Paretian similarity for partial comparison of non-rigid objects

Authors:
Alexander M. Bronstein;Michael M. Bronstein;Alfred M. Bruckstein;Ron Kimmel
Affiliations:
Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel;Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel;Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel;Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel
Venue:
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Year:
2007

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Abstract

In this paper, we address the problem of partial comparison of non-rigid objects. We introduce a new class of set-valued distances, related to the concept of Pareto optimality in economics. Such distances allow to capture intrinsic geometric similarity between parts of non-rigid objects, obtaining semantically meaningful comparison results. The numerical implementation of our method is computationally efficient and is similar to GMDS, a multidimensional scaling-like continuous optimization problem.