1. A Local Descriptor for Finding Corresponding Points in Vector Fields Liefei Xu and H. Quynh Dinh Dept of Computer Science Stevens Institute of Technology ICPR 2008 Tampa, Florida

2. Outline Examples of Vector Fields Related Work Vector Spin Image Results Tracking Example Summary

3. Vector Fields Examples Video AnalysisWeather Monitoring From Center for Maritime Systems at Stevens Inst. of Tech. Simulation of water current in the New York Harbor Region. Computational Fluid Dynamics Visualization of the flow inside a diesel engine. [Image courtesy of Laramee et al. 04, Chen et al. 07]

4. Related Work Vector Field Analysis – Singularity classification [Helman & Hesselink 90, Scheuermann et al. 98, Tricoche et al. 01, Zhang et al. 06] – Comparing Vector Fields [Lavin et al. 98, Tovar 98, Theisel &Weinkauf 02, Ebling et al. 03] Shape Matching – Global geometric distributions [Ankerst et al. 99, Osada et al. 02] – Local geometric distributions [Johnson and Hebert 99, Belongie et al. 02, Frome et al. 04]

5. Local Descriptor for 3D Shapes – Spin Image  (radial) values  (depth) values spin-images [Johnson & Hebert 99]

6. Local Descriptor for Vector Fields – Vector Spin Image [Frome et al. 04] Distribution of  and  values  values (radius)  values few many Vector Field  vector dot product test pt  neighbor

7. Comparing Vector Spin Images - χ 2 statistical distance different similar

8. Vector Spin Image: Boundary Issue vector fieldboundary problemVector field reflected around edges and normalized different similar Solved by Reflection

9. Vector Spin Image: Radius of Support vector field 512 X 512 r min = 5 r max = 60 r min = 3 r max = 40 r min = 2 r max = 20 different similar Larger radius, more discriminating

10. Vector Spin Image: Resolution vector field # of bins (r X dot) 10 X 10 5 X 5 5 X 10 different similar Dot-product is the key dimension

11. Identify Features different similar

12. Test on Real Vector Fields x x

13. Timing Computation of vector spin images – 57 microsecs for each point for r max =60 – 7 microsecs for each point for r max =20 Computation of χ 2 statistical distance – < 1 second (262144 comparisons)

14. Application - Tracking x 10% 50% 100% [Image courtesy of Laramee et al. 04, Chen et al. 07]

16. Summary Statistical Method Discriminative Robust Efficient A Local Descriptor – Vector Spin Image

17. Thanks! Liefei Xu lxu1@stevens.edu lxu1@stevens.edu Quynh Dinh quynh@stevens.eduquynh@stevens.edu