Shape from Texture Via Fourier Analysis

Many models and algorithms have been proposed since the shape from texture problem was tackled by the pioneering work of Gibson in 1950. In the present work, a general assumption of stochastic homogeneity is chosen so as to include a wide range of natural textures. Under this assumption, the Fourier transform of the image and a minimal set of Gabor filters are used to efficiently estimate all the main local spatial frequencies of the texture, i.e. so as to compute distortion measures. Then a known method which uses singular value decomposition to process the frequencies under orthographic projection is considered. The method is extended to general perspective cases and used to reconstruct the 3D shape of real pictures and video sequences. The robustness of the algorithm is proven on general shapes, and results are compared with the literature when possible.