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Variational methods in image processing Segmentation I Week 8

Advanced Course 048926. Variational methods in image processing Segmentation I Week 8. Guy Gilboa. Mumford-Shah Functional. Minimizing an image + curve based (non-convex ) energy functional:. “u ≈ f” + ”u smooth, + ”curve C except on C” short”.

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Variational methods in image processing Segmentation I Week 8

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  1. Advanced Course 048926 Variational methods in image processingSegmentation IWeek 8 Guy Gilboa

  2. Mumford-Shah Functional Minimizing an image + curve based (non-convex) energy functional: “u ≈ f” + ”u smooth, + ”curve C except on C” short” f – original image, u – piece-wise smooth approx. of f separated by the contour – C Mumford, David, and Jayant Shah. "Optimal approximations by piecewise smooth functions and associated variational problems." Communications on pure and applied mathematics 42.5 (1989): 577-685.

  3. Segmentation of Brain Tumor using the Mumford-Shah functional http://www.youtube.com/watch?v=_ixLHcr8U-U

  4. Image approximation • Mumford-Shah functional for image approximation [Pock et al 2009]

  5. Segmentation Active contours (snakes) original (Kass et al): Emin(C)  “smooth”+”elastic”+”on edges” Evolving a curve like a rubber-band, with the aim to “close” on the object to be segmented, creating a continuous, smooth curve.

  6. Segmentation without edges: Chan-Vese Chan, Tony F., and Luminita A. Vese. "Active contours without edges." Image Processing, IEEE Transactions on 10.2 (2001): 266-277.

  7. Chan-Vese IPOL simulations http://www.ipol.im/pub/art/2012/g-cv/ By Pascal Getreuer.

  8. Image binarization Vertex penalizing functionals [Bredies-Pock-Wirth 2012]. K – is the number of orientations.

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