1;

end

disp(['ii = ',num2str(hh),' first window']);

ok=1; fl=1;


112




end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%% SECOND WINDOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


if fl==0

% Local mean %

for ii=xx:xx+3

for jj=yy:yy+6


end

end

Loc_mean=sum./28;


for ii=1:4

for jj=1:7

mm=mm+1;


end

end


Varx=(Var-Mean^2*0.31^2)/(1+0.31^2);

if Varx<0

Varx=0;

end


b=Varx/Var;


for jj=cur_y:cur_y+6


end

end

disp(['ii = ',num2str(hh),' second window']);

fl=1; ok=2;


113




end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% THIRD WINDOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


if fl==0

n=0;

% Local mean %

for ii=xx:xx+6

for jj=yy+n:yy+6


end

n=n+1;

end

Loc_mean=sum./28;


n=0;

for ii=1:7

for jj=1+n:7

mm=mm+1;


end

n=n+1;

end


Varx=(Var-Mean^2*0.31^2)/(1+0.31^2);

if Varx<0

Varx=0;

end


b=Varx/Var;

n=0;


for jj=cur_y+n:cur_y+6


114





end

n=n+1;

end

disp(['ii = ',num2str(hh),' third window']);

fl=1;ok=3;

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%% FOURTH WINDOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


if fl==0

% Local mean %

for ii=xx:xx+6

for jj=yy:yy+3


end

end

Loc_mean=sum./28;


n=0;

for ii=1:7

for jj=1:4

mm=mm+1;


end

end


Varx=(Var-Mean^2*0.31^2)/(1+0.31^2);

if Varx<0

Varx=0;

end



115




b=Varx/Var;




end

end

disp(['ii = ',num2str(hh),' fourth window']);

fl=1;ok=4;

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIFTH WINDOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%


if fl==0

% Local mean %

for ii=xx:xx+6

for jj=yy+3:yy+6


end

end

Loc_mean=sum./28;


for ii=1:7

for jj=4:7

mm=mm+1;


end

end


Varx=(Var-Mean^2*0.31^2)/(1+0.31^2);

if Varx<0

Varx=0;

end



116




b=Varx/Var;


for jj=cur_y+3:cur_y+6


end

end

disp(['ii = ',num2str(hh),' fifth window']);

fl=1; ok=5;

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SIXTH WINDOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


if fl==0

% Local mean %

n=6;

for ii=xx:xx+6

for jj=yy:yy+6-n


end

n=n-1;

end

Loc_mean=sum./28;


n=6;

for ii=1:7

for jj=1:7-n

mm=mm+1;


end

n=n-1;

end


Varx=(Var-Mean^2*0.31^2)/(1+0.31^2);

if Varx<0

Varx=0;


117




end


b=Varx/Var;

n=6;


for jj=cur_y+3:cur_y+6-n


end

n=n-1;

end

disp(['ii = ',num2str(hh),' sixth window']);

fl=1; ok=6;

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%% SEVENTH WINDOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


if fl==0

% Local mean %

for ii=xx+3:xx+6

for jj=yy:yy+6


end

end

Loc_mean=sum/28;


for ii=4:7

for jj=1:7

mm=mm+1;


end

end


Varx=(Var-Mean^2*0.31^2)/(1+0.31^2);


118




if Varx<0

Varx=0;

end


b=Varx/Var;

for ii=cur_x+3:cur_x+6



end

end

disp(['ii = ',num2str(hh),' seventh window']);

fl=1; ok=7;

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% EIGHTH WINDOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%


if fl==0

% Local mean %

n=6;

for ii=xx:xx+6

for jj=yy+n:yy+6


end

n=n-1;

end

Loc_mean=sum./28;


n=6;

for ii=1:7

for jj=1+n:7

mm=mm+1;


end

n=n-1;

end


119




Var=var(c11); Mean=mean(c11); Varx=(Var-Mean^2*0.31^2)/(1+0.31^2);

if Varx<0

Varx=0;

end


b=Varx/Var;

n=6;


for jj=cur_y+n:cur_y+6


end

n=n-1;

end

disp(['ii = ',num2str(hh),' eighth window']);

fl=1; ok=8;

end

end

Mat(ffx,1)=Mean; Mat(ffx,2)=Var; Mat(ffx,3)=Varx; Mat(ffx,4)=ok;

ffx=ffx+1;

end

end

CM=zeros(3,3,L*L); kk=1;

for ii=4:L+3

for jj=4:L+3

CM(:,:,kk)=Cov(:,:,ii,jj); kk=kk+1;

