Shape from Texture
In Sect. 2.7, we gave an analysis of the shape-from-texture problem. There, we assumed that the “texture density” was somehow observed on the image plane. Then, we showed that the surface parameters were computed in an analytically closed form in terms of invariants. We also studied the ambiguity in interpretation of the surface shape. In this chapter, we give a rigorous mathematical treatment for characterizing discrete textures. In particular, we give precise definitions of texture density and homogeneity in terms of the theory of distributions and differential geometry. Then, we present numerical schemes for solving the resulting 3D recovery equations. We also give some numerical examples for synthetic data.
KeywordsLine Segment Image Plane Planar Surface Fundamental Form Surface Equation
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