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Matteo Soccorsi(1) and Mihai Datcu(1,2)

A Complex GMRF for SAR Image Analysis:A Bayesian Approach

(1) German Aerospace Center (DLR), Remote Sensing Technology Institute (IMF), Photogrammetry and Image Analysis (PB)

(2) École Nationale Supérieure de Télécomunication, Paris, France

7th CNES/DLR Workshop on Information Extraction and Scene Understanding for Meter

Resolution ImagesDLR, Oberpfaffenhofen, 28th to 30th of March,

2007

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Outline

High Resolution (HR) Synthetic Aperture Radar (SAR) images

Image model: complex Gauss-Markov Random Fields (GMRF)

Bayesian frame Case study Evidence maximization information extraction from

detected images Classification Comparison Conclusion

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Outline

HR SAR images Image model: complex GMRF Bayesian frame Case study Evidence maximization information extraction from

detected images Classification Comparison Conclusion

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High Resolution SAR Images 1/3

Complex data (E-SAR X band, Dresden):

Image interpretation is a difficult task.

Amplitude

Phase

Real channel

Imaginary channel

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High Resolution SAR Images 2/3

Examples of different textures:

High resolution SAR images show different phase behavior.

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High Resolution SAR Images 3/3

Example of structured target with correlated phase (E-SAR X band, DLR area):

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General Concept

There is information in the phase of HR SAR data; It is important to exploit this information for

better scene understanding; The task is to model complex data with phase

correlation pattern; We assume the data to be modeled by GMRF; We extend the definition of real GMRF to complex

domain.

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Outline

HR SAR images Image model: complex GMRF Bayesian frame Case study Evidence maximization information extraction from

detected images Classification Comparison Conclusion

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Image Model: Complex GMRF

GMRF model is characterized by the following conditional distribution:

Neighborhood

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GMRF Concept

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Simulation of Complex GMRF

Phase image examples:

By varying the number of the parameters and their values we can model different kinds of textures.

Model order 1 Model order 2 Model order 6

Model order 3 Model order 5 Model order 8

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Outline

HR SAR images Image model: complex GMRF Bayesian frame Case study Evidence maximization information extraction from

detected images Classification Comparison Conclusion

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Model Fitting

In the model fitting we apply Bayes’ rule to maximize the probability distribution of the parameter θ given the likelihood of the observation xs and the prior of the parameter:

The evidence p(xs|Hi) is neglected at this level of inference (because it is a constant factor) and the equation of the MAP estimate is:

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Model selection We find the most plausible model Hi out of a set of

existing models {Hj} given the image data xs:

The task is obtained through selecting the model which maximize the evidence obtained by marginalization:

Where the integral is over the multidimensional parameters space and p(θ |Hi) is the prior of the parameters.

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Outline

HR SAR images Image model: complex GMRF Bayesian frame Case study Evidence maximization information extraction from

detected images Classification Comparison Conclusion

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Parameter Estimation

Block diagram of the algorithm:

The number of the output parameters depends on the model order complexity.

CliqueMatrix

MAPEstimate

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Classification Results

We processed and classified an E-SAR scene of Dresden city, Germany. Azimuth resolution 0.72 m, range resolution 1.99 m, covering an area of about 5.2x2.0 Km2

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n Parameter Estimation for Model Order Selection

We chose three classes and performed the model order selection by evidence computation:

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Texture Feature 1/2

Amplitude

Phase

Variance

Vertical clique (real part)

Horizontal clique (real

part)

Evidence

Vertical clique (imaginary part)

Horizontal clique (imaginary part)

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Texture Feature 2/2

Amplitude

Phase

Variance

Vertical clique (real part)

Horizontal clique (real

part)

Evidence

Vertical clique (imaginary part)

Horizontal clique (imaginary part)

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HR SAR images Image model: complex GMRF Bayesian frame Case study Evidence maximization information extraction from

detected images Classification Comparison Conclusion

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n Block Diagram of Evidence Maximization Algorithm

Updateθ

MAPEstimator

Evidence Optimizer

E-step

M-step

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n Evidence Maximization Texture Parameters and Despeckling

Amplitude

Despeckled image

Vertical clique

Variance

Horizontal clique

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Outline

HR SAR images Image model: complex GMRF Bayesian frame Case study Evidence maximization information extraction from

detected images Classification Comparison Conclusion

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Classification Comparison and Assessment 1/3

Slant range

Ground range

Ground truth

Complex GMRF Complex GMRF (*) Evidence Maximization

(*)

(*) Sampled data of a factor 1/2

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Classification Comparison and Assessment 2/3

Slant range

Ground range

Ground truth

Complex GMRF Complex GMRF (*) Evidence Maximization

(*)(*) Sampled data of a factor 1/2

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Classification Comparison and Assessment 3/3

Slant range

Ground range

Ground truth

Complex GMRF Complex GMRF (*) Evidence Maximization

(*)

(*) Sampled data of a factor 1/2

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Outline

HR SAR images Image model: complex GMRF Bayesian frame Case study Evidence maximization information extraction from

detected images Classification Comparison Conclusion

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Conclusion

Complex GMRF is a tool for texture feature extraction.

It is able to model phase correlation pattern. The comparison with Evidence Maximization

algorithm provides that: Complex GMRF is at about one order of magnitude faster than Evidence Maximization, thanks to the linearity of the model;

Complex GMRF results in a better scene classification: the classes of the image are better represented.

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n Coming soon…

Further analysis on feature extraction from complex phase;

Statistical analysis of polarimetric data: TerraSAR X dual/quad-polarization product;

Azimuth multi-look analysis; Study of MDL formalism in relation with ICA; Conclusion on the best model space; Integration and validation in KIM.

Thank you for your attention!