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

DATA RESULTS - Three Component Scattering model

120




Part IV DATA RESULTS


121




Chapter 1 THREE COMPONENT SCATTERING

MODEL

1.1 TABLES OF POWERS

1.1.1 BEETS

Field 30

Band Month mean_Pdb mean_Pv mean_Ps

C April -14,19 -4,65 -7,98

C May -12,76 -4,31 -8,66

C June -9,70 -1,48 -5,86

C July -9,69 -0,54 -6,02

L April -13,97 -8,75 -9,97

L May -12,69 -8,66 -9,24

L June -8,69 -4,33 -5,68

L July -10,36 -2,22 -6,95


122




1.1.2 GRASS

Field 4


C April -12,94 -3,77 -8,07

C May -13,60 -8,72 -9,76

C June -9,10 -7,88 -6,17

C July -9,26 -4,64 -7,21

L April -18,44 -15,02 -14,64

L May -15,07 -12,50 -11,34

L June -16,45 -13,11 -11,35

L July -13,58 -8,28 -9,65


123




1.1.3 PEAS

Field 7


C April -12,11 -5,85 -8,50

C May -15,98 -9,96 -11,28

C June -15,00 -9,74 -11,57

C July -8,13 -6,83 -6,79

L April -23,98 -19,04 -17,90

L May -17,87 -17,36 -16,00

L June -18,52 -16,19 -13,50

L July -15,98 -11,62 -11,13

Field 15


C April -17,66 -9,57 -11,14

C May -13,92 -5,86 -9,87

C June -10,43 -3,49 -7,35

C July -7,58 -2,78 -5,33

L April -25,67 -20,41 -19,81

L May -17,83 -17,71 -14,89

L June -14,72 -13,04 -10,51

L July -11,51 -7,41 -8,10


124




Field 18


C April -13,79 -6,40 -7,83

C May -11,59 -4,60 -7,91

C June -8,03 -0,50 -5,03

C July -7,78 -0,02 -5,17

L April -23,69 -17,69 -16,85

L May -22,41 -22,36 -18,64

L June -15,53 -13,03 -12,08

L July -8,32 -6,30 -6,42

Field 24


C April -15,43 -5,55 -10,13

C May -14,48 -6,11 -10,78

C June -14,58 -6,09 -10,60

C July -12,85 -4,78 -8,98

L April -9,86 -4,85 -7,20

L May -11,77 -5,44 -8,63

L June -12,56 -6,40 -9,99

L July -12,32 -5,26 -8,93


125




Field 28


C April -15,17 -7,55 -9,46

C May -13,29 -6,06 -9,72

C June -12,41 -6,48 -9,00

C July -9,28 -2,14 -6,47

L April -19,22 -14,09 -14,46

L May -12,13 -13,12 -9,78

L June -16,25 -12,64 -12,31

L July -12,46 -7,92 -9,36

Field 37


C April -15,84 -7,12 -9,06

C May -15,43 -7,12 -10,83

C June -12,24 -9,02 -8,61

C July -10,15 -1,88 -6,24

L April -17,78 -13,78 -11,85

L May -9,90 -11,92 -8,04

L June -9,93 -13,03 -7,96

L July -10,62 -7,88 -7,67


126




1.1.4 RYE

Field 1


C April -15,53 -5,60 -9,58

C May -14,54 -6,18 -10,82

C June -13,54 -4,32 -9,33

C July -9,58 -2,25 -5,83

L April -9,44 -6,32 -7,60

L May -4,61 -7,95 -3,09

L June -7,35 -7,49 -4,76

L July -10,50 -4,63 -6,66

Field 8


C April -12,14 -3,72 -8,31

C May -14,23 -8,80 -10,44

