Shape from Texture: General Principle.
MARYLAND UNIV COLLEGE PARK CENTER FOR AUTOMATION RESEARCH
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The 3D shape of a textured surface is recovered from its projected image on the assumption that the texture is homogeneously distributed. First, the homogeneity of a discrete texture consisting of dots and line segments is defined in terms of the theory of distributions. Next, distortion of the observed texture density due to perspective projection is described in terms of the first fundamental form, which is expressed with respect to the image coordinate system. Based on this result, the basic equations to determine the surface shape are derived for both planar and curved surfaces, and numerical schemes are proposed to solve them. Necessary data obtained in the form of summation or integration of functions over the texture elements on the image plane. Ambiguity in the interpretation of curved surfaces is also analyzed. Finally, numerical examples for synthetic data are presented, and our method is compared with other existing methods. It is shown that all other methods can be explained in terms of our formulation.
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