Unwrapping low-rank textures on generalized cylindrical surfaces

In this paper, we show how to reconstruct both 3D shape and 2D texture of a class of surfaces from a single perspective image. We consider the so-called the generalized cylindrical surfaces that are wrapped with low-rank textures. They can be used to model most curved building facades in urban areas or deformed book pages scanned for text recognition. Our method leverages on the recent new techniques for low-rank matrix recovery and sparse error correction and it generalizes existing techniques from planar surfaces to a much larger class of important 3D surfaces. As we will show with extensive simulations and experiments, the proposed algorithm can precisely rectify deformation of textures caused by both perspective projection and surface shape. It works for a wide range of symmetric or regular textures that are ubiquitous in images of urban environments, objects, or texts, and it is very robust to sparse occlusion, noise, and saturation.