The radial basis functions are deformed by adjusting their centers, widths, and weights such that the intensity errors are minimized. The initial centers and widths are arranged hierarchically to speed up convergence and to stabilize the solution. Although the smoothness constraint is used, it can be eventually dropped out without causing instabilities in the solution. It is further demonstrated that even qualitative knowledge can be used in shape from shading to improve 3D reconstruction. Experimental comparisons of our method with several existing ones are made by using both synthetic and real images.
Results show that our solution is more accurate than the others.
Index Terms Shape from shading, radial basis functions, hierarchical structure, depth constraints, normals constraints, qualitative knowledge, stochastic gradient method. IEEE Transactions on Pattern Analysis and Machine Intelligence , Vol. Inc. All rights reserved.