Embedding Shapes with Green's functions for Global Shape Matching
In: Computers & Graphics (2017), 68C(1-10)
Abstract
We present a novel approach for the calculation of dense correspondences between non-isometric shapes. Our work builds on the well known functional map framework and investigates a novel embedding for the alignment of shapes. We therefore identify points with their Green’s functions of the Laplace–Beltrami operator, and hence, embed shapes into their own function space. In our embedding the L2 distances are known as the biharmonic distances, so that our embedding preserves the intrinsic distances on the shape. In the novel embedding each point-to-point map between two shapes becomes and can be represented as an affine map. Functional constraints and novel conformal constraints can be used to guide the matching process.
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Bibtex
@ARTICLE{burghard2017embedding,
author = {Burghard, Oliver and Dieckmann, Alexander and Klein, Reinhard},
pages = {1--10},
title = {Embedding Shapes with Green's functions for Global Shape Matching},
journal = {Computers {\&} Graphics},
volume = {68C},
year = {2017},
abstract = {We present a novel approach for the calculation of dense correspondences between non-isometric
shapes. Our work builds on the well known functional map framework and investigates a novel
embedding for the alignment of shapes. We therefore identify points with their Green’s functions
of the Laplace–Beltrami operator, and hence, embed shapes into their own function space. In our
embedding the L2 distances are known as the biharmonic distances, so that our embedding preserves
the intrinsic distances on the shape. In the novel embedding each point-to-point map between two
shapes becomes and can be represented as an affine map. Functional constraints and novel conformal
constraints can be used to guide the matching process.},
doi = {10.1016/j.cag.2017.06.004}
}