Formont.ppt

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  • Gamma classification : no information relative to the polarimetric phase information: ONLY SPAN
  • Rajouter slide pour M chapeau. Eventuellement rajouter un slide pour présenter diff SCM et FP.
  • Citer papier de Lee
  • Interprétation difficile, premiers résultats
  • Formont.ppt

    1. 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
    2. 2. K-MEANS CLASSIFIER <ul><li>Conventional clustering algorithm: </li></ul><ul><li>Initialisation: Assign pixels to classes. </li></ul><ul><li>Centers computation: Compute the centers of each class as follows: </li></ul><ul><li>Reassignment: Reassign each pixel to the class whose center minimizes a certain distance. </li></ul>
    3. 3. OUTLINE <ul><li>Non-Gaussian clutter model: the SIRV model </li></ul><ul><li>Contribution of the geometry of information </li></ul><ul><li>Results on real data </li></ul><ul><li>Conclusions and perspectives </li></ul>
    4. 4. OUTLINE
    5. 5. CONVENTIONAL COVARIANCE MATRIX ESTIMATE <ul><li>With low resolution, clutter is modeled as a Gaussian process. </li></ul><ul><li>Estimation of the covariance matrix of a pixel, characterized by its target vector k , thanks to N secondary data: k 1 , …, k N . </li></ul><ul><li>Maximum Likelihood estimate of the covariance matrix, the Sample Covariance Matrix (SCM): </li></ul>
    6. 6. SCM IN HIGH RESOLUTION Gamma classification Wishart classification with SCM Results are very close from each other : influence of polarimetric information ?
    7. 7. THE SIRV MODEL Non-Gaussian SIRV (Spherically Invariant Random Vector) representation of the scattering vector : <ul><li>where is a random positive variable (texture) and (speckle). </li></ul><ul><ul><li>The texture pdf is not specified : large class of stochastic processes can be described. </li></ul></ul><ul><ul><li>Texture : local spatial variation of power. </li></ul></ul><ul><ul><li>Speckle : polarimetric information. </li></ul></ul><ul><ul><li>Validated on real data measurement campaigns. </li></ul></ul>
    8. 8. COVARIANCE MATRIX ESTIMATE : THE SIRV MODEL COVARIANCE MATRIX ESTIMATE : THE SIRV MODEL ML ESTIMATE UNDER SIRV ASSUMPTION <ul><ul><li>Under SIRV assumption, the SCM is not a good estimator of M . </li></ul></ul><ul><ul><li>ML estimate of the covariance matrix: </li></ul></ul><ul><ul><li>Existence and unicity. </li></ul></ul><ul><ul><li>Convergence whatever the initialisation. </li></ul></ul><ul><ul><li>Unbiased, consistent and asymptotically Wishart-distributed. </li></ul></ul>
    9. 9. DISTANCE BETWEEN COVARIANCE MATRICES UNDER SIRV ASSUMPTION <ul><li>Non Gaussian Process ↔ Generalized LRT ↔ SIRV distance between the two FP covariance matrices </li></ul><ul><li>Gaussian Process ↔ Generalized LRT ↔ Wishart distance between the two SCM covariance matrices </li></ul>
    10. 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. 11. OUTLINE
    12. 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. 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. 14. OUTLINE
    15. 15. CLASSIFICATION RESULTS Wishart classification with SCM, Arithmetical mean SIRV classification with FPE, Arithmetical mean SIRV classification with FPE, Geometrical mean
    16. 16. CLASSES IN THE H- α PLANE
    17. 17. PARACOU, FRENCH GUIANA <ul><li>Acquired with the ONERA SETHI system </li></ul><ul><li>UHF band </li></ul><ul><li>1.25m resolution </li></ul>
    18. 18. CLASSIFICATION RESULTS Classification with Wishart distance, Arithmetical mean Classification with Wishart distance, Geometrical mean Classification with geometric distance, Geometrical mean
    19. 19. OUTLINE
    20. 20. CONCLUSIONS <ul><ul><li>Further investigation of the distance is required. </li></ul></ul><ul><ul><li>Interpretation is difficult because no literature. </li></ul></ul><ul><ul><li>Span can give information for homogeneous areas. </li></ul></ul><ul><ul><li>Necessity of a non-Gaussian model for HR SAR images. </li></ul></ul><ul><ul><li>Geometric definition of the class centers in line with the structure of the covariance matrices space. </li></ul></ul>

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