1. R-snakes Lyubomir Zagorchev, Ardeshir Goshtasby, Martin Satter Speaker: HongxingShi 2007.11.01 Image and Vision Computing 25 (2007) 945–959

2. Author Ardeshir Goshtasby · Postion Professor of Department of Computer Science and Engineering, Wright State University · Education B.E. Electronics Engineering, University of Tokyo M.S. Computer Science, University of Kentucky Ph.D. Computer Science, Michigan State University · Journal Special Issues Edited Pattern Recognition on Image Registration Computer Vision and Image Understanding Information Fusion on Image Fusion

3. Introduction and background What is snake? · An energy minimizing countours · Continuously deform to minimize its energy · Slither while deforming, like snake

5. Energy Contours Internal force · Constrain the smoothness of contours External force · Push the contours toward image features

6. Situations of curves’ definition Discrete Defined by a sequence of points Continuous Defined by a parametric curve, such as B-Splines, NURBS,RaG curves, and so on…

7. Energy definition Total energy Internal energy External energy

8. Compute From the calculas of variations, obtain: After discrezing….

9. Result The equations can be written where A is a pentadiagonal matrix.

10. B-snakes Definition Energy function

11. B-snakes Minimize the total energy Obtain

13. Rational Gaussian curves Definition Control points Blending functions

14. Rational Gaussian curves Where is the weight, and are standard deviation are nodes The blending function can be varied.

16. RaG curves are (a)0.05 (b)0.1 (c)0.15

17. Closed RaG curves Replaced the Gaussian function with are (a) 0.045 (b) 0.06 (c) 0.085

18. RaG snakes As the situation of discrete snakes: Let

19. RaG snakes Discrete, and obtain The extern energy

20. Synthetical images

24. Parameters in synthetic image

25. CT images

31. Parameters in CT images

32. Parameters analyse Standard deviation and the number of nodes n –bigger, smoother shapes –larger n,smoother shapes Experientially, we let

33. Standard deviations: (c)-(h)0.015, 0.025, 0.035, 0.045, 0.055, 0.065

37. Coarse-to-fine segmention How to select the n, number of nodes? –First, with a small n and a large, find a coarse boundary –Then, increase n until the finest resolution image is segmented

39. Conclusions Advantages over B-snakes –The stiffness can be varied to recover shapes containing smooth as well as detailed parts –The stiffness can be continuously varied to track a boundary from coarse to fine Disadvantage –Complexity

40. References [1] L Zagorchev, A Goshtasby, M Satter, R-snakes, Image and Vision Computing, 2007 [2] M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active contour models, International journal of computer vision. 321-331, 1988 [3] A. Goshtasby, Geometric modelling using rational Gaussian curves and surfaces, Computer Aided Design 27 (5) (1995) 363–375

41. Q&A