1. Particle Filtering for Symmetry Detection and Segmentation Pramod Vemulapalli

2. Outline Previous Work Introduction Problem Statement Particle Filtering -- Idea Problem Formulation Results Conclusions

3. Previous Work Tyng-Luh Liu; Geiger, D.; Yuille, A.L., "Segmenting by seeking the symmetry axis," Pattern Recognition, 1998. Proceedings. Fourteenth International Conference on, vol.2, no., pp.994- 998 vol.2, 16-20 Aug 1998 T. Riklin Raviv, N. Kiryati and N. Sochen, “Segmentation by Level Sets and Symmetry,” Proc. IEEE CS Conf. Computer Vision and Pattern Recognition (CVPR "06), June 2006.

4. Introduction Loy & Eklundh’s SIFT Based Symmetry Detection Step 1: Obtain the SIFT Features G. Loy and J.-O. Eklundh. Detecting symmetry and symmetric constellations of features. In ECCV, 2006.

5. Introduction Loy & Eklundh’s SIFT Based Symmetry Detection Step 2: Obtain prospective matches G. Loy and J.-O. Eklundh. Detecting symmetry and symmetric constellations of features. In ECCV, 2006.

6. Introduction Loy & Eklundh’s SIFT Based Symmetry Detection Step 3: Eliminate based on scale and orientation G. Loy and J.-O. Eklundh. Detecting symmetry and symmetric constellations of features. In ECCV, 2006.

7. Introduction Loy & Eklundh’s SIFT Based Symmetry Detection Step 4: Obtain Reflection Axes from Hough Space G. Loy and J.-O. Eklundh. Detecting symmetry and symmetric constellations of features. In ECCV, 2006.

8. Problem StatementP1 How to improve the support region for symmetry hypothesis Consequences ▫Lesser False Positives ▫Easier Segmentation 1 ▫Better Recognition 1. Shi, J., & Malik, J. (1997). Normalized cuts and image segmentation. IEEE Conf. Computer Vision and Pattern Recognition (pp. 731–737).

9. Problem StatementP1 G. Loy and J.-O. Eklundh. Detecting symmetry and symmetric constellations of features. In ECCV, 2006. Increase the number of hypothesis 1510

10. Theory Sequential Importance Sampling ▫Particle Filtering 1 ▫Bootstrap Filtering ▫Condensation Algorithm 2 ▫Survival of the Fittest General Idea ▫Importance Sampling on time series data ▫Weights updated at each step 1.C.T. Kwok, D. Fox, and M. Meila. Adaptive real-time particle filters for robot localization. In Proceedings of the 2003 IEEE International Conference on Robotics Automation (ICRA ’03), Taipei, Taiwan, September 2003. 2.M.W. Lee, I. Cohen, and S.K. Jung. Particle Filter with Analytical Inference for Human Body Tracking. In IEEE Workshop on Motion and Video Computing, 2002.

11. Theory – Particle Filters in Robotics Source: http://www.cs.washington.edu/ai/Mobile_Robotics/mcl/

12. Theory - Particle Filter Weight the particles depending on the distance from the position Start with a set of particles Resample the Particles Estimate the new position

13. Problem Formulation Looking at the search space ▫Given ‘n’ particles the number of pairs that can be formed are n c 2 = n(n-1)/2 ▫Given ‘a’ particle pairs the number of possible combinations that can be included in the final object are a! or factorial(a) Search Space is huge ▫Search space can be considerably reduced by intuition ▫Particle Filtering helps formulate these intuitive notions 1.Arulampalam, M.S.; Maskell, S.; Gordon, N.; Clapp, T., "A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking," Signal Processing, IEEE Transactions on, vol.50, no.2, pp.174-188, Feb 2002 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=978374&isnumber=21093http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=978374&isnumber=21093

14. Problem Formulation Given a hypothesis ▫Search around the initial hypothesis Weight the results from the search process ▫Continue search around points with more weight End the search process when particle weight drops below a given threshold

15. Particle Filtering : Step 1 Start with the Initial Hypothesis 1. Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Transactions on Mathematical Software, Vol. 22, No. 4, Dec. 1996, p. 469-483.

16. Particle Filtering – Step 2 Search around the initial hypothesis

17. Particle Filtering – Step 3 Weight the Child Particles 1.Arulampalam, M.S.; Maskell, S.; Gordon, N.; Clapp, T., "A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking," Signal Processing, IEEE Transactions on, vol.50, no.2, pp.174-188, Feb 2002 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=978374&isnumber=21093http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=978374&isnumber=21093 Feature Descriptor Match Angular Deformation Distance Deformation

18. Particle Filtering – Step 4 Continue the Propagation 1.Arulampalam, M.S.; Maskell, S.; Gordon, N.; Clapp, T., "A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking," Signal Processing, IEEE Transactions on, vol.50, no.2, pp.174-188, Feb 2002 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=978374&isnumber=21093http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=978374&isnumber=21093

19. Particle Filtering – Video

20. Final Results

22. Performance – Under Stress With large number of features

23. Performance – Under Stress With a sparse feature set

24. Conclusions & Future Work Restricted and Effective search to improve region of support Can be extended to rotational symmetry Computationally efficient Performance can be improved by considering different weighting functions or by combining SIFT with other features

25. Questions ?