Relating Shapes via Geometric Symmetries and Regularities
Abstract
In this paper we address the problem of finding correspondences between
related shapes of widely varying geometry. We propose a new method based
on the observation that symmetry and regularity in shapes is often
associated with their function. Hence, they provide cues for matching
related geometry even under strong shape variations.
Correspondingly, we decomposes shapes into overlapping regions determined
by their regularity properties. Afterwards, we form a graph that
connects these pieces via pairwise relations that capture geometric
relations between rotation axes and reflection planes as well as
topological or proximity relations. Finally, we perform graph matching to
establish correspondences.
The method yields certain more abstract but semantically meaningful
correspondences between man-made shapes that are too difficult to
recognize by traditional geometric methods.
Keywords:
symmetries, shape matching, registration, regularity, symmetry graph, matching
Paper [final version] (~13MB)
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Bibliography
A. Tevs, Q. Huang, M. Wand, H.-P. Seidel, L. Guibas "Relating Shapes via Geometric Symmetries and Regularities" , Proc. of Siggraph, 2014, Vol. 33, 4, 12 pages.