Equi-affine invariant geometries of articulated objects

Authors:
Dan Raviv;Alexander M. Bronstein;Michael M. Bronstein;Ron Kimmel;Nir Sochen
Affiliations:
Computer Science Department, Technion, Israel;School of Electrical Engineering, Tel Aviv University, Israel;Faculty of Informatics, Università della Svizzera Italiana, Switzerland;Computer Science Department, Technion, Israel;Department of Applied Mathematics, Tel Aviv University, Israel
Venue:
Proceedings of the 15th international conference on Theoretical Foundations of Computer Vision: outdoor and large-scale real-world scene analysis
Year:
2011

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Abstract

We introduce an (equi-)affine invariant geometric structure by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to evaluate a new form of geodesic distances and to construct an invariant Laplacian from which local and global diffusion geometry is constructed. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.