  We introduce a variational method for multi-view shape-from-shading under
natural illumination. The key idea is to couple PDE-based solutions for
single-image based shape-from-shading problems across multiple images and
multiple color channels by means of a variational formulation. Rather than
alternatingly solving the individual SFS problems and optimizing the
consistency across images and channels which is known to lead to suboptimal
results, we propose an efficient solution of the coupled problem by means of an
ADMM algorithm. In numerous experiments on both simulated and real imagery, we
demonstrate that the proposed fusion of multiple-view reconstruction and
shape-from-shading provides highly accurate dense reconstructions without the
need to compute dense correspondences. With the proposed variational
integration across multiple views shape-from-shading techniques become
applicable to challenging real-world reconstruction problems, giving rise to
highly detailed geometry even in areas of smooth brightness variation and
lacking texture.
