Total variation on a tree

TL;DR

This paper introduces fast dynamic programming algorithms for minimizing total variation on trees, applicable to image processing and vision, with improved complexity and parallelism over existing methods.

Contribution

It develops efficient algorithms for total variation minimization on trees, handling convex and non-convex cases, with applications to image processing and vision.

Findings

Algorithms are faster and more memory-efficient than existing methods.

Applicable to 2D image processing and computer vision tasks.

Offer high parallelism and improved worst-case complexity.

Abstract

We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the non-convex case and derive worst case complexities that are equal or better than existing methods. We show applications to total variation based 2D image processing and computer vision problems based on a Lagrangian decomposition approach. The resulting algorithms are very efficient, offer a high degree of parallelism and come along with memory requirements which are only in the order of the number of image pixels.