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Manifold-valued image processing with SPD matrices

Xavier Pennec    Université Côte d'Azur and Inria, Epione team, Sophia Antipolis, France

Abstract

Symmetric positive definite (SPD) matrices are geometric data that appear in many applications. They are used in particular in Diffusion Tensor Imaging (DTI) as a simple model of the anisotropic diffusion of water in the tissues. This chapter extends the Riemannian computing statistical estimation framework of chapters 1 and 2 to manifold-valued images with the example of SPD matrices. SPD matrices constitute a smooth but incomplete manifold with the classical Euclidean metric on matrices. This creates important computational problems for image processing since we easily pass the boundaries to end-up ...

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