Variational Methods for Normal Integration

TL;DR

This paper explores variational methods for normal integration in computer vision, focusing on handling non-rectangular domains, free boundaries, and depth discontinuities with new discretization and segmentation strategies.

Contribution

Introduces a new discretization for quadratic integration and compares discontinuity-preserving strategies inspired by segmentation and diffusion methods.

Findings

New discretization ensures fast recovery and handles non-rectangular domains.

Discontinuity-preserving strategies effectively recover depth discontinuities.

Segmentation-based methods outperform others in preserving scene boundaries.

Abstract

The need for an efficient method of integration of a dense normal field is inspired by several computer vision tasks, such as shape-from-shading, photometric stereo, deflectometry, etc. Inspired by edge-preserving methods from image processing, we study in this paper several variational approaches for normal integration, with a focus on non-rectangular domains, free boundary and depth discontinuities. We first introduce a new discretization for quadratic integration, which is designed to ensure both fast recovery and the ability to handle non-rectangular domains with a free boundary. Yet, with this solver, discontinuous surfaces can be handled only if the scene is first segmented into pieces without discontinuity. Hence, we then discuss several discontinuity-preserving strategies. Those inspired, respectively, by the Mumford-Shah segmentation method and by anisotropic diffusion, are shown to be the most effective for recovering discontinuities.