The Computation of Visible-Surface Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
IEEE Transactions on Image Processing
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We present a discontinuity-preserving moving-least-squares (MLS) method with applications in curve and surface reconstruction, domain partitioning, and image restoration. The fundamental power of this strategy rests with the moving support domain selection for each data point from its neighbors and the associated notion of compactly supported weighting functions, and the inclusion of singular enhancement techniques aided by the data-dependent singularity detection. This general framework meshes well with the multi-scale concept, and can treat uniformly and non-uniformly distributed data in a consistent manner. In addition to the smooth approximation capability, which is essentially the basis of the emerging meshfree particle methods for numerical solutions of partial differential equations, MLS can also be used as a general numerical method for derivative evaluation on irregularly spaced points, which has a wide variety of important implications for computer vision problems.