Discontinuity-Preserving Moving Least Squares Method

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.