Adaptive smoothing: a general tool for early vision

We present a method to smooth a signal-whether it is an intensity image, a range image or a planar curve-while preserving discontinuities. 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. The method is extremely attractive since edge detection can be performed after a few iterations, and features extracted from the smoothed signal are correctly localized. Hence no tracking is needed, as in Gaussian scale-space. This last property allows us to derive a new scale-space representation of a signal using the adaptive smoothing parameter k as the scale dimension. We then show how this process relates to anisotropic diffusion. When a large amount of smoothing is desired, we propose a multigrid implementation which reduces the computational time significantly. Given the local nature of the algorithm, we also propose a parallel implementation: the running time on a 16K Connection Machine is three orders of magnitude faster than on a serial machine. We then present several applications of adaptive smoothing: edge detection, range image feature extraction, comer detection, and stereo matching. Examples are given throughout the text using real images.