1. Jianke Zhu From Haibin Ling’s ICCV talk Fast Marching Method and Deformation Invariant Features

2. Outline  Introduction  Fast Marching Method  Deformation Invariant Framework  Experiments  Conclusion and Future Work

3. General Deformation One-to-one, continuous mapping. Intensity values are deformation invariant.  (their positions may change)

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

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]

6. Outline  Introduction  Deformation Invariant Framework  Intuition through 1D images  2D images  Experiments  Conclusion and Future Work

7. 1D Image Embedding 1D Image I(x) EMBEDDING I(x)  ( (1-α)x, αI ) αIαI (1-α)x Aspect weight α : measures the importance of the intensity

8. Geodesic Distance αIαI (1-α)x p q g(p,q) Length of the shortest path along surface

9. Geodesic Distance and α I1I1 I2I2 Geodesic distance becomes deformation invariant for α close to 1 embed

10. Image Embedding & Curve Lengths Depends only on intensity I  Deformation Invariant Image I Embedded Surface Curve on Length of Take limit

11. Computing Geodesic Distances Fast Marching [Sethian96] Geodesic level curves  Moving front Varying speed p

12. Deformation Invariant Sampling Geodesic Sampling 1. Fast marching: get geodesic level curves with sampling interval Δ 2. Sampling along level curves with Δ p sparse dense Δ Δ Δ Δ Δ

13. Deformation Invariant Sampling Geodesic Level Curves Geodesic Sampling 1. Fast marching: get geodesic level curves with sampling gap Δ 2. Sampling along level curves with Δ p

14. Geodesic Distance & Fast Marching

15. Deformation Invariant Descriptor p q p q Geodesic-Intensity Histogram (GIH) geodesic distance intensity geodesic distance intensity

16. Real Example p q

17. Deformation Invariant Framework Image Embedding ( close to 1) Deformation Invariant Sampling Geodesic Sampling Build Deformation Invariant Descriptors (GIH)

18. 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

19. Invariant vs. Descriminative

20. Outline  Introduction  Deformation Invariance for Images  Experiments  Interest-point matching  Conclusion and Future Work

21. Data Sets Synthetic Deformation & Lighting Change (8 pairs) Real Deformation (3 pairs)

22. Interest-Points * Courtesy of Mikolajczyk, http://www.robots.ox.ac.uk/~vgg/research/affine/ 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

23. 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/

24. Synthetic Image Pairs

25. Real Image Pairs

26. Study of Interest-Points

27. Outline  Introduction  Deformation Invariance for Images  Experiments  Conclusion and Future Work

28. Thank You!