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<p><it>Abstract</it>—We present a non-feature-based solution to the problem of computing the shape of curved surfaces from texture information. First, the use of local spatial-frequency spectra and their moments to describe texture is discussed and motivated. A new, more accurate method for measuring the local spatial-frequency moments of an image texture using Gabor elementary functions and their derivatives is presented. Also described is a technique for separating shading from texture information, which makes the shape-from-texture algorithm robust to the shading effects found in real imagery. Second, a detailed model for the projection of local spectra and spectral moments of any surface reflectance patterns (not just textures) is developed. Third, the conditions under which the projection model can be solved for the orientation of the surface at each point are explored. Unlike earlier non-feature-based, curved surface shape-from-texture approaches, the assumption that the surface texture is isotropic is not required; surface texture homogeneity can be assumed instead. The algorithm’s ability to operate on anisotropic and non-deterministic textures, and on both smooth- and rough-textured surfaces, is demonstrated.</p>
Shape from texture, shape recovery, surface orientation, moments, wavelet, spatial frequency, Gabor functions, texture, projection.

A. C. Bovik and B. J. Super, "Shape from Texture Using Local Spectral Moments," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 17, no. , pp. 333-343, 1995.
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