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   -> Volume 3, Issue 3


Preprint: Fast Surface Interpolation Using Wavelet Transform
 
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to u7811837@cc.nctu.edu.tw (Ming-Haw Yaou).
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PostPosted: Mon Dec 02, 2002 12:45 pm    
Subject: Preprint: Fast Surface Interpolation Using Wavelet Transform
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Preprint: Fast Surface Interpolation Using Wavelet Transform

Preprint of the following paper is availiable. If interested, please email
to u7811837@cc.nctu.edu.tw(Ming-Haw Yaou).

(Accepted by IEEE Trans. on PAMI 1993)

Fast Surface Interpolation Using Multi-Resolution Wavelet Transform

Ming-Haw Yaou and Wen-Thong Chang

Institute of Communication Engineering
Center for Telecommunication Research
National Chiao Tung University, Hsinchu, Taiwan, R.O.C

KEYWORDS: Surface Interpolation, Regularization, Discretization,
Wavelet transform, Basis transfer scheme, Preconditioning.

ABSTRACT:

Discrete formulation of the surface interpolation problem usually leads to a
large sparse linear equation system. Due to the poor convergence condition of
the equation system, the convergence rate of solving this problem with iterative
method is very slow. To improve this condition, a multi-resolution basis
transfer scheme based on the wavelet transform is proposed.
By applying the wavelet transform, the original interpolation basis is
transformed into two sets of bases with larger supports while the admissible
solution space remains unchanged. With this basis transfer, a new set of nodal
variables results and an equivalent equation system with better convergence
condition can be solved. The basis transfer can be easily implemented by using
an QMF matrix pair associated with the chosen interpolation basis. The
consequence of the basis transfer scheme can be regarded as a preconditioner to
the subsequent iterative computation method. The effect of the transfer
is that the interpolated surface is decomposed into its low frequency
and high frequency portions in the frequency domain.
It has been indicated that the convergence rate of the interpolated
surface is dominated by the low frequency portion. With this frequency domain
decomposition, the low frequency portion of the interpolated surface can be
emphasized. As compared with other acceleration methods, this basis transfer
scheme provides a more systematical approach for fast surface interpolation.
The easy implementation and high flexibility of the proposed algorithm also
make it applicable to various regularization problems.
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