Fast Approximation of Distance Between Elastic Curves using Kernels

Hedi Tabia 1 David Picard 2 Hamid Laga 3 Philippe-Henri Gosselin 1, 4
2 MIDI
ETIS - Equipes Traitement de l'Information et Systèmes
4 TEXMEX - Multimedia content-based indexing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : Elastic shape analysis on non-linear Riemannian manifolds provides an efficient and elegant way for simultaneous comparison and registration of non-rigid shapes. In such formulation, shapes become points on some high dimensional shape space. A geodesic between two points corresponds to the optimal deformation needed to register one shape onto another. The length of the geodesic provides a proper metric for shape comparison. However, the computation of geodesics, and therefore the metric, is computationally very expensive as it involves a search over the space of all possible rotations and re- parameterization. This problem is even more important in shape retrieval scenarios where the query shape is compared to every element in the collection to search. In this paper, we propose a new procedure for metric approximation using the framework of kernel functions. We will demonstrate that this provides a fast approximation of the metric while preserving its invariance properties.
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Hedi Tabia, David Picard, Hamid Laga, Philippe-Henri Gosselin. Fast Approximation of Distance Between Elastic Curves using Kernels. British Machine Vision Conference, Sep 2013, United Kingdom. pp.11. ⟨hal-00861369⟩

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