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Medical Image Segmentation: Beyond Level Sets (Ismails part) 1 Slide 2 Basics of Level Sets (Ismail) 14 Slide 3 Active Curves 1 Slide 4 1 S S Slide 5 Gradient Descent (1) 2 Functional derivative Regional terms of the form Slide 6 Gradient Descent (2) 3 E S E S - S = tt E S E S Slide 7 Gradient Descent (2) 3 E S E S - E S E S - S = tt E S E S Slide 8 Gradient Descent (2) 3 E S E S - E S E S - S = tt E S E S Slide 9 Standard boundary terms: Geodesic Active Contours 4 e.g., Caselles et al., 97 Slide 10 5 Standard boundary terms: General derivative with E-L equations Slide 11 5 1 Boundary length Standard boundary terms: General derivative with E-L equations Slide 12 5 Standard boundary terms: General derivative with E-L equations Depends on image gradient Attracts curve to strong edges Slide 13 5 Standard boundary terms: General derivative with E-L equations Depends on image gradient Attracts curve to strong edges Slide 14 6 Standard region terms: Piecewise constant case e.g., Chan and et Vese, 01 Slide 15 6 Standard region terms: Piecewise constant case e.g., Chan and et Vese, 01 Alternate minimization (1) Fix parameters and evolve the curve (2) Fix curve, optimize w.r.t parameters Slide 16 7 Standard region terms: Log-Likelihood Slide 17 7 Standard region terms: Log-Likelihood Distributions fixed by prior learning e.g., Paragios and Dercihe, 02 Slide 18 7 Standard region terms: Log-Likelihood Distributions updated iteratively e.g., Gaussian: Rousson and Deriche 02 Gamma: Ben Ayed et al., 05 Slide 19 Functional derivatives for region terms (E-L equations and Greens theorem) 8 See Zhu and Yuille, 96 Mitiche and Ben Ayed, 11 Slide 20 8 Curve flow in the log-likelihood case S Functional derivatives for region terms (E-L equations and Greens theorem) See Zhu and Yuille, 96 Mitiche and Ben Ayed, 11 Slide 21 8 >0 Curve flow in the log-likelihood case S Functional derivatives for region terms (E-L equations and Greens theorem) Slide 22 8