C June -6,55 -6,64 -4,75

C July -8,63 -3,71 -7,03

L April -21,98 -17,51 -16,32

L May -18,96 -14,74 -13,00

L June -19,03 -15,82 -12,39

L July -15,21 -9,57 -11,44


127




Field 12


C April -14,08 -4,38 -8,45

C May -13,01 -5,66 -8,76

C June -9,86 -3,38 -6,73

C July -9,85 -2,47 -6,74

L April -13,12 -8,33 -9,59

L May -12,10 -6,93 -8,58

L June -12,96 -6,72 -9,16

L July -10,38 -5,17 -7,23

Field 23


C April -15,68 -8,38 -9,10

C May -13,79 -5,42 -8,95

C June -12,84 -6,71 -8,96

C July -8,29 0,02 -5,22

L April -22,38 -15,97 -15,68

L May -12,22 -14,29 -10,20

L June -15,77 -12,72 -12,14

L July -12,26 -6,20 -9,41


128




1.1.5 SPRING BARLEY

Field 6


C April -13,46 -5,16 -7,96

C May -13,37 -5,55 -8,43

C June -13,23 -5,95 -8,80

C July -8,96 -1,93 -6,06

L April -15,59 -10,05 -11,24

L May -17,08 -11,74 -13,43

L June -13,53 -9,97 -10,22

L July -11,21 -5,19 -8,10

Field 13


C April -14,18 -5,25 -8,50

C May -14,07 -6,28 -9,68

C June -10,24 -3,09 -7,26

C July -7,95 -2,58 -5,50

L April -13,32 -10,06 -8,60

L May -11,25 -9,95 -8,01

L June -11,78 -8,83 -8,53

L July -8,42 -6,30 -5,62


129




Field 14


C April -17,27 -6,83 -12,08

C May -16,23 -6,02 -11,30

C June -10,94 -1,70 -7,99

C July -9,61 -4,18 -5,93

L April -12,01 -9,45 -10,54

L May -4,49 -11,07 -3,58

L June -16,33 -8,86 -13,62

L July -11,54 -8,74 -8,19

Field 29


C April -14,93 -5,37 -8,74

C May -15,73 -7,94 -11,55

C June -15,13 -7,68 -10,67

C July -11,71 -3,32 -8,39

L April -13,64 -7,01 -8,79

L May -16,55 -9,88 -11,29

L June -17,57 -10,06 -11,45

L July -13,27 -5,85 -8,75


130




Field 31


C April -14,54 -7,12 -8,25

C May -13,06 -5,14 -8,98

C June -10,39 -1,60 -6,01

C July -9,72 -1,40 -6,21

L April -18,31 -13,01 -14,21

L May -16,13 -12,29 -12,55

L June -10,40 -5,16 -7,17

L July -11,04 -4,08 -7,80

Field 34


C April -18,19 -10,63 -9,60

C May -16,29 -7,67 -10,91

C June -13,69 -7,31 -9,92

C July -6,90 -0,67 -4,31

L April -27,65 -21,74 -19,61

L May -16,27 -19,31 -14,82

L June -16,42 -14,15 -13,06

L July -9,84 -7,33 -8,22


131




Field 36


C April -14,47 -4,93 -8,21

C May -13,61 -5,55 -9,62

C June -12,13 -6,69 -8,73

C July -9,04 -3,49 -6,54

L April -17,35 -13,73 -11,97

L May -10,69 -11,24 -9,00

L June -11,00 -11,36 -8,84

L July -11,36 -7,24 -8,65


132




1.1.6 SPRING OATS

Field 9


C April -15,56 -7,69 -10,42

C May -14,87 -7,53 -10,44

C June -10,31 -6,76 -6,58

C July -8,30 -3,62 -6,45

L April -27,29 -21,71 -20,20

