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A Local Descriptor for Finding Corresponding Points in Vector Fields

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

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A Local Descriptor for Finding Corresponding Points in Vector Fields

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  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 Analysis Weather Monitoring Computational Fluid Dynamics Simulation of water current in the New York Harbor Region. From Center for Maritime Systems at Stevens Inst. of Tech. 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 spin-images b (depth) values a (radial) values [Johnson & Hebert 99]

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

  7. Comparing Vector Spin Images - χ2 statistical distance different similar

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

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

  10. Vector Spin Image:Resolution different similar # of bins (r X dot) 10 X 10 vector field 5 X 10 5 X 5 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 rmax =60 • 7 microsecs for each point for rmax =20 • Computation of χ2 statistical distance • < 1 second (262144 comparisons)

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

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

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

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