Shape from Texture of Developable Surfaces Via Fourier Analysis

Shape from texture has received much attention in the past few decades. We propose a computationally efficient method to extract the 3D shape of developable surfaces from the spectral variations of a visual texture. Under the assumption of homogeneity, the texture is represented by the novel method of identifying ridges of its Fourier transform. Local spatial frequencies are then computed using a minimal set of selected Gabor filters. In both orthographic and perspective projection cases, new geometric equations are presented to compute the shape of developable surfaces from frequencies. The results are validated with semi-synthetic and real pictures.