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.>

The authors present a method to smooth a signal-whether it is an intensity image, a range image, or a contour-which preserves discontinuities and thus facilitates their detection. This is achieved by repeatedly convolving the signal with a very small averaging filter modulated by a measure of the signal discontinuity at each point. This process is related to the anisotropic diffusion reported by P. Perona and J. Malik (1987) but it has a much simpler formulation and is not subject to instability or divergence. Real examples show how this approach can be applied to the smoothing of various types of signals. The detected features do not move, and thus no tracking is needed. The last property makes it possible to derive a novel scale-space representation of a signal using a small number of scales. Finally, this process is easily implemented on parallel architectures: the running time on a 16 K connection machine is three orders of magnitude faster than on a serial machine.>

A method to detect, locate, and estimate edges in a one-dimensional signal is presented. It is inherently more accurate than all previous schemes as it explicitly models and corrects interaction between nearby edges. The method is iterative with initial estimation of edges provided by the zero crossings of the signal convolved with Laplacian of Gaussian (LoG) filter. The necessary computations necessitate knowledge of this convolved output only in a neighborhood around each zero crossing and in most cases, could be performed locally by independent parallel processors. Results on one-dimensional slices extracted from real images, and on images which have been proposed independently in the row and column directions are shown. An analysis of the method is provided including issues of complexity and convergence, and directions of future research are outlined.>

We present a technique for computing the convolution of an image with LoG (Laplacian-of-Gaussian) masks. It is well known that a LoG of variance a can be decomposed as a Gaussian mask and a LoG of variance a1 < a. We take advantage of the specific spectral characteristics of these filters in our computation: the LoG is a bandpass filter; we can therefore fold the spectrum of the image (after low pass filtering) without loss of information, which is equivalent to reducing the resolution. We present a complete evaluation of the parameters involved, together with a complexity analysis that leads to the paradoxical result that the computation time decreases when a increases. We illustrate the method on two images.