Regularization of discontinuous flow fields

Inverse problems in low-level vision tend to be ill-posed and smoothness assumptions (regularization) need to be made to obtain unique solutions that vary continuously as a function of the data. But the solution must not smooth over discontinuities in the image, and allowance must be made for the fact that the probability distributions of the smoothness measures are unknown. The authors apply the theory of robust statistics (M-statistics) to obtain a convex regularization that is also maximally robust against misspecification of the probability distribution of large jumps in the unknown. This theory is applied to the optical flow constraint, which is known to be noisy and inaccurate. The authors present some preliminary results showing that convex regularization theory seems to accurately preserve depth boundary information