WE3.L09 - POLARIMETRIC SAR IMAGE VISUALIZATION AND INTERPRETATION WITH COVARIANCE MATRIX INVARIANTS

POLARIMETRIC SAR IMAGE VISUALIZATION AND INTERPRETATION WITHCOVARIANCE MATRIX INVARIANTS

Jaan Praks, Aalto University, FinlandElise Colin Koeniguer, ONERA, FranceMartti Hallikainen, Aalto University, Finland

Polarimatric SAR images are often presented as false color images. Many approaches is used. Simple RGB color composite image of three polarimetric channel amplitudes is used most often, but its has some limitations.

How colors should be used to achieve easiliy interpretative polarimetric SAR image for image browsing and quick interpretation?

In this study we try to give some hints, how good visualisation results can be achieved.

Introduction

Jaan PraksElise Colin KoeniguerMartti Hallikainen

To represent any numerical data in colors, we need a color model. The color model converts numbers to colors and vice a versa.

A brief history of Color Models

1610 Sigfridus Aronus Forsius (basic colors and color wheel)

1666 Isaac Newton, Color wheel

1766 Moses Harris adds color shades

1810 Philipp-Otto Runge

Thomas Young and H. Helmholtz - thrichromatic vision

1855 J. C. Maxwell – color matching functions

1931 CIE color system

Color Modelshistory

The color models can be divided roughly into two categories:

1. The parameter triplet is based on direct sensory input values.

Red Green Blue (RGB) values in Cartesian coordinates, parameters

are linear.

2. The parameter triplet tries to mimic human comprehension of colors. HSV, HSI, HSL. Uses cylindrical or spherical coordinate system.

Parameters like hue, saturation, lightness etc. Some parameters are

periodic. Perceptual parameters are also often interconnected (if the

saturation is zero, the hue has no values).

Color ModelsRGB and HSV

Images by SharkD

y

xz

EHuman eye does not sense polarization, and therefore our understanding of polarization is based on abstract models

There are many ways to visualize polarization

• Stokes parameters• Polarization ellipse• Poincare sphere

Polarimetric measurement systems like SAR • Target polarimetric signature

Visualising polarization

0

90

180

-45

0

450

0.2

0.4

0.6

0.8

1

ellipticity angle

CO-POL RESPONSE

orientation anglenorm

alis

ed p

ow

er

Similarities between color- and polarization models

Philipp-Otto Runge color sphere

Poincare polarization sphere

Poincaré sphere and Runge color sphere are similar

Both use spherical coordinates, and periodic parameters

Fully polarized radiation can be presented in colors unambiguously

Maxwell color triangle and ternary use the same technique to represent three variables restricted by constant sum a + b + c = const

Situation where a = b = c has a special meaning (white color)

In polarimetry, we have similar variables, for example normalized eigenvalues (scattering mechanism probability) or normalized covariance matrix diagonal elements

Similarities between color- and polarization models

Maxwell color triangle

Polarimetric classification with ternary plot

SAR image has more dimensions than is possible to represent in color image

- all parameters cannot be visualized in the same image

- there will always be more than few representation approaches

Color model should be selected according to image parameter relations and nature, periodic variables should be connected with periodic and linear parameters with linear

Cylindrical color systems often provide easier way to separate different parameters for independent processing

(P. Imbo, J.C. Souyris, A. Lopes, and P. Marthon, “Synoptic representation of the polarimetric

information,” in Proceedings CEOS SAR Workshop, Toulouse, France, October 26-29 1999.)

Some remarks on polarimetric SAR image color representation

Parameter scaling and histogram equalization changes often also interpretation

Intensity of the SAR image is similar to optical image - intensity is easy to treat separately

In some color systems, different parameters can have different resolution

Parameter relations should be taken into account

- equal RGB give white color and it should have physical meaning in visualization

- saturation affects also hue parameter

Some remarks on polarimetric SAR image color representation

Different parameter layers can have different resolution in HSl type of color models without effect to interpretation.

This can be utilized in synoptic representation where depolarization related parameters are calculated for averaged image.

ExamplesLayers with different resolution

Z-4Z-5Z-6

Z-7Z-8

Z-9

Z-4Z-5Z-6

Z-7Z-8Z-9

Hue - hi-res alphaSaturation - entropyIntensity - hi-res span

Hue - alphaSaturation - entropyIntensity - span

When histogram of the parameter is narrow, parameter image has low dynamics. Histogram equalization gives usually visually pleasing results.

However, histogram manipulation can change also interpretation and/or physical relation between the parameters, if parameters are related.

Examplesparameter scaling

Nicolas Trouve, Preliminary

Polarimetric Segmentation on

SAR images. EUSAR 2010.

In addition to intensity, polarimetric parameters can be divided roughly into three classes

1. Parameters connected to phase change of eigenpolarization states

- often periodic variables, suitable for hue

2. Parameters connected to change of amplitude

- periodic and linear parameters

3. Parameters connected depolarization properties

- controls also other polarimetric parameters, suitable for saturation

E. Colin-Koeniguer, N. Trouvé, J. Praks ”A review about alternatives to classical Polarimetric SAR parameters”, EUSAR

2010

Classes of polarimetric parameters

Normalized eigenvalues in trenary plot

Normalized eigenvalues in trenary plot, modulated with intensity

Covariance matrix and normalized covariance matrix

Surface scattering fraction (similar to alpha angle)

Scattering diversity (similar to entropy)

Normalized covariance Matrix invariants

k a b c S S S S S ST

hh vv hh vv hv vh

T , , , ,

1

2

cabab

bcbab

acaba

spankkkkN

**

**1* 1

Praks, Jaan; Koeniguer, Elise Colin; Hallikainen, Martti T., Alternatives to Target Entropy and Alpha Angle in SAR Polarimetry, IEEE Trans. Geoscience Rem. Sens., vol. 47, issue 7, pp. 2262-2274

span

SSN

vvhh

2

11

2

)1(2

3ˆ 2

FNH

Normalized Pauli components (N main diagonal)

Normalized Pauli components with intensity

Intensity, scattering diveristy and surface scattering fraction in synoptic representation

When visualizing SAR images with colors, special attention should be paid to color model selection for given parameters

Well selected color model and visualization scheme can be in the best case self explaining

Visualization scheme can explain also physical meaning of selected parameters

Parameter scaling for SAR images should be done with care and consideration, in order not to loose physical interpretation

Normalized covariance matrix provides suitable parameters for several good visualization schemes

Conclusions

Thank you!

WE3.L09 - POLARIMETRIC SAR IMAGE VISUALIZATION AND INTERPRETATION WITH COVARIANCE MATRIX INVARIANTS

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