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Math 3360: Mathematical Imaging

Math 3360: Mathematical Imaging. Lecture 14: Illustration of Isotropic diffusion & Anisotropic diffusion Image denoising through energy minimization. Prof. Ronald Lok Ming Lui Department of Mathematics, The Chinese University of Hong Kong. Isotropic diffusion. Original image.

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Math 3360: Mathematical Imaging

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  1. Math 3360: Mathematical Imaging Lecture 14: Illustration of Isotropic diffusion & Anisotropic diffusion Image denoising through energy minimization Prof. Ronald Lok Ming LuiDepartment of Mathematics, The Chinese University of Hong Kong

  2. Isotropic diffusion Original image Sigma = 1.98 Sigma = 4.28 Sigma = 8.24

  3. Anisotropic diffusion

  4. Today we will look at: • Image denoising problem as energy minimization problem: • Fidelity term to find a denoised image, which is close to the input image; • Regularization term, which enhances the smoothness of the image. • Edge-preserving energy minimization problem: • Total variation model or Rudin, Osher, Fatemi (ROF) model • Minimize L1 norm of the gradient • TV minimization favors piecewise constant function = ideal for image • Minimization through a gradient descent algorithm • Boundary condition given by reflection. Image denoising through Energy Minimization

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