1. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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 7 th CNES/DLR Workshop on Information Extraction and Scene Understanding for Meter Resolution Images DLR, Oberpfaffenhofen, 28 th to 30 th of March, 2007

2. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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

3. Competence Centre on Information Extraction and Image Understanding for Earth Observation Outline  HR SAR images  Image model: complex GMRF  Bayesian frame  Case study  Evidence maximization information extraction from detected images  Classification Comparison  Conclusion

4. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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

5. Competence Centre on Information Extraction and Image Understanding for Earth Observation High Resolution SAR Images 2/3  Examples of different textures:  High resolution SAR images show different phase behavior.

6. Competence Centre on Information Extraction and Image Understanding for Earth Observation High Resolution SAR Images 3/3  Example of structured target with correlated phase (E-SAR X band, DLR area):

7. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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.

8. Competence Centre on Information Extraction and Image Understanding for Earth Observation Outline  HR SAR images  Image model: complex GMRF  Bayesian frame  Case study  Evidence maximization information extraction from detected images  Classification Comparison  Conclusion

9. Competence Centre on Information Extraction and Image Understanding for Earth Observation Image Model: Complex GMRF  GMRF model is characterized by the following conditional distribution: Neighborhood

10. Competence Centre on Information Extraction and Image Understanding for Earth Observation GMRF Concept

11. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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 1Model order 2Model order 6 Model order 3Model order 5Model order 8

12. Competence Centre on Information Extraction and Image Understanding for Earth Observation Outline  HR SAR images  Image model: complex GMRF  Bayesian frame  Case study  Evidence maximization information extraction from detected images  Classification Comparison  Conclusion

13. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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 x s and the prior of the parameter:  The evidence p( x s |H i ) is neglected at this level of inference (because it is a constant factor) and the equation of the MAP estimate is:

14. Competence Centre on Information Extraction and Image Understanding for Earth Observation Model selection  We find the most plausible model H i out of a set of existing models {H j } given the image data x s :  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 |H i ) is the prior of the parameters.

15. Competence Centre on Information Extraction and Image Understanding for Earth Observation Outline  HR SAR images  Image model: complex GMRF  Bayesian frame  Case study  Evidence maximization information extraction from detected images  Classification Comparison  Conclusion

16. Competence Centre on Information Extraction and Image Understanding for Earth Observation Parameter Estimation  Block diagram of the algorithm:  The number of the output parameters depends on the model order complexity. Clique Matrix MAP Estimate G

17. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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 Km 2

18. Competence Centre on Information Extraction and Image Understanding for Earth Observation Parameter Estimation for Model Order Selection  We chose three classes and performed the model order selection by evidence computation:

19. Competence Centre on Information Extraction and Image Understanding for Earth Observation Texture Feature 1/2 Amplitude Phase Variance Vertical clique (real part) Horizontal clique (real part) Evidence Vertical clique (imaginary part) Horizontal clique (imaginary part)

20. Competence Centre on Information Extraction and Image Understanding for Earth Observation Texture Feature 2/2 Amplitude Phase Variance Vertical clique (real part) Horizontal clique (real part) Evidence Vertical clique (imaginary part) Horizontal clique (imaginary part)

21. Competence Centre on Information Extraction and Image Understanding for Earth Observation Outline  HR SAR images  Image model: complex GMRF  Bayesian frame  Case study  Evidence maximization information extraction from detected images  Classification Comparison  Conclusion

22. Competence Centre on Information Extraction and Image Understanding for Earth Observation Block Diagram of Evidence Maximization Algorithm Update θ MAP Estimator EvidenceOptimizer E-step M-step

23. Competence Centre on Information Extraction and Image Understanding for Earth Observation Evidence Maximization Texture Parameters and Despeckling Amplitude Despeckled image Vertical clique Variance Horizontal clique

24. Competence Centre on Information Extraction and Image Understanding for Earth Observation Outline  HR SAR images  Image model: complex GMRF  Bayesian frame  Case study  Evidence maximization information extraction from detected images  Classification Comparison  Conclusion

25. Competence Centre on Information Extraction and Image Understanding for Earth Observation Classification Comparison and Assessment 1/3 Slant rangeGround rangeGround truth Complex GMRF Complex GMRF (*) Evidence Maximization (*) (*) Sampled data of a factor 1/2

26. Competence Centre on Information Extraction and Image Understanding for Earth Observation Classification Comparison and Assessment 2/3 Slant rangeGround rangeGround truth Complex GMRFComplex GMRF (*)Evidence Maximization (*) (*) Sampled data of a factor 1/2

27. Competence Centre on Information Extraction and Image Understanding for Earth Observation Classification Comparison and Assessment 3/3 Slant rangeGround rangeGround truth Complex GMRFComplex GMRF (*) Evidence Maximization (*) (*) Sampled data of a factor 1/2

28. Competence Centre on Information Extraction and Image Understanding for Earth Observation Outline  HR SAR images  Image model: complex GMRF  Bayesian frame  Case study  Evidence maximization information extraction from detected images  Classification Comparison  Conclusion

29. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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.

30. Competence Centre on Information Extraction and Image Understanding for Earth Observation 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!