Ll. Kontsevich et al., RECONSTRUCTION OF SHAPE FROM SHADING IN COLOR IMAGES, Journal of the Optical Society of America. A, Optics, image science,and vision., 11(3), 1994, pp. 1047-1052
We propose a method for shape reconstruction from color shades produce
d by multiple chromatic light sources. The linear relation between sur
face-normal vectors and three-dimensional response vectors for a unifo
rmly colored and illuminated region of a surface can be reconstructed
in two steps. In the first step a quadratic form of metric in response
space induced from a natural metric in normal space is reconstructed.
At this stage proper image segmentation can be obtained. In the secon
d step an exact mapping from response space into the space of surface
normals is reconstructed. The matrix for this mapping is one of the sq
uare roots of the quadratic-form matrix that satisfies the integrabili
ty constraint. The method is in all respects much simpler than existin
g methods for solving the depth-from-shading task for monochromatic im
ages.