DIRECT ANALYTICAL METHODS FOR SOLVING POISSON EQUATIONS IN COMPUTER VISION PROBLEMS.

The need to solve one or more Poisson equation of the general form: DELTA mu equals f arises in several computer vision problems, such as enforcing integrability in shape from shading, and the lightness and optical flow problems. Direct analytical methods for solving these equations on a rectangular domain are first discussed, then some embedding techniques are suggested that may be useful when boundary conditions (obtained from stereo, self shadowing and occluding boundary) are defined on arbitrary contours. The suggested algorithms are computationally efficient due to the use of fast orthogonal transforms. Application to lightness problems and optical flow are also discussed. A proof for the existence and convergence of the flow estimates is also given.