In this talk, I will present a novel low dimensional manifold model for some image processing problem.
This model is based on the observation that for many natural images, the patch manifold usually has low dimension
structure. Then, we use the dimension of the patch manifold as a regularization to recover the original image.
Using some formula in differential geometry, this problem is reduced to solve Laplace-Beltrami equation on manifold.
The Laplace-Beltrami equation is solved by the point integral method. Numerical tests show that this method gives very good results in image inpainting, denoising and super-resolution problem.
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