Novel variational approach for the perspective shape from shading problem using calibrated images

In this paper, We propose a new approach for solving the Lambertian shape from shading (SFS) problem. The proposed technique employs image information as well as camera calibration parameters. We claim that the incorporation of camera parameters results in a better surface reconstruction. In this work, we slightly modify this more realistic model in order to take into account the attenuation of the illumination due to distance. We propose a new variational formulation that relates an evolving surface model with image information, taking into consideration that the image is taken by a perspective camera with known parameters. A new energy functional is formulated to incorporate brightness, smoothness, and integrability constraints. All of these terms assume a hyper surface that evolves in time to meet their criteria. Gradient descent optimization with Euler-Lagrange is used for optimization. We constructed a database of real surfaces as a ground-truth for the experiments. The proposed approach shows superior performance when compared with other approaches in the literature.