Fast approximation of distance between elastic curves using Kernels
Date
2013
Authors
Tabia, H.
Picard, D.
Laga, H.
Grosselin, P.H.
Editors
Burghardt, T.
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Conference paper
Citation
Proceedings of the British Machine Vision Conference, 2013 / Burghardt, T. (ed./s), pp.1-11
Statement of Responsibility
Conference Name
24th British Machine Vision Conference (9 Sep 2013 - 13 Sep 2013 : Bristol, England)
DOI
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 reparameterizations. 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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Copyright 2013 The Authors. The copyright of this document resides with its authors. It may be distributed unchanged freely in print or electronic forms.