Shape From Bandwidth: Central Projection Case

Consider an unknown surface painted with a band-limited texture. We show that only the knowledge of the bandwidth of the texture is enough to estimate the shape of the surface from a single image taken by a camera. We model the problem as a central projection operation in 2D and propose a two step approach for finding the surface from the observed image. Our proposed algorithm first estimates the arc-length of the surface using the texture bandwidth and then reconstructs the surface from the estimated arc-length. We evaluate our algorithm with a simulation as well as real experiments.