@inproceedings{charpiat:learningshapemetrics,
   author = {Charpiat, G.},
   title = {Learning Shape Metrics based on Deformations and Transport},
   year = {2009},
   publisher = {},
   pages = {},
   month = {09},
   booktitle = {Proceedings of the Second Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment (NORDIA) in Proceedings of ICCV 2009 and its Workshops},
   editor = {},
   abstract = {Shape evolutions, as well as shape matchings or image segmentation with 
shape prior, involve the preliminary choice of a suitable metric in the 
space of shapes. Instead of choosing a particular one, we propose a 
framework to learn shape metrics from a set of examples of shapes, 
designed to be able to handle sparse sets of highly varying shapes, 
since typical shape datasets, like human silhouettes, are intrinsically 
high-dimensional and non-dense. We formulate the task of finding the 
optimal metrics on an empirical manifold of shapes as a classical 
minimization problem ensuring smoothness, and compute its global optimum 
fast.
First, we design a criterion to compute point-to-point matching between 
shapes which deals with topological changes. Then, given a training set 
of shapes, we use these matchings to transport deformations observed on 
any shape to any other one. Finally, we estimate the metric in the 
tangent space of any shape, based on transported deformations, weighted 
by their reliability. Experiments on difficult sets are shown, and 
applications are proposed.},
   address = {Kyoto, Japan},
   URL = {http://tosca.cs.technion.ac.il/nordia09/}
}