Direct Computation of Depth from Shading for Perspective Projection

We present a method for recovering shape from shading in which the surface depth is directly computed. The already proposed method solving the same problem assumes that images are captured under the parallel projection, and hence, it can be correctly used only for the relative thin objects compared with the distance from the camera. If this method is formally extended for the perspective projection completely, the complicated calculations for differential are required. This gives rise to unstable recovery. In this study, we examine an extension of this method so as to treat the perspective projection approximately. In order to keep the simplicity of the original method, we propose the simple approximation of the derivative of the surface with respect to the image coordinate.