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Distance-based shape statistics for image segmentation with priors

Guillaume Charpiat 1
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : The variational approach in image segmentation consists in defining a criterion depending on a contour and in computing its derivative with respect to the contour in order to minimize it with a gradient descent method. We propose a way to compute shape statistics of a sample set of contours and to incorporate them as a shape prior in the variational framework. We first define the set of "all shapes" as the set of "regular enough" shapes. We study several metrics on it and show they are topologically equivalent. One of them, the Hausdorff distance, is considered in the sequel. With the only knowledge of the distance between shapes we build a low-dimensional map thanks to the graph Laplacian technique. We then build a differentiable approximation of the Hausdorff distance. This allows to define the "mean" shape of a sample set of shapes and to find it with a variational approach. It happens that the notion of "shape gradient" depends strongly on the underlying inner product structure, and that consequently we also have to choose a convenient inner product in order to set priors on the deformation fields that a shape undergoes during the gradient descent process. We then compute statistics based on the instantaneous deformation fields that the "mean shape" should undergo to move towards each example of the sample set of shapes. The application of PCA to the fields leads to sensible characteristic modes of deformation that convey the shape variability. Contour statistics are turned into a shape prior; an example of image segmentation with this criterion is shown. A similar approach is also tried on images instead of contours: eigenmodes are shown for a human face database, and an expression recognition task is performed using SVM on deformation fields.
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Guillaume Charpiat. Distance-based shape statistics for image segmentation with priors. Human-Computer Interaction [cs.HC]. Ecole Polytechnique X, 2006. English. ⟨tel-00457462⟩

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