L May -10,05 -17,65 -7,49

L June -19,41 -16,26 -13,74

L July -13,68 -10,44 -10,41


133




1.1.7 WINTER WHEAT

Field 3


C April -17,76 -8,33 -12,05

C May -16,40 -7,77 -12,86

C June -13,28 -3,88 -9,42

C July -9,84 -2,64 -5,75

L April -8,85 -7,92 -7,56

L May -2,12 -11,36 -2,65

L June -7,59 -10,45 -6,46

L July -11,48 -6,22 -8,00

Field 5


C April -14,38 -5,46 -9,12

C May -14,63 -6,33 -10,53

C June -12,88 -4,81 -9,08

C July -10,12 -2,72 -6,57

L April -8,36 -5,66 -6,35

L May -7,44 -9,99 -6,05

L June -9,93 -8,64 -7,87

L July -11,09 -6,15 -8,32


134




Field 11


C April -11,62 -1,61 -6,98

C May -10,13 -1,89 -6,45

C June -10,35 -2,04 -6,37

C July -9,23 -1,50 -5,75

L April -5,03 -12,20 -3,27

L May -6,73 -14,64 -3,48

L June -8,12 -14,77 -4,91

L July -7,41 -11,19 -4,25

Field 20


C April -13,32 -5,29 -7,71

C May -11,22 -3,73 -7,99

C June -8,80 -0,93 -5,52

C July -8,21 -0,47 -5,34

L April -19,11 -13,29 -13,28

L May -18,17 -16,35 -15,48

L June -13,58 -9,64 -10,09

L July -9,23 -5,04 -6,78


135




Field 27


C April -14,14 -3,56 -8,18

C May -14,98 -9,02 -10,80

C June -9,22 -8,26 -7,36

C July -8,96 -6,22 -7,04

L April -20,70 -16,20 -16,22

L May -17,34 -14,64 -13,62

L June -12,67 -14,77 -10,11

L July -11,18 -11,19 -8,38

Field 33


C April -13,67 -4,74 -7,11

C May -12,96 -5,70 -9,40

C June -10,68 -6,28 -8,32

C July -9,50 -5,02 -7,51

L April -18,72 -14,65 -13,38

L May -9,02 -12,08 -7,23

L June -12,28 -11,34 -9,66

L July -11,68 -8,94 -8,59


136




1.2 IMAGE RESULT

1.2.1 APRIL

Figure 46. C-band of the April acquisition applying Three Component Scattering model

Figure 47. L-band of the April acquisition applying Three Component Scattering model


137




1.2.2 MAY

Figure 48. C-band of the May acquisition applying Three Component Scattering model

Figure 49. L-band of the May acquisition applying Three Component Scattering model


138




1.2.3 JUNE

Figure 50. C-band of the June acquisition applying Three Component Scattering model

Figure 51. L-band of the June acquisition applying Three Component Scattering model


139




1.2.4 JULY

Figure 52. C-band of the July acquisition applying Three Component Scattering model

Figure 53. L-band of the July acquisition applying Three Component Scattering model

DATA RESULTS – Entropy Based Scattering model

140




Chapter 2 ENTROPY BASED SCATTERING

MODEL

2.1 TABLES OF ENTROPY & ALPHA

2.1.1 BEETS

Field 30

Band Month mean_H mean_alpha_av (rad) mean_alpha_av (deg)

