Shape From Shading: A B-Splines Based Algorithm

In this paper, we propose a B-spline based approach to the "Shape from Shading " problem. Its basis lies in approximating a smooth surface by uniform bicubic B-spline basis functions. Since the surface normal in a patch is uniquely determined by heights of its sixteen neighbour vertices, the image brightness is directly related to the control vertices. The control vertices are then determined by minimising a cost functional corresponding to the squared brightness error, optimised by conjugate gradient method. The proposed algorithm does not require any integrability constraint or knowledge of boundary condition. Using several experiments with synthetic images, we demonstrate the performance of the algorithm.