Fast algorithms for low-level vision

A recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing, performing the first and second directional derivatives, and carrying out the Laplacian of an image. These operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered. The key to the approach is, first, the use of an exponentially based filter family and, second, the use of the recursive filtering. Applications to edge detection problems and multiresolution techniques are considered, and an edge detector allowing the extraction of zero-crossings of an image with only 14 operations per output element at any resolution is proposed. Various experimental results are shown.>