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

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Presentation transcript:

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

Diffusion in real life

Scale Space for feature extraction

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

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

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 , 1990.

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 , 1999.

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 PDE formulation (with anisotropic diffusion smoothing), very similar to optical flow solutions:

Medical images 3D Ultrasound of 10 -week old human fetus [from ]

Guy Gilboa – course website Web info: Guy Gilboa website -> Teaching hnion.ac.il/teaching// Then on course icon /teaching/variational-methods-in- image-processing /