Shape from Shading with Interreflections Under a Proximal Light Source: Distortion-Free Copying of an Unfolded Book

Abstract

We address the problem of recovering the 3D shape of an unfolded book surface from the shading information in a scanner image. This shape-from-shading problem in a real world environment is made difficult by a proximal, moving light source, interreflections, specular reflections, and a nonuniform albedo distribution. Taking all these factors into account, we formulate the problem as an iterative, non-linear optimization problem. Piecewise polynomial models of the 3D shape and albedo distribution are introduced to efficiently and stably compute the shape in practice. Finally, we propose a method to restore the distorted scanner image based on the reconstructed 3D shape. The image restoration experiments for real book surfaces demonstrate that much of the geometric and photometric distortions are removed by our method.