Authors:
Jun Yang
1
;
Alexander Jesuorobo Obaseki
1
and
Jim X. Chen
2
Affiliations:
1
School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou, Gansu 730070 and China
;
2
Department of Computer Science, George Mason University, Fairfax, VA 22030-4444 and U.S.A.
Keyword(s):
Canonical Forms, Laplace-Beltrami Operator, Biharmonic Distance, Spectral Multidimensional Scaling (S-MDS).
Related
Ontology
Subjects/Areas/Topics:
Computer Vision, Visualization and Computer Graphics
;
Geometric Computing
;
Geometry and Modeling
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 res
ult 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.
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