Surface Reconstruction and Discontinuity Detection: A Fast Hierarchical Approach on a Two-Dimensional Mesh

Recently multigrid techniques have been proposed for solving low-level vision problems in optimal time (i.e. time proportional to the number of pixels). In the present work this method is extended to incorporate a discontinuity detection process cooperating with the smoothing phase on all scales. Activation of line element detectors that signal the presence of relevant discontinuities is based on information gathered from neighboring points at the same and different scales. Because the required computation is local, parallelism can be profitably used. A mapping of the required data structure onto a two dimensional mesh of processors is suggested. Domain decomposition is shown to be efficient on MIMD computers capable of containing many individual cells in each processor. Some examples of the proposed multiscale solution techniques are shown for two different applications. In the first case a surface is reconstructed from first derivative information (extracted from the intensity data), in the second case from noisy depth constraints.