| Paper: | SS-1.1 | ||
| Session: | Statistical Inferences on Nonlinear Manifolds with Applications in Signal and Image Processing | ||
| Time: | Tuesday, May 16, 10:30 - 10:50 | ||
| Presentation: | Special Session Lecture | ||
| Topic: | Special Sessions: Statistical inferences on nonlinear manifolds with applications in signal and image processing | ||
| Title: | Distance-Based Shape Statistics | ||
| Authors: | Guillaume Charpiat, Ecole Normale Supérieure, France; Olivier Faugeras, INRIA Sophia-Antipolis, France; Renaud Keriven, Ecole Nationale des Ponts et Chaussées, France; Pierre Maurel, Ecole Normale Supérieure, France | ||
| Abstract: | This article deals with statistics on sets of shapes. The approach is based on the Hausdorff distance between shapes. The choice of the Hausdorff distance between shapes is itself not fundamental since the same framework could be applied with another distance. We first define a smooth approximation of the Hausdorff distance and build non-supervised warpings between shapes by a gradient descent of the approximation. Local minima can be avoided by changing the scalar product in the tangent space of the shape being warped.When non-supervised warping fails, we present a way to guide the evolution with a small number of landmarks. Thanks to the warping fields, we can define the mean of a set of shapes and express statistics on them. Finally, we come back to the initial distance between shapes and use it to represent a set of shapes by a graph, which with the technic of graph Laplacian leads to a way of projecting shapes onto a low dimensional space. | ||
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