Disparity and optical flow partitioning using extended Potts priors

Abstract

This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notion of asymptotically level stable (als) functions, we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of multipliers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method.

Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation

“…Optimisation algorithms. There are many convex minimisation methods that can be used to solve the MAP estimation problems with form (3) efficiently, such as forward-backward splitting, Douglas-Rachford splitting, primal-dual, or alternating direction method of multipliers (see [10], [20], [21] and references therein for more detail). Furthermore, algorithmic structures that allow computations to be highly distributed and parallelised have also been developed, see e.g.…”

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