  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.
