Analysis of two-dimensional non-rigid shapes

Alexander M. Bronstein, Michael M. Bronstein*, Alfred M. Bruckstein, Ron Kimmel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper.

Original languageEnglish
Pages (from-to)67-88
Number of pages22
JournalInternational Journal of Computer Vision
Volume78
Issue number1
DOIs
StatePublished - Jun 2008
Externally publishedYes

Funding

FundersFunder number
Center for Security Science and Technology

    Keywords

    • GMDS
    • Gromov-Hausdorff distance
    • Intrinsic geometry
    • Multidimensional scaling
    • Non-rigid shapes
    • Pareto optimum
    • Partial similarity

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