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Defocus can be modeled as a diffusion process and represented mathematically using the heat equation, where image blur corresponds to the diffusion of heat. This analogy can be extended to non-planar scenes by allowing a space-varying diffusion coefficient. The inverse problem of reconstructing 3-D structure from blurred images corresponds to an “inverse diffusion” that is notoriously ill-posed. We show how to bypass this problem by using the notion of relative blur. Given two images, within each neighborhood, the amount of diffusion necessary to transform the sharper image into the blurrier one depends on the depth of the scene. This can be used to devise a global algorithm to estimate the depth profile of the scene without recovering the deblurred image, using only forward diffusion.
Shape, Reconstruction, Depth cues, Gradient methods, Iterative methods, Partial differential equations, Inverse problems, Sharpening and Deblurring

M. Burger, S. J. Osher, S. Soatto and P. Favaro, "Shape from Defocus via Diffusion," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 30, no. , pp. 518-531, 2007.
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