A Frequency-Domain Approach to Watermarking 3D Shapes by Ohbuchi, Mukaiyama, Takahashi

By Ohbuchi, Mukaiyama, Takahashi

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This analysis is based upon the following ideas. Selecting Subspaces Through the SVD Decomposition JuPP and YOZOFF (1975) introduced the idea of relevant and irrelevant parameters, based on Singular Value Decomposition linearized analysis. We first write the Taylor expansion of the misfit vector around a given point x: g(x + bx) = g(x) + J(x)bx + R(g, bx), ( 41) where J is the Jacobian (30) and R represents high order terms in the perturbation bx. From (32) we derive that the pseudoinverse of J can be written as: 378 V.

In any case, the most expensive part of the derivative calculation is by-passed when the expected outcome is zero, since that can be detected early on. In this way we do not prejudge the type of parameterization, and thus obtain a more general and simpler code. After all the rays have been calculated, we process the temporary compressed structure to determine which one of the original variables appears in at least one row of it. Those will be the variables that will be included in the final compressed matrix.

And MIRANKER, W. (1969), Chaotic Relaxation, Linear Alg. and App!. 2, 199 - 222. , A Practical Guide to Splines (Springer-Verlag, New York 1978). FAGIN, S. , Seismic Modeling of Geologic Structures (Geophysical Development Series, Society of Exploration Geophysicists, Tulsa 1991). , and MADARIAGA, R. (1988), Nonlinear Reflection Tomography, Geophysical Journal 95, 135 - 147. FAWCETI, J. D. Thesis, Caltech, Pasadena, CA 1983). , Propagation of Elastic Waves in Transversely Isotropic Media (Report CWP-074R, Colorado School of Mines, Golden, CO 1988).

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