1. ON THE EXTENSION OF THE PRODUCT MODEL IN POLSAR PROCESSING FOR UNSUPERVISED CLASSIFICATION USING INFORMATION GEOMETRY OF COVARIANCE MATRICES P. Formont 1,2 , J.-P. Ovarlez 1,2 , F. Pascal 2 , G. Vasile 3 , L. Ferro-Famil 4 1 ONERA, 2 SONDRA, 3 GIPSA-lab, 4 IETR

4. OUTLINE

6. SCM IN HIGH RESOLUTION Gamma classification Wishart classification with SCM Results are very close from each other : influence of polarimetric information ?

10. COVARIANCE MATRIX ESTIMATE : THE SIRV MODEL COVARIANCE MATRIX ESTIMATE : THE SIRV MODEL RESULTS ON REAL DATA Color composition of the region of Brétigny, France Wishart classification with SCM Wishart classification with FPE

11. OUTLINE

12. Euclidian Mean: CONVENTIONAL MEAN OF COVARIANCE MATRICES The mean in the Euclidean sense of n given positive-definite Hermitian matrices M 1 ,.., M n in P ( m ) is defined as: Barycenter:

13. Riemannian Mean: A DIFFERENTIAL GEOMETRIC APPROACH TO THE GEOMETRIC MEAN OF HERMITIAN DEFINITE POSITIVE MATRICES The mean in the Riemannian sense of n given positive-definite Hermitian matrices M 1 ,.., M n in P ( m ) is defined as: Geodesic: Riemannian distance:

14. OUTLINE

15. CLASSIFICATION RESULTS Wishart classification with SCM, Arithmetical mean SIRV classification with FPE, Arithmetical mean SIRV classification with FPE, Geometrical mean

16. CLASSES IN THE H- α PLANE

18. CLASSIFICATION RESULTS Classification with Wishart distance, Arithmetical mean Classification with Wishart distance, Geometrical mean Classification with geometric distance, Geometrical mean

19. OUTLINE