Variational Methods for Normal Integration
This addresses the need for efficient normal integration in computer vision tasks like shape-from-shading and photometric stereo, representing an incremental improvement over existing methods.
The paper tackles the problem of integrating dense normal fields for computer vision applications by developing variational methods that handle non-rectangular domains, free boundaries, and depth discontinuities. It introduces a new discretization for quadratic integration and shows that discontinuity-preserving strategies based on Mumford-Shah segmentation and anisotropic diffusion are most effective for recovering discontinuities.
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.