The differential structure of surfaces captured by the Laplace Beltrami Operator (LBO) can be used to construct a space for analyzing visual and geometric information. The decomposition of the LBO at one end, and the heat operator at the other end provide us with efficient tools for dealing with images and shapes. Denoising, matching, segmenting, filtering, exaggerating are just few of the problems for which the LBO provides a convenient operating environment. We will review the optimality of a truncated basis provided by the LBO, and a selection of relevant metrics by which such optimal bases are constructed. A specific example is the scale invariant metric for surfaces, that we argue to be a natural choice for the study of articulated shapes and forms. Prof. Kimmel will comment about Intel’s RealSense geometry sensor, the intrinsic and extrinsic transformations applied to Alice in Wonderland, and the benefit of having an axiomatic model when valid.
Ron Kimmel. A Spectral Perspective on Shapes. In Xianghua Xie, Mark W. Jones, and Gary K. L. Tam, editors, Proceedings of the British Machine Vision Conference (BMVC), pages 2.1-2.1. BMVA Press, September 2015.
Bibtex
@inproceedings{BMVC2015_2,
title={A Spectral Perspective on Shapes},
author={Ron Kimmel},
year={2015},
month={September},
pages={2.1-2.1},
articleno={2},
numpages={1},
booktitle={Proceedings of the British Machine Vision Conference (BMVC)},
publisher={BMVA Press},
editor={Xianghua Xie, Mark W. Jones, and Gary K. L. Tam},
doi={10.5244/C.29.2},
isbn={1-901725-53-7},
url={https://dx.doi.org/10.5244/C.29.2}
}