C April 0,63 0,69 39,6

C May 0,82 0,72 41,4

C June 0,86 0,74 42,4

C July 0,85 0,78 44,4

L April 0,70 0,69 39,7

L May 0,72 0,70 40,0

L June 0,81 0,81 46,5

L July 0,81 0,81 46,3


141




2.1.2 GRASS

Field 4


C April 0,74 0,72 41,4

C May 0,76 0,76 43,8

C June 0,79 0,78 44,9

C July 0,85 0,83 47,7

L April 0,60 0,71 40,7

L May 0,61 0,65 37,0

L June 0,56 0,55 31,7

L July 0,70 0,67 38,5


142




2.1.3 PEAS

Field 7


C April 0,72 0,73 41,9

C May 0,74 0,80 46,0

C June 0,82 0,70 40,2

C July 0,83 0,83 47,6

L April 0,50 0,61 35,0

L May 0,59 0,71 40,8

L June 0,50 0,49 28,2

L July 0,62 0,57 32,5

Field 15


C April 0,52 0,71 40,4

C May 0,80 0,73 41,7

C June 0,87 0,77 44,2

C July 0,84 0,82 46,9

L April 0,58 0,61 34,7

L May 0,64 0,72 41,3

L June 0,63 0,67 38,6

L July 0,67 0,69 39,3


143




Field 18


C April 0,44 0,58 33,2

C May 0,78 0,70 40,3

C June 0,89 0,81 46,1

C July 0,87 0,82 46,8

L April 0,53 0,58 33,1

L May 0,48 0,55 31,4

L June 0,70 0,69 39,4

L July 0,78 0,80 45,8

Field 24


C April 0,69 0,74 42,3

C May 0,82 0,75 43,3

C June 0,83 0,70 40,2

C July 0,81 0,74 42,6

L April 0,77 0,79 45,0

L May 0,84 0,80 45,9

L June 0,83 0,82 47,2

L July 0,82 0,80 46,1


144




Field 28


C April 0,57 0,73 41,6

C May 0,81 0,76 43,3

C June 0,81 0,77 44,0

C July 0,79 0,83 47,3

L April 0,62 0,68 38,7

L May 0,76 0,80 45,6

L June 0,70 0,69 39,7

L July 0,75 0,77 44,3

Field 37


C April 0,57 0,60 34,3

C May 0,76 0,69 39,7

C June 0,77 0,72 41,4

C July 0,78 0,80 45,9

L April 0,49 0,58 33,1

L May 0,80 0,83 47,8

L June 0,77 0,85 48,5

L July 0,79 0,84 48,0


145




2.1.4 RYE

Field 1


C April 0,70 0,66 37,6

C May 0,83 0,76 43,6

C June 0,83 0,76 43,7

C July 0,80 0,79 45,3

L April 0,71 0,79 45,5

L May 0,82 0,91 52,0

L June 0,84 0,88 50,6

L July 0,79 0,82 46,8

Field 8


C April 0,77 0,78 44,5

C May 0,76 0,75 42,8

C June 0,82 0,81 46,6

C July 0,87 0,86 49,6

L April 0,50 0,68 39,2

L May 0,54 0,50 28,5

L June 0,47 0,42 23,9

L July 0,72 0,67 38,3


146




Field 12


C April 0,67 0,70 39,9

C May 0,77 0,73 41,8

C June 0,83 0,78 44,6

C July 0,84 0,79 45,2

L April 0,71 0,74 42,7

L May 0,78 0,77 44,4

L June 0,76 0,76 43,3

L July 0,79 0,80 46,0

Field 23


C April 0,43 0,61 35,0

C May 0,77 0,67 38,2

C June 0,79 0,71 40,6

C July 0,81 0,83 47,3

L April 0,55 0,59 33,8

L May 0,76 0,80 46,0

L June 0,72 0,77 43,9

L July 0,79 0,82 47,0


147




2.1.5 SPRING BARLEY

Field 6


C April 0,61 0,66 37,8

C May 0,74 0,64 36,7

C June 0,79 0,67 38,3

C July 0,82 0,80 45,6

L April 0,68 0,69 39,5

L May 0,77 0,73 41,8

L June 0,77 0,78 44,9

L July 0,80 0,82 46,8

Field 13


C April 0,62 0,66 37,7

C May 0,77 0,72 41,2

C June 0,85 0,79 45,3

C July 0,83 0,81 46,2

L April 0,58 0,68 38,8

L May 0,74 0,77 43,9

L June 0,73 0,77 44,4

L July 0,78 0,83 47,5


148




Field 14


C April 0,74 0,72 41,3

C May 0,81 0,74 42,4

C June 0,89 0,84 48,1

C July 0,80 0,83 47,7

L April 0,68 0,80 45,6

L May 0,88 0,94 54,0

L June 0,84 0,85 48,6

L July 0,83 0,89 51,0

Field 29


C April 0,66 0,61 35,1

C May 0,79 0,70 40,3

C June 0,83 0,66 37,8

C July 0,85 0,77 44,1

L April 0,71 0,66 38,0

L May 0,68 0,59 33,6

L June 0,65 0,59 33,9

L July 0,75 0,75 43,0


149




Field 31


C April 0,59 0,63 36,1

C May 0,81 0,72 41,1

C June 0,84 0,73 41,6

C July 0,83 0,76 43,8

L April 0,69 0,67 38,7

L May 0,71 0,73 41,7

L June 0,78 0,77 44,3

L July 0,78 0,78 44,7

Field 34


C April 0,44 0,48 27,7

C May 0,76 0,64 36,5

C June 0,80 0,73 42,0

C July 0,78 0,84 48,1

L April 0,42 0,47 27,2

L May 0,73 0,74 42,3

L June 0,72 0,78 44,6

L July 0,83 0,86 49,1


