Affine-invariant geodesic geometry of deformable 3D shapes |
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Authors: | Dan Raviv Alexander M. Bronstein |
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Affiliation: | a Department of Computer Science, Technion, Israel b Department of Electrical Engineering, Tel Aviv University, Israel c Institute of Computational Science, Faculty of Informatics, Università della Svizzera Italiana, Lugano, Switzerland d Department of Applied Mathematics, Tel Aviv University, Israel |
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Abstract: | Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R3 in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis. |
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Keywords: | Equi-affine Affine Geodesics |
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