Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the multi-level splitting of finite element spaces
Numerische Mathematik
Image Analysis Using Multigrid Relaxation Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using disparity functional for stereo correspondence and surface reconstruction
Computer Vision, Graphics, and Image Processing
The Computation of Visible-Surface Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surfaces from Stereo: Integrating Feature Matching, Disparity Estimation, and Contour Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Surface Interpolation Using Hierarchical Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Iterative methods for large linear systems
Iterative methods for large linear systems
Wavelet methods for fast resolution of elliptic problems
SIAM Journal on Numerical Analysis
An introduction to wavelets
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
Interpolation Using Wavelet Bases
IEEE Transactions on Pattern Analysis and Machine Intelligence
Vision: A Computational Investigation into the Human Representation and Processing of Visual Information
Physically Based Adaptive Preconditioning for Early Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Fast Gibbs Sampler for Synthesizing Constrained Fractals
IEEE Transactions on Visualization and Computer Graphics
Feature Enhancement in Low Quality Images with Application to Echocardiography
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
Locally adapted hierarchical basis preconditioning
ACM SIGGRAPH 2006 Papers
Edge-Preserving Image Reconstruction with Wavelet-Domain Edge Continuation
ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
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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.