Shape from Shading Based on Lax-Friedrichs Fast Sweeping and Regularization Techniques With Applications to Document Image Restoration

In this paper, we describe a 2-pass iterative scheme to solve the general partial differential equation (PDE) related to the Shape-from-Shading (SFS) problem under both distant and close point light sources. In particular, we discuss its applications in restoring warped document images that often appear in the daily snapshots. The proposed method consists of two steps. First the image irradiance equation is formulated as a static Hamilton-Jacobi (HJ) equation and solved using a fast sweeping strategy with Lax-Friedrichs Hamiltonian. However, abrupt errors may arise when applying to real document images due to noises in the approximated shading image. To reduce the noise sensitivity, a minimization method thus follows to smooth out the abrupt ridges in the initial result and produce a better reconstruction. Experiments on synthetic surfaces show promising results comparing to the ground truth data. Moreover, a general framework is developed, which demonstrates that the SFS method can help to remove both geometric and photometric distortions in warped document images for better visual appearance and higher recognition rate.