Efficient Regularization of Squared Curvature

TL;DR

This paper introduces an efficient integral geometry-based model for squared curvature regularization in computer vision, preserving details and structures while minimizing artifacts and computational costs.

Contribution

A novel squared curvature model based on line triple cliques that is efficiently minimized with high angular resolution using trust region optimization.

Findings

Accurate and visually pleasing results without artifacts

Efficient minimization at high angular resolutions

Reasonable computational run times

Abstract

Curvature has received increased attention as an important alternative to length based regularization in computer vision. In contrast to length, it preserves elongated structures and fine details. Existing approaches are either inefficient, or have low angular resolution and yield results with strong block artifacts. We derive a new model for computing squared curvature based on integral geometry. The model counts responses of straight line triple cliques. The corresponding energy decomposes into submodular and supermodular pairwise potentials. We show that this energy can be efficiently minimized even for high angular resolutions using the trust region framework. Our results confirm that we obtain accurate and visually pleasing solutions without strong artifacts at reasonable run times.