A Shape-from-shading Framework for Satisfying Data-closeness and Structure-preserving Smoothness Constraints

A key problem in shape-from-shading is how to simultaneously satisfy data-closeness and regularisation (such as surface smoothness) constraints. This paper makes two contributions towards solving this problem. The first is to describe a smoothness constraint which preserves surface structure by adaptively smoothing according to the intensity gradient magnitude. The second is to derive a framework which seeks to strictly satisfy this constraint while maintaining zero brightness error. Experimental results on both synthetic and real world imagery demonstrate that our method is both robust and accurate and outperforms a number of existing techniques. We propose an alternative regularisation constraint which employs information about the intensity gradient in all directions over a local neighbourhood. For a pixel (x,y), we define the local neighborhood as Ω(x,y)= {(x + 1,y),(x−1,y),(x,y + 1),(x,y−1)}. We precompute the change in incident angle between all pairs of neighboring pixels: