1. Local or Global Minima: Flexible Dual-Front Active Contours Hua Li Anthony Yezzi

2. Outline Introduction Introduction Dual-Front Active Contours Dual-Front Active Contours Properties of Dual-Front Active Contours Properties of Dual-Front Active Contours Comparison With Other Boundary Extraction Methods and Experimental Results Comparison With Other Boundary Extraction Methods and Experimental Results

3. Introduction Original snake model Original snake model 1. P(C) is a potential which depends upon some desirable image feature. desirable image feature. 2. internal forces which control the regularity on curve C while the potential P attracts the curve C while the potential P attracts the curve C toward the desired boundary. curve C toward the desired boundary.

4. defect ： 1. snakes approach the nearest local minimum of the initial contour 2. difficult to extend the approach to segment 3D objects

5. Flexible Dual-Front Active Contours Flexible Dual-Front Active Contours we propose a novel, fast and flexible dual front we propose a novel, fast and flexible dual front implementation of active contours motivated by implementation of active contours motivated by 1. minimal path techniques 2. utilizing fast sweeping algorithms

6. Dual-Front Active Contours background-Minimal Path Technique background-Minimal Path Technique

7. background-Minimal Path Technique  a boundary extraction approach which detects the global minimum of a contour energy between two points the global minimum of a contour energy between two points  Thereby avoiding local minima arising from the sensitivity to initializations in snakes

8.  Energy minimization model 1. s represents the arc-length parameter, i.e i.e 2.. 3. E(C) includes the internal regularization energy in potential P, and controls the smoothness of in potential P, and controls the smoothness of curve C using P and w > 0. curve C using P and w > 0.

9.  Minimal action map model 1. corresponds to the minimal energy integrated along a path starting from point p0 integrated along a path starting from point p0 to point p. to point p. 2. sliding back from point p to point p0 on this action map according to the gradient action map according to the gradient descent. descent. 3..

10.  Minimal Action Level Sets Evolution 1. is the normal to the closed curve 2. ‘ low cost ’ area the velocity is high while at a ‘ high cost ’ area the velocity is low a ‘ high cost ’ area the velocity is low 3..

12. Principle of Dual-Front Active Contours Principle of Dual-Front Active Contours  We choose a set of points Xi from R0 and another set of points Xj from R1  define two minimal action maps  All points satisfying,form a partition boundary

14.  Summarized in following steps

15. Comments Comments  Two ways to decide the labels of the separated boundaries in Step 2 1. the labels may be reset in each iteration loop. 2. In each iteration loop, the labels of the separated boundaries of the new active region are decided by the result from the previous iteration iteration

16. Properties of Dual-Front Active Contours Flexible Local or Global Minima Flexible Local or Global Minima Numerical Implementation Numerical Implementation Evolution Potentials Evolution Potentials Simple Regularization Terms Simple Regularization Terms Automatic Evolution Convergence Automatic Evolution Convergence

17. Flexible Local or Global Minima Flexible Local or Global Minima  size and shape of active regions affects final segmentation results segmentation results  Use morphological dilation and erosion to generate an active region around the current curve.  when an initial curve is far from the desired object, we may first use wider active regions  when curve nears the desired boundary, we may use narrower active regions

19. Numerical Implementation Numerical Implementation

20. Evolution Potentials Evolution Potentials

21. Simple Regularization Terms Simple Regularization Terms 1..

22. 2. Smoothing the original images  using isotropic nonlinear diffusion operator to smoothing the original images

23. Automatic Evolution Convergence Automatic Evolution Convergence 1. 1.  an automatic stopping criterion in each iteration.  initial contours are classified into multiple groups, all contours evolute simultaneously but based on different potentials.  two contours from the same group meet, they merge into a single contour  two contours from different groups meet, both contours stop evolving and a common boundary is formed by the meeting points automatically

24. 2. 2.  when current global minimum partition curve is the same as that of last iteration or the difference between them is less than a predefined tolerance, the procedure may be stopped.

25. Comparison With Other Boundary Extraction Methods and Experimental Results comparison comparison

28. results results

32. The End Thanks to everyone