Abstract

We show how local spatial image frequency is related to the surface normal of a textured surface. We find that the Fourier power spectra of any two similarly textured patches on a plane are approximately related to each other by an affine transformation. The transformation parameters are a function of the plane’s surface normal. We use this relationship as the basis of a new algorithm for finding surface normal of textured shapes using the spectrogram, which is one type of local spatial frequency representation. We validate the relationship by testing the algorithm on real textures. By analyzing shape and texture in terms of the local spatial frequency representation, we can exploit the advantages of the representation for the shape-from-texture problem. Specifically, our algorithm requires no feature detection and can give correct results even when the texture is aliased.