Reconstruction of shape from shading in color images

We propose a method for shape reconstruction from color shades produced by multiple chromatic light sources. The linear relation between surface-normal vectors and three-dimensional response vectors for a uniformly 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 second step an exact mapping from response space into the space of surface normals is reconstructed. The matrix for this mapping is one of the square roots of the quadratic-form matrix that satisfies the integrability constraint. The method is in all respects much simpler than existing methods for solving the depth-from-shading task for monochromatic images.