Rational Spline Approach To Recover Shape From Shading

As a main research direction of computer vision, reconstructing the surface shape from the shading in a single image has shown its importance in the domain of engineering.A review of the methods in recent years comes first. Based on the substantial understanding of SFS problem, a systematic summary is made for all the current SFS algorithms in the world, that is, minimization approaches, propagation approaches, local approaches and linear approaches. With the different assumptions of the four algorithms, I have analyzed their applicability and compared them in terms of convergence rate, uniqueness and existence.The general SFS problem is obviously ill-posed. Regularization is, therefore, necessary for adding a priori constraint to make it well-posed. Thus, minimization approaches have been introduced and extensively discussed since the concept of SFS was proposed.Wedge function approach is used to solve shape from shading problem: removing the smoothness and integrability restrictions from the objective functional formulation, avoiding the influence of Lagrangian. With the application of minimization approaches and linear approaches, a reflectance map can be illustrated by the Wedge function. By doing Taylor expansion at the reference point and minimizing the energy function, the controlling coefficient will be obtained. Accuracy can be ensured by avoiding the use of these restrictions, but the rationality of the algorithm need to be proved through further study. The result of a tentative experiment shows the efficiency of this new approach.