The Thirteenth Israeli Mini-Workshop in Applied and Computational Mathematics

Yaron Lipman (Computer Science and Applied Math, Weizmann Institute for Science)

A few applications of conformal mappings for surface comparison

One of the core problems in geometry processing is the problem of comparing shapes and finding correspondences between different, but similar shapes. Maybe the most popular instance of this problem is matching and comparing surfaces (2-dimensional manifolds), a crucial component in a large number of applications ranging from matching of cortical surfaces, faces, bones or other biological surfaces, to more synthetic applications like shape morphing and attribute transfer. In this talk we will present a few applications of conformal geometry to the problems of surface matching and comparison. In particular, we will show how certain ideas originated in the theory of conformal geometry can be used to define novel metrics measuring dissimilarities and finding correspondences between pairs of surfaces automatically. The key idea is to utilize the prominent low-dimensionality of conformal mappings to construct metrics that are computationally efficient. I will report results on a few datasets of biological surfaces as well as other standard 3D surface datasets.

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