Local interaction fields and adaptive regularizers for surface reconstruction and image relaxation

A set of novel local interaction fields associated with input point data and adaptive regularizers are introduced for some problems in image processing and early-middle vision. The local interaction field is used to take the place of the delta-error term in conventional approaches. It consists of two parts; one is the usual error term, the other is a window function whose shape, size and orientation can be adapted to local structures in specific applications. Unlike the usual delta-error term, local interaction fields favour local flatness and thus impose smoothing implicitly. Several adaptive regularizers are introduced to keep discontinuities while smoothing. In finding solutions, even the simplest gradient descent algorithm is efficient in many examples. The results are stable under varying parameters and quite robust against noise.