1. CS 641 Term project Level-set based segmentation algorithms Presented by- Karthik Alavala (under the guidance of Dr. Jundong Liu)

2. References Caselles Method V. Caselles, R. Kimmel, and G. Sapiro. Geodesic active contours. Int. J. of Computer Vision, volume 22, pp.61{79, 1997. Chan & Vese Method T. Chan and L. Vese. Active contours without edges. IEEE Trans. Image Process., volume 10, no.02, pp.266{277, 2001. Lankton Method S. Lankton and A. Tannenbaum. Localizing region-based active contours. IEEE Trans. Image Process., volume 17, no 11, pp.2029{2039, 2008. Li Method C. Li, C.-Y. Kao, J. C. Gore, and Z. Ding. Minimization of region-scalable tting energy for image segmentation. IEEE Trans. Image Process., volume 17, no.10, pp.1940{1949, 2008. Shi Method Y. Shi and W. C. Karl. A real-time algorithm for the approximation of level-set based curve evolution. IEEE Trans. Image Process., volume 17, no.05, pp.645{656, 2008.

3. Caselles Contour based method. – Motivated by curve evolution approach and not an energy minimization. Approach- deforming the initial contour Beta is set to zero

4. I(.) corresponds to the image intensity, (tow) is the parametric curve and G is a gaussian filter of variance 1.

5. g(I) is the stopping function. Goal of this function? Intensity obtained is a smoothed version. No regularization term Evolution equation: Speed of convergence can be varied. Last term is called “area constraint”.

7. Limitations Due to large variation of the gradient along the object boundaries and high noise in the image. The curve did not stop at the correct position and the tumor was detected. Remedy Incorporating prior information about the image quality(?) More stopping conditions.

9. CHAN- VESE Region based method. It tends to separate the image into two homogeneous region. Snake Model: Minimizing the above equation, we are trying to locate at maximum. This acts as an edge detector. Edge detector function:

10. Model: Fitting terms: Our motive is to minimize this term Energy criterion:

11. three blurred objectsdifferent objects from a noisy image

13. Limitations Examples of images for which the averages “inside” and “outside” the objects are the same. Remedy: Make use of prior information from the image.

14. Chunming Li Active contour model: This algorithm is a region based active contour model. Energy Criterion: Where I(y) is the image intensity at point x and can be controlled by Kernel function. Fitting functions: They optimally approximate the local image intensities.

15. Minimizing Energy function: To minimize the above function, its gradient flow is used as the level set evolution equation Properties: – This algorithms segments the whole image. – Works with different modalities. – The functions are marginally affected by the noise Results: – Emergence of new contours during the curve evolution. – Detection of interior boundaries

18. Limitations: – Not clear information about the region scalability. – This is a two phase model and cannot segment regions with multiple junctions. Results: Remedy: – Changing the local intensity fitting energy for ‘x’ number of disjoint regions. – Extracting as much as prior information about the image.

19. Lankton method Synthetic image of a blob with heterogeneous intensity on a background of similar heterogeneous intensity. (a) Initial contour. (b) Unsuccessful result of region-based segmentation. (c) Successful result of edge- based segmentation technique.

20. Energy criterion: B is a ball of radius r centered at point x Segmentations are not based on global region models, instead it is done locally. So, it allows to segment non homogeneous objects. Implementation: Energies are expressed in terms of a signed distance function (phi).

21. Evolution equation Here Au and Av are the area of the local interior and local exterior regions

22. Comparison of global vs local. Advantages: – Comparison with global energies – Multiple interacting contours – Analyzing the localization radius

24. Limitations: – Sensitivity to Initialization ( localized contour may not use enough information). Remedy: - Extreme care should be taken while initializing the contour.

25. Shi Curve evolution: Powerful technique in many image and video analysis problems. Fast algorithm based on the approximation of level-set based curve evolution. Piecewise constant function

26. Curve evolution equation: Curve evolution process: F = F (d) + F (int) – curve evolve using the data attachment term F (d) – smoothness term F (int)

28. Limitations: It needs to maintain the level-set function as a signed distance function, which is computationally expensive.

29. Thank you..