Direct shape from shading with improved rate of convergence

摘要

In this paper, new direct shape from shading algorithms with improved rate of convergence for inclined and perpendicular light source are presented. The algorithms are mainly based on optimal dynamic system control with dynamic programming. Unlike the previous shading algorithms which first estimate the gradient of surface instead of depth using variational approaches, our algorithms provide a direct relative depth perception. Here the maximum uphill principle for inclined and perpendicular light source is derived instead of using the existing minimum downhill criteria in order to perceive the normal shape of the object. Also the convergence conditions for the algorithms are derived and proven under zero-initial condition. We show that the learning rate is linearly proportional to the minimum value of the input image in the discrete case. Furthermore, in order to increase the rate of convergence, the momentum factor is introduced.