The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-110

“Direct Analytical Methods for Solving Poisson Equations in Computer Vision Problems”

by Tal Simchony and Rama Chellappa

July 1987

The need to solve one or more Poisson equation of the general form:

Du = f

arises in several computer vision problems such as enforcing integrability in shape from shading, the lightness and optical flow problems equations are iterative. In this paper we first discuss direct analytical methods for solving these equations on a rectangular domain. We then suggest some embedding techniques 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 resulting from the direct analytical methods for the computation of optical flow are also discussed. The algorithm resulting from the direct analytical methods for the computation of optical flow is new. A proof for the existence and convergence of the flow estimates is also given.

To download the report in PDF format click here: USC-SIPI-110.pdf (2.3Mb)