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Deformation Invariant Image Matching

Deformation Invariant Image Matching. Haibin Ling and David W. Jacobs Center for Automation Research Computer Science Department University of Maryland, College Park Oct, 20, 2005, ICCV. Outline. Introduction Deformation Invariant Framework Experiments Conclusion and Future Work.

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Deformation Invariant Image Matching

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  1. Deformation Invariant Image Matching Haibin Ling and David W. Jacobs Center for Automation Research Computer Science Department University of Maryland, College Park Oct, 20, 2005, ICCV Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  2. Outline • Introduction • Deformation Invariant Framework • Experiments • Conclusion and Future Work Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  3. General Deformation • One-to-one, continuous mapping. • Intensity values are deformation invariant. • (their positions may change) Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  4. Our Solution • A deformation invariant framework • Embed images as surfaces in 3D • Geodesic distance is made deformation invariant by adjusting an embedding parameter • Build deformation invariant descriptors using geodesic distances Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  5. Related Work • Embedding and geodesics • Beltrami framework [Sochen&etal98] • Bending invariant [Elad&Kimmel03] • Articulation invariant [Ling&Jacobs05] • Histogram-based descriptors • Shape context [Belongie&etal02] • SIFT [Lowe04] • Spin Image [Lazebnik&etal05, Johnson&Hebert99] • Invariant descriptors • Scale invariant descriptors [Lindeberg98, Lowe04] • Affine invariant [Mikolajczyk&Schmid04, Kadir04, Petrou&Kadyrov04] • MSER [Matas&etal02] Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  6. Outline • Introduction • Deformation Invariant Framework • Intuition through 1D images • 2D images • Experiments • Conclusion and Future Work Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  7. 1D Image Embedding 1D Image I(x) EMBEDDING I(x)  ( (1-α)x, αI ) (1-α)x αI Aspect weight α: measures the importance of the intensity Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  8. q p Geodesic Distance • Length of the shortest path along surface αI g(p,q) (1-α)x Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  9. Geodesic Distance and α I1 I2 embed embed Geodesic distance becomes deformation invariant for α close to 1 Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  10. Embedded Surface Curve on Length of Image Embedding & Curve Lengths ImageI Take limit Depends only on intensity I Deformation Invariant Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  11. T=1 T=2 T=3 T=4 Geodesic Distance for 2D Images • Geodesic distance • Shortest path • Deformation invariant • Computation • Geodesic level curves • Fast marching [Sethian96] p F q T is the geodesic distance is the marching speed Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  12. Δ Δ Δ Δ Δ Deformation Invariant Sampling Geodesic Sampling • Fast marching: get geodesic level curves with sampling interval Δ • Sampling along level curves with Δ p sparse dense Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  13. p q intensity intensity geodesic distance geodesic distance Deformation Invariant Descriptor Geodesic-Intensity Histogram (GIH) p q Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  14. Real Example p q Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  15. Deformation Invariant Framework Image Embedding ( close to 1) Deformation Invariant Sampling Geodesic Sampling Build Deformation Invariant Descriptors (GIH) Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  16. Practical Issues • Lighting change • Affine lighting model • Normalize the intensity • Interest-Point • No special interest-point is required • Extreme point (LoG, MSER etc.) is more reliable and effective Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  17. Invariant vs. Descriminative Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  18. Outline • Introduction • Deformation Invariance for Images • Experiments • Interest-point matching • Conclusion and Future Work Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  19. Data Sets Synthetic Deformation & Lighting Change (8 pairs) Real Deformation (3 pairs) Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  20. Interest-Points Interest-point Matching • Harris-affine points [Mikolajczyk&Schmid04] * • Affine invariant support regions • Not required by GIH • 200 points per image • Ground-truth labeling • Automatically for synthetic image pairs • Manually for real image pairs * Courtesy of Mikolajczyk, http://www.robots.ox.ac.uk/~vgg/research/affine/ Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  21. Descriptors and Performance Evaluation Descriptors • We compared GIH with following descriptors: Steerable filter [Freeman&Adelson91], SIFT [Lowe04], moments [VanGool&etal96], complex filter [Schaffalitzky&Zisserman02], spin image [Lazebnik&etal05] * Performance Evaluation • ROC curve: detection rate among top N matches. • Detection rate * Courtesy of Mikolajczyk, http://www.robots.ox.ac.uk/~vgg/research/affine/ Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  22. Synthetic Image Pairs Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  23. Real Image Pairs Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  24. Outline • Introduction • Deformation Invariance for Images • Experiments • Conclusion and Future Work Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  25. Conclusion and Future Work • Conclusion • A new deformation invariant framework • Deformation invariant descriptor (GIH) • Future Work • Understanding how to effectively vary α • Noise & Occlusion • Fast algorithm • Real application • … Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  26. Acknowledgement • Krystian Mikolajczyk and Cordelia Schmid for the feature extraction code. • Paolo Favaro and Kevin S. Zhou for discussion. • NSF (ITR- 03258670325867). • The Horvitz Assistantship. Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

  27. Thank You! Haibin Ling and David Jacobs, Deformation Invariant Image Matching, ICCV, Oct. 20, 2005

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