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New Spectral Decomposition Method for Three-Dimensional Shape Models and Its Applications

[+] Author and Article Information
Kohei Murotani

Department of Mathematical Informatics, Graduate School of Information Science and Technology,  The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japanmuro@simplex.t.u-tokyo.ac.jp

Kokichi Sugihara

Department of Mathematical Informatics, Graduate School of Information Science and Technology,  The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japansugihara@mist.i.u-tokyo.ac.jp

J. Comput. Inf. Sci. Eng 5(4), 277-282 (Jul 04, 2005) (6 pages) doi:10.1115/1.2052849 History: Received October 03, 2004; Revised July 04, 2005

This paper presents a generalization of a data analysis technique called a singular spectrum analysis (SSA). The original SSA is a tool for analyzing one-dimensional data such as time series, whereas the generalization presented in this paper is suitable for multidimensional data such as three-dimensional polygonal meshes. The basic idea is to generalize the autocorrelation matrix so as to represent mutual relations of multidimensional data flexibly. Two applications of the proposed generalization are also shown briefly.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

A vertex of the mesh and the set of vertices with the same Dijkstra distances

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Figure 2

Decomposed bunny model for L=21; (b), (c), and (d) show the sums of d̂ lower frequency components

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Figure 3

Sums of d̂ lower frequency components of the decomposed bunny model for L=10

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Figure 4

Sums of d̂ lower frequency components of the decomposed bunny model for L=5

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Figure 5

Assumed net to cover the hole

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Figure 6

Estimation of missing vertices at the nose in an incomplete bunny mesh

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Figure 7

Estimation of missing vertices at the leg in an incomplete bunny mesh

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Figure 8

Watermarked bunny meshes

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