Fast surface interpolation using multiresolution wavelet transform
Ming-Haw Yaou
Wen-Thong Chang
Inst. of Commun. Eng., Nat. Chiao Tung Univ., Hsinchu;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Jul 1994
Volume: 16,
Issue: 7
On page(s): 673-688
ISSN: 0162-8828
References Cited: 40
CODEN: ITPIDJ
INSPEC Accession Number: 4742137
Digital Object Identifier: 10.1109/34.297948
Current Version Published: 2002-08-06
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 multiresolution 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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