M. Clerc and S. Mallat, The Texture Gradient Equation for Recovering Shape from Texture, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 24, No. 4, April 2002, pp 536-549.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....this purpose. Key Words: Texture, orientation, wavelet, spectral energy, separable analysis, variance 1. Introduction In the field of computer vision and pattern recognition, the problem of extracting 3 D surface orientation from a monocular texture image has received a great deal of attention [1 3, 6, 7, 10, 11, 14 16, 18, 19]. If the surface exhibits a textured pattern, it is often easy for a human being to extract the structure information from the image. But the problem is ill posed for a machine to solve. This paper presents analytical expressions using separable 1 D analysis of 2 D images for extraction of surface ....

....surface orientation using spectral gradient, peaks and distortion. Most of the earlier work [1, 2, 6, 7, 18, 19] involved an exhaustive numerical search. Ribeiro and Hancock [14] uses the eigenstructure of an affine distortion matrix to extract orientation. The most recent work by Clerc and Mallat [3] uses Warplets (affine transformation of the mother wavelets) to recover shape using statistical estimates. Texture is realized as a stochastic process. Deformation gradient is estimated using the texture gradient equation which models the Warpogram (variance of the wavelet coefficients) of ....

M. Clerc and S. Mallat, The Texture Gradient Equation for Recovering Shape from Texture, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 24, No. 4, April 2002, pp 536-549.

....easier problem of recovering surface geometry for a specular surface of known reflectance under unknown real world illumination. If one thinks of real world illumination patterns as instances of a random process with known statistical properties, this problem parallels that of shape fromtexture [17, 62]. Its solution may exploit the analysis of Appendix C.1, which relates the local statistics of a surface image under real world illumination to its geometry as well as its reflectance. One rarely begins image analysis with an image segmented into surfaces of di#erent materials. Instead, one must ....

M. Clerc and S. Mallat. The texture gradient equation for recovering shape from texture. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(4):536--549, 2002.

....texture to be parallel transported on a surface, which appears restrictive, as discussed in [5] The thrust of this paper is to introduce a weak homogeneity condition, which is sucient for recovering shape from texture. Section II brie y summarizes recent Shape from Texture results from [3]. Section III explains the local attening of general, non developable surfaces, and provides the de nition of weak homogeneity, with some examples. II. Shape from Texture A. Imaging Model The goal of Shape from Texture is to estimate the shape of a textured surface from a perspective image ....

.... of position u: for k = 1; 2, wR (u; S) 0 : 6) Because of the deformation d(x) The warpograms of I and of R are related by a migration property: w I (u; J d (u) S) wR (d(u) S) 7) Di erentiating (7) with respect to u k , and using (6) one obtains the Texture Gradient Equation [3]: u; S) D k (u) s ij S i;j (u; S) 0 (8) where : denotes the inner product between two matrices A : B = X i;j=1 a ij b ij = T r(A B) Let us comment upon the Texture Gradient Equation: The partial derivatives uk and s ij of the warpogram with ....

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Clerc, M. and Mallat, S. (2002). The Texture Gradient Equation for Recovering Shape from Texture. IEEE Trans. Patt. Anal. and Mach. Intell. 24-4.

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