2016/10/19 by Martin Bähr, Bähr, Martin, Michael Breuß +7
Computer Science · Engineering · #3D Shape Modeling and Analysis #68U10 #Advanced Vision and Imaging #Computer Graphics and Visualization Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1610.06049
openalex publication_date 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.