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# Variational methods in image processing Functionals Week 4 PowerPoint PPT Presentation

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

Variational methods in image processing Functionals Week 4

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## Variational methods in image processingFunctionalsWeek 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

• Spatial smoothness, e.g. total variation:

• Fidelity term (distance to input image):

### 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

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

### 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

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

• Model – energy to be minimized

• Euler-Lagrange

• Numerical implementation

• Matlab files and results