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Variational methods in image processing Functionals Week 4

Advanced Course 048926. Variational methods in image processing Functionals Week 4. Guy Gilboa. Ex 1. Web info: http ://visl.technion.ac.il/~ gilboa/teaching/048926/. Modeling by Energies. Variational methods – optimize with respect to some energy E

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Variational methods in image processing Functionals Week 4

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  1. Advanced Course 048926 Variational methods in image processingFunctionalsWeek 4 Guy Gilboa

  2. Ex 1 • Web info: http://visl.technion.ac.il/~gilboa/teaching/048926/

  3. Modeling by Energies • Variational methods – optimize with respect to some energy E • Spatial smoothness, e.g. total variation: • Fidelity term (distance to input image):

  4. Link between TV and length Taken from http://hci.iwr.uni-heidelberg.de/Staff/bgoldlue/crvia_ws_2010/crvia_ws_2010_04_minimal_surfaces.pdf

  5. TV Denoising Taken from http://yosinski.com/mlss12/MLSS-2012-Bach-Learning-with-Submodular-Functions/

  6. TV-L1 – removing outliers Mila Nikolova. "A variational approach to remove outliers and impulse noise."Journal of Mathematical Imaging and Vision 20.1-2 (2004): 99-120.

  7. Highly missing information Recovering 70% salt & pepper noise by 2 steps: • Detecting corrupted pixels • Energy minimization based on “good pixels”. Original Input Mediean Chen-Wu Eng-Ma Variational [*] [*] Chan, Raymond H., Chung-Wa Ho, and Mila Nikolova. "Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization."Image Processing, IEEE Transactions on 14.10 (2005): 1479-1485.

  8. TV deconvolution • Model – energy to be minimized • Euler-Lagrange • Numerical implementation • Matlab files and results

  9. MRI Denoising video http://www.youtube.com/watch?v=MNMDtoY4jRQ

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