Disparity and Optical Flow Partitioning Using Extended Potts Priors

TL;DR

This paper introduces new variational methods with Potts priors for disparity and optical flow partitioning, proving existence of solutions and demonstrating strong numerical performance.

Contribution

It develops a novel variational framework with Potts priors for disparity and optical flow partitioning, including convergence proofs and efficient algorithms.

Findings

Proved existence of global minimizers for the proposed models.

Developed an efficient alternating direction algorithm with convergence guarantees.

Numerical examples show high performance of the partitioning method.

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 notation of asymptotically level stable functions we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of minimizers. 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.