One Point Isometric Matching with the Heat Kernel

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dc.contributor.authorMaks Ovsjanikoven_US
dc.contributor.authorQuentin Merigoten_US
dc.contributor.authorFacundo Memolien_US
dc.contributor.authorLeonidas Guibasen_US
dc.date.accessioned2015-02-23T17:15:32Z
dc.date.available2015-02-23T17:15:32Z
dc.date.issued2010en_US
dc.description.abstractA common operation in many geometry processing algorithms consists of finding correspondences between pairs of shapes by finding structure-preserving maps between them. A particularly useful case of such maps is isometries, which preserve geodesic distances between points on each shape. Although several algorithms have been proposed to find approximately isometric maps between a pair of shapes, the structure of the space of isometries is not well understood. In this paper, we show that under mild genericity conditions, a single correspondence can be used to recover an isometry defined on entire shapes, and thus the space of all isometries can be parameterized by one correspondence between a pair of points. Perhaps surprisingly, this result is general, and does not depend on the dimensionality or the genus, and is valid for compact manifolds in any dimension. Moreover, we show that both the initial correspondence and the isometry can be recovered efficiently in practice. This allows us to devise an algorithm to find intrinsic symmetries of shapes, match shapes undergoing isometric deformations, as well as match partial and incomplete models efficiently.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume29en_US
dc.identifier.doi10.1111/j.1467-8659.2010.01764.xen_US
dc.identifier.pages1555-1564en_US
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/CGF.v29i5pp1555-1564en_US
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/CGF.v29i5pp1555-1564
dc.titleOne Point Isometric Matching with the Heat Kernelen_US
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29-Issue 5
SGP10: Eurographics Symposium on Geometry Processing