On obtaining shape from color shading

Color and Grassmann-Cayley Coordinates of Shape are considered in this article. The image irradiance equation for colored surfaces and the Grassman manifold λ of orbits Q = {B · h + c; detB ≠ 0} Where c is a vector sweeping the color space H, B is a 3 × 3 matrix, and h(x, y) is the color image of a Lambertian surface assumed to be a linear vector-function of the normal vectors. Different orbits Q(n) correspond to different shapes but they are invariant under color and illuminant transformation. Coordinates of an orbit Q in λ can be computed as 3 × 3 (2 × 2, sometimes) determining the elements of which are values of some linear functionals (receptive fields) of h(x, y). Based on the approach, a shape-from-shading algorithm was developed and successfully tested on the threeband color images of various real objects (an egg, cylinders and cones made of paper, etc.). © 1993 John Wiley & Sons, Inc.