Computation of stereo disparity using regularization

The computation of stereo disparity is a mathematically ill-posed problem. However, using regularization theory it may be transformed into a well-posed problem. Standard regularization can be employed to solve ill-posed problems by using stabilizing functionals that impose global smoothness constraints on acceptable solutions. However, the presence of depth discontinuities causes serious difficulties in standard regularization, since smoothness assumptions do not hold across discontinuities. This paper presents a regularization approach to stereopsis based on controlled-continuity stabilizing functionals. These functionals provide a spatial control over smoothness, allowing the introduction of discontinuities into the solution. An iterative method for the computation of stereo disparity is derived, and the result of a computer simulation with a synthetic stereo pair of images is shown.