1. Variational methods in image processing Variational methods in image processing Week 2: Diffusion Guy Gilboa Advanced Course 049064

2. Diffusion in real life http://www.youtube.com/watch?v=STLAJH7_zkY

3. Scale Space for feature extraction

4. 1D zero-crossing evolution SignalZero crossing (edges) Time t

5. SIFT – use of scale space SIFT – use of scale space Scale-invariant feature transform

6. 6 Linear vs. Nonlinear diffusion Linear Nonlinear (Perona-Malik) Noisy input P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion”, IEEE Trans. PAMI, 12(7), pp. 629-639, 1990.

7. 7 Tensor diffusion coefficient D Weickert’s coherence enhancing flow: D is a 2x2 tensor (directional diffusion coefficient) with: ◦ Strong diffusion along the edge. ◦ Weak diffusion across the edge. J. Weickert, “Coherence-enhancing diffusion filtering”, IJCV Vol. 31, pp. 111-127, 1999.

8. Stereo H. Zimmer, A. Bruhn, L. Valgaerts, M. Breuß, J. Weickert, B. Rosenhahn, H.-P. Seidel: PDE-based anisotropic disparity-driven stereo vision. Vision, Modeling, and Visualization 2008. PDE formulation (with anisotropic diffusion smoothing), very similar to optical flow solutions:

9. Medical images 3D Ultrasound of 10 -week old human fetus [from http://www.mia.uni-saarland.de/weickert/demos.html ]http://www.mia.uni-saarland.de/weickert/demos.html

10. Guy Gilboa – course website Web info: Guy Gilboa website -> Teaching http://guygilboa.eew.tec hnion.ac.il/teaching// Then on course icon http://guygilboa.eew.technion.ac.il /teaching/variational-methods-in- image-processing-048926-2/