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Mathieu Carrière, Steve Y. Oudot, and Maksim Ovsjanikov. Stable
Topological Signatures for Points on 3D Shapes. Proc. Sympos. on
Geometry Processing,
2015. To appear.
Abstract:
Comparing points on 3D shapes is among the fundamental operations in
shape analysis. To facilitate this task, a great number of local point
signatures or descriptors have been proposed in the past
decades. However, the vast majority of these descriptors concentrate
on the local geometry of the shape around the point, and thus are
insensitive to its connectivity structure. By contrast, several global
signatures have been proposed that successfully capture the overall
topology of the shape and thus characterize the shape as a whole. In
this paper, we propose the first point descriptor that captures the
topology structure of the shape as ‘seen’ from a single point, in a
multiscale and provably stable way. We also demonstrate how a large
class of topological signatures, including ours, can be mapped to
vectors, opening the door to many classical analysis and learning
methods. We illustrate the performance of this approach on the
problems of supervised shape labeling and shape matching. We show that
our signatures provide complementary information to existing ones and
allow to achieve better performance with less training data in both
applications.
Bibtex:
@inproceedings{coo-stbp3ds-15,
author = {M. Carrière and S. Y. Oudot and M. Ovsjanikov},
title = {Stable Topological Signatures for Points on 3D Shapes},
booktitle = {Proc. Sympos. on Geometry Processing},
year = {2015}
}
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