@article{Bähr2017, 
author = {Martin Bähr and Michael Breuß and Yvain Quéau and Ali Sharifi Boroujerdi and Jean-Denis Durou},
title = {Fast and accurate surface normal integration on non-rectangular domains},
year = {2017},
journal = {Computational Visual Media},
volume = {3},
number = {2},
pages = {107-129},
keywords = {surface normal integration, Poisson integration, conjugate gradient method, preconditioning, fast marching method, Krylov subspace methods, photometric stereo, 3D reconstruction},
url = {https://www.sciopen.com/article/10.1007/s41095-016-0075-z},
doi = {10.1007/s41095-016-0075-z},
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 is flexible enough 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 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 suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose. To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate 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.}
}