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

7th CNES/DLR Workshop on Information Extraction and Scene Understanding for Meter Resolution Images DLR, Oberpfaffenhofen, 28th to 30th of March, 2007 A Complex GMRF for SAR Image Analysis: A Bayesian Approach Matteo Soccorsi(1) and Mihai Datcu(1,2) (1) German Aerospace Center (DLR), Remote Sensing Technology Institute (IMF), Photogrammetry and Image Analysis (PB) (2) École Nationale Supérieure de Télécomunication, Paris, France

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

Outline • HR SAR images • Image model: complex GMRF • Bayesian frame • Case study • Evidence maximization information extraction from detected images • Classification Comparison • Conclusion

High Resolution SAR Images 1/3 • Complex data (E-SAR X band, Dresden): • Image interpretation is a difficult task. Amplitude Real channel Phase Imaginary channel

High Resolution SAR Images 2/3 • Examples of different textures: • High resolution SAR images show different phase behavior.

High Resolution SAR Images 3/3 • Example of structured target with correlated phase (E-SAR X band, DLR area):

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.

Image Model: Complex GMRF • GMRF model is characterized by the following conditional distribution: Neighborhood

GMRF Concept

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

Model Fitting • In the model fitting we apply Bayes’ rule to maximize the probability distribution of the parameter θgiven 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:

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.

Clique Matrix MAP Estimate G Parameter Estimation • Block diagram of the algorithm: • The number of the output parameters depends on the model order complexity.

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

Parameter Estimation for Model Order Selection • We chose three classes and performed the model order selection by evidence computation:

Texture Feature 1/2 Amplitude Variance Evidence Phase Vertical clique (real part) Vertical clique (imaginary part) Horizontal clique (real part) Horizontal clique (imaginary part)

Texture Feature 2/2 Amplitude Variance Evidence Phase Vertical clique (real part) Vertical clique (imaginary part) Horizontal clique (real part) Horizontal clique (imaginary part)

Block Diagram of Evidence Maximization Algorithm E-step MAP Estimator Evidence Optimizer M-step Update θ

Evidence Maximization Texture Parameters and Despeckling Amplitude Variance Despeckled image Vertical clique Horizontal clique

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

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

Classification Comparison and Assessment 3/3 Slant range Ground range Ground truth Evidence Maximization (*) Complex GMRF Complex GMRF (*) (*) Sampled data of a factor 1/2

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.

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!

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