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.

Issue Section:
Special Issue Papers
Keywords:
spectral analysis, data analysis, mesh generation, matrix algebra
Topics:
Emission spectroscopy, Shapes, Spectroscopy, Theorems (Mathematics), Trajectories (Physics), Watermarking, Matrix algebra, Mesh generation, Time series
1.
Hoppe
,
H.
, 1996, “
Progressive Meshes
,”
SIGGRAPH ’96: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques
, pp.
99
–
108
.
2.
Kanai
,
S.
,
Date
,
H.
, and
Kishinami
,
T.
, 1998, “
Digital Watermarking for 3D Polygons Using Multiresolution Wavelet Decomposition
,”
Proceedings of the Sixth IFIP WG 5.2 International Workshop on Geometric Modeling: Fundamentals and Applications (GEO-6)
, pp.
296
–
307
.
3.
Ohbuchi
,
R.
, and
Takahashi
,
S.
,
Miyazawa
,
T.
, and
Mukaiyama
,
A.
, 2001, “
Watermarking 3D Polygonal Meshes in the Mesh Spectral Domain
,”
GRIN’01: No Description on Graphics Interface 2001
, pp.
9
–
17
.
4.
Broomhead
,
S.
, and
King
,
P.
, 1986, “
Extracting Qualitative Dynamics from Experimental Data
,”
Physica D
0167-2789,
20
(
2–3
), pp.
217
–
236
.
5.
Elsner
,
J. B.
, and
Tsonis
,
A. A.
, 1996,
Singular Spectrum Analysis—A New Tool in Time Series Analysis
.
6.
Vautard
,
R.
,
Yiou
,
P.
, and
Ghil
,
M.
, 1992, “
Singular Spectrum Analysis: A Toolkit for Short Noisy Chaotic Signals
,”
Physica D
0167-2789,
58
, pp.
95
–
126
.
Crossref
Search ADS
 
7.
Murotani
,
K.
, and
Sugihara
,
K.
, 2004, “
Generalized SSA and Its Applications to Watermarking 3D Polygonal Meshes
,” METR METR 2004–17, pp.
1
–
23
.
8.
Murotani
,
K.
, and
Sugihara
,
K.
, 2004, “
Watermarking 3D Polygonal Meshes Using Generalized Singular Spectrum Analysis
,”
NICOGRAPH International Conference 2004 in Taiwan
, pp.
121
–
126
.
9.
Murotani
,
K.
, 2004, “
Spectral Decomposition Method for Three-Dimensional Shape Models and Its Applications (in Japanese)
,” Doctoral thesis, Information Science and Technology, University of Tokyo.
10.
Golyandina
,
N.
,
Nekrutkin
,
V.
, and
Zhigljavsky
,
A.
, 2001,
Analysis of Time Series Structure–SSA and Related Techniques
.
11.
Matsui
,
K.
, 1998,
Basic of watermarks (in Japanese)
.
12.
Praun
,
E.
,
Hoppe
,
H.
, and
Finkelstein
,
A.
, 1999, “
Robust Mesh Watermarking
,”
SIGGRAPH ’99: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques
, pp.
49
–
56
.
13.
Wagner
,
M. G.
, 2000, “
Robust Watermarking of Polygonal Meshes
,”
Proceedings of Geometric Modeling & Processing 2000
, pp.
201
–
208
.
14.
Yin
,
K.
,
Pan
,
Z.
,
Shi
,
J.
, and
Zhang
,
D.
, 1999, “
Robust Mesh Watermarking Based on Multiresolution Processing
,”
IEEE Comput. Graphics Appl.
0272-1716,
19
(
1
) pp.
36
–
45
.
Copyright © 2005
 by American Society of Mechanical Engineers
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