Spectral Multi-Dimensional Scaling using Biharmonic Distance

Jun Yang, Alexander Jesuorobo Obaseki, Jim X. Chen

2019

Abstract

The spectral property of the Laplace-Beltrami operator has become relevant in shape analysis. One of the numerous methods that employ the strength of Laplace-Beltrami operator eigen-properties in shape analysis is the spectral multidimensional scaling which maps the MDS problem into the eigenspace of its Laplace-Beltrami operator. Using the biharmonic distance we show a further reduction in the complexities of the canonical form of shapes making similarities and dissimilarities of isometric shapes more efficiently computed. With the theoretical sound biharmonic distance we embed the intrinsic property of a given shape into a Euclidean metric space. Utilizing the farthest-point sampling strategy to select a subset of sampled points, we combine the potency of the spectral multidimensional scaling with global awareness of the biharmonic distance operator to propose an approach which embeds canonical forms images that shows further “resemblance” between isometric shapes. Experimental result shows an efficient and effective approximation with both distinctive local features and yet a robust global property of both the model and probe shapes. In comparison to a recent state-of-the-art work, the proposed approach can achieve comparable or even better results and have practical computational efficiency as well.

Paper Citation

in Harvard Style

Yang J., Obaseki A. and Chen J. (2019). Spectral Multi-Dimensional Scaling using Biharmonic Distance. In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019) - Volume 1: GRAPP; ISBN 978-989-758-354-4, SciTePress, pages 161-168. DOI: 10.5220/0007242901610168

in Bibtex Style

@conference{grapp19,
author={Jun Yang and Alexander Jesuorobo Obaseki and Jim X. Chen},
title={Spectral Multi-Dimensional Scaling using Biharmonic Distance},
booktitle={Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019) - Volume 1: GRAPP},
year={2019},
pages={161-168},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0007242901610168},
isbn={978-989-758-354-4},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019) - Volume 1: GRAPP
TI - Spectral Multi-Dimensional Scaling using Biharmonic Distance
SN - 978-989-758-354-4
AU - Yang J.
AU - Obaseki A.
AU - Chen J.
PY - 2019
SP - 161
EP - 168
DO - 10.5220/0007242901610168
PB - SciTePress