Shape from periodic texture using the spectrogram

It is shown how local spatial image frequency is related to the surface normal of a textured surface. It is found 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. This relationship is used as the basis of an algorithm for finding surface normals of textured shapes using the spectrogram, which is one type of local spatial frequency representation. The relationship is validated by testing the algorithm on real textures. By analyzing shape and texture in terms of the local spatial frequency representation, the advantages of the representation for the shape-from-texture problem can be exploited. Specifically, the algorithm requires no feature detection and can give correct results even when the texture is aliased