  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.
