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.

Bilder

Paper herunterladen

Paper herunterladen

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}
}