Research Papers

3D Shape Classification Based on Spectral Function and MDS Mapping

[+] Author and Article Information
Zhanqing Chen

Department of Mechanical Engineering, Hong Kong University of Science and Technology, Hong Kong, China

Kai Tang1

Department of Mechanical Engineering, Hong Kong University of Science and Technology, Hong Kong, Chinamektang@ust.hk


Corresponding author.

J. Comput. Inf. Sci. Eng 10(1), 011004 (Feb 16, 2010) (10 pages) doi:10.1115/1.3290769 History: Received September 22, 2008; Revised August 09, 2009; Published February 16, 2010; Online February 16, 2010

This paper reports a new method for 3D shape classification. Given a 3D shape M, we first define a spectral function at every point on M that is a weighted summation of the geodesics from the point to a set of curvature-sensitive feature points on M. Based on this spectral field, a real-valued square matrix is defined that correlates the topology (the spectral field) with the geometry (the maximum geodesic) of M, and the eigenvalues of this matrix are then taken as the fingerprint of M. This fingerprint enjoys several favorable characteristics desired for 3D shape classification, such as high sensitivity to intrinsic features on M (because of the feature points and the correlation) and good immunity to geometric noise on M (because of the novel design of the weights and the overall integration of geodesics). As an integral part of the work, we finally apply the classical multidimensional scaling method to the fingerprints of the 3D shapes to be classified. In all, our classification algorithm maps 3D shapes into clusters in a Euclidean plane that possess high fidelity to intrinsic features—in both geometry and topology—of the original shapes. We demonstrate the versatility of our approach through various classification examples.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

All the three figures will have a constant spectral function μ(x) according to (1)

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Figure 2

A simple solid: red lines are “1” feature points and blue lines are “−1” feature points

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Figure 3

Spectral curve μ(x): two shapes ((a) and (b)) and their respective μ(x) ((c) and (d))

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Figure 4

The four false feature points cancel each other as two have weight 1 and the other two −1 and the four points are close to each other

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Figure 5

In the case of all 1 weight, the μ(x) of Figs.  33 ((a) and (b), respectively)

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Figure 6

A mechanical part (a) and its spectral field μ(x) ((b) and (c))

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Figure 7

Abnormities in a mesh due to geometric noises (a and b)

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Figure 8

Spectral eigensequences of three eccentric cams

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Figure 9

The final MDS result of five eccentric cams (a); (b) is the zoomed view of one cam with noise

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Figure 10

The final MDS classification result of seven tables

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Figure 11

Classification of four washers: (a) their SESs and (b) the MDS result

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Figure 12

The MDS classification result of the fixtures from Table 1



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