Adaptive smoothing: a general tool for early vision

A method to smooth a signal while preserving discontinuities is presented. This is achieved by repeatedly convolving the signal with a very small averaging mask weighted by a measure of the signal continuity at each point. Edge detection can be performed after a few iterations, and features extracted from the smoothed signal are correctly localized (hence, no tracking is needed). This last property allows the derivation of a scale-space representation of a signal using the adaptive smoothing parameter k as the scale dimension. The relation of this process to anisotropic diffusion is shown. A scheme to preserve higher-order discontinuities and results on range images is proposed. Different implementations of adaptive smoothing are presented, first on a serial machine, for which a multigrid algorithm is proposed to speed up the smoothing effect, then on a single instruction multiple data (SIMD) parallel machine such as the Connection Machine. Various applications of adaptive smoothing such as edge detection, range image feature extraction, corner detection, and stereo matching are discussed