150




Field 36


C April 0,66 0,62 35,4

C May 0,81 0,74 42,7

C June 0,83 0,74 42,3

C July 0,84 0,81 46,1

L April 0,51 0,57 32,9

L May 0,82 0,83 47,6

L June 0,74 0,78 44,8

L July 0,78 0,78 44,7


151




2.1.6 SPRING OATS

Field 1


C April 0,58 0,71 40,6

C May 0,76 0,70 40,2

C June 0,75 0,67 38,1

C July 0,82 0,82 47,2

L April 0,49 0,56 32,2

L May 0,66 0,77 44,3

L June 0,52 0,51 29,0

L July 0,73 0,73 41,8


152




2.1.7 WINTER WHEAT

Field 3


C April 0,71 0,65 37,0

C May 0,84 0,77 44,3

C June 0,86 0,80 46,0

C July 0,78 0,82 46,7

L April 0,57 0,83 47,5

L May 0,77 0,93 53,3

L June 0,87 0,93 53,4

L July 0,81 0,89 50,8

Field 5


C April 0,70 0,67 38,6

C May 0,80 0,73 41,9

C June 0,84 0,76 43,3

C July 0,81 0,77 44,4

L April 0,65 0,81 46,2

L May 0,80 0,86 49,0

L June 0,83 0,86 49,4

L July 0,81 0,84 48,3


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Field 11


C April 0,76 0,77 43,9

C May 0,83 0,76 43,8

C June 0,84 0,74 42,3

C July 0,84 0,77 44,4

L April 0,81 0,84 48,0

L May 0,84 0,84 48,4

L June 0,82 0,82 47,2

L July 0,83 0,83 47,6

Field 20


C April 0,52 0,65 37,1

C May 0,84 0,77 44,3

C June 0,88 0,78 44,9

C July 0,86 0,80 45,9

L April 0,58 0,63 36,2

L May 0,65 0,73 41,8

L June 0,73 0,74 42,1

L July 0,80 0,80 46,0


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Field 27


C April 0,67 0,74 42,4

C May 0,74 0,74 42,6

C June 0,81 0,78 44,6

C July 0,82 0,80 45,9

L April 0,61 0,67 38,3

L May 0,65 0,65 37,3

L June 0,65 0,72 41,2

L July 0,64 0,71 40,5

Field 33


C April 0,61 0,57 32,5

C May 0,80 0,77 44,0

C June 0,85 0,80 46,0

C July 0,84 0,82 46,8

L April 0,53 0,54 30,9

L May 0,80 0,84 48,4

L June 0,75 0,76 43,8

L July 0,74 0,74 42,6


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2.2 ENTROPY ALPHA PLANES

2.2.1 APRIL

Figure 54. Entropy-alpha planes of the April acquisition at C-band

Figure 55. Entropy-alpha planes of the April acquisition at L-band


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2.2.2 MAY

Figure 56. Entropy-alpha planes of the May acquisition at C-band

Figure 57. Entropy-alpha planes of the May acquisition at L-band


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2.2.3 JUNE

Figure 58. Entropy-alpha planes of the June acquisition at C-band

Figure 59. Entropy-alpha planes of the June acquisition at L-band


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2.2.4 JULY

Figure 60. Entropy-alpha planes of the July acquisition at C-band

Figure 61. Entropy-alpha planes of the July acquisition at L-band


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2.3 IMAGE RESULTS

2.3.1 APRIL

Figure 62. C-band of the April acquisition applying Entropy Based Scattering model

Figure 63. L-band of the April acquisition applying Entropy Based Scattering model


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2.3.2 MAY

Figure 64. C-band of the May acquisition applying Entropy Based Scattering model

Figure 65. L-band of the May acquisition applying Entropy Based Scattering model


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2.3.3 JUNE

Figure 66. C-band of the June acquisition applying Entropy Based Scattering model

Figure 67. L-band of the June acquisition applying Entropy Based Scattering model


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2.3.4 JULY

Figure 68. C-band of the July acquisition applying Entropy Based Scattering model

Figure 69. L-band of the July acquisition applying Entropy Based Scattering model

Fdo.: …………………… Fecha: - IIT · finalidad de monitorizar y mapear los cultivos...

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