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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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Presentation Transcript
slide2
Ex 1
  • Web info:

http://visl.technion.ac.il/~gilboa/teaching/048926/

modeling by energies
Modeling by Energies
  • Variational methods – optimize with respect to some energy E
    • Spatial smoothness, e.g. total variation:
    • Fidelity term (distance to input image):
link between tv and length
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

tv denoising
TV Denoising

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

tv l1 removing outliers
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.

highly missing information
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.

tv deconvolution
TV deconvolution
  • Model – energy to be minimized
  • Euler-Lagrange
  • Numerical implementation
  • Matlab files and results
mri denoising video
MRI Denoising video

http://www.youtube.com/watch?v=MNMDtoY4jRQ