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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 Formont.ppt Presentation Transcript

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