Fast and Accurate Surface Normal Integration on Non-Rectangular Domains

TL;DR

This paper introduces a fast, accurate, and robust surface normal integration method for non-rectangular domains, combining classical Poisson models with modern iterative solvers and preconditioning, validated on real-world datasets.

Contribution

It presents a novel integration framework that unites classical Poisson models with Krylov subspace solvers, optimized by preconditioning and fast marching initialisation, for improved accuracy and efficiency on complex domains.

Findings

Efficient solver with high accuracy on non-trivial domains

Preconditioning significantly accelerates convergence

Effective on real-world photometric stereo data

Abstract

The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However, even nowadays it is still a challenging task to devise a method that combines the flexibility to work on non-trivial computational domains with high accuracy, robustness and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques we construct a solver that fulfils these requirements. Building upon the Poisson integration model we propose to use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with a suitable numerical preconditioning and a problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for our purpose. To address the issue of a suitable initialisation we propose to compute this initial state via a recently developed fast marching integrator. Detailed numerical experiments illuminate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.