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P robing t he L ocal- F eature S pace of I nterest P oints

P robing t he L ocal- F eature S pace of I nterest P oints. ICIP 2010. Wei-Ting Lee, H wann- T zong C hen Department of Computer Science National Tsing Hua University, Taiwan. OUTLINE. Introduction Approach Locality-Sensitive Hashing (LSH) Sketching the Feature Space

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P robing t he L ocal- F eature S pace of I nterest P oints

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  1. Probing the Local-Feature Space of Interest Points ICIP 2010 Wei-Ting Lee, Hwann-TzongChen Department of Computer Science National TsingHua University, Taiwan

  2. OUTLINE • Introduction • Approach • Locality-Sensitive Hashing (LSH) • Sketching the Feature Space • Experiments • Fast Matching • Conclusion

  3. INTRODUCTION Local feature have been extensively used to represent image for various problem Lots of local feature detector and local feature descriptor have been proposed recent years

  4. Recent History For example

  5. INTRODUCTION • Present an empirical analysis of the feature space of interest points detected in natural image • Perform an approximate method for the fast matching between two sets of interest points detected in two images • Show that the complexity of matching M points to N points can be reduced from O(MN) to O(M+N)

  6. Locality-Sensitive Hashing • p-stable Distribution:

  7. Locality-Sensitive Hashing based on 2-Stable Distribution

  8. Hash Family The dot-product a‧v projects each vector to the real line a : random vector sampled from a Gaussian distribution b : real value chosen uniformly from the range [0 , r] r : line width

  9. Building Hash table

  10. Building Hash table a‧b = |a| |b| θ Index function =？ t = 5 , K=3 [5] [5] [5] = 125 = (5-1) * 52+ (5-1) * 51 + 4 * 50 + 1 = 4 * 25 + 20 + 4 + 1 = 125 Choose the width r based on the minimum and maximum

  11. Sketching the Feature Space Berkeley segmentation database [14] Use difference of Gaussian (DOG) [2] & Hessian-affine [3] detector detect about 200,000 interest points Extract image patches by SIFT descriptor [2] Create a hash table (L = 1) with five projection(K = 5) and 15 segments on each dot-product real line (t = 15) The total number of buckets is 155 = 759,375

  12. Sketching the Feature SpaceDistribution and Entropy Entropy = 4.2251 (a) DOG Entropy = 4.0622 (b) Hessian-affine

  13. Sketching the Feature Space Natural image patches (from Berkeley segmentation database ) Noise image patches (Randomly-generated noise patches) Collect three image patchesof different size 16x16 , 32x32 , 64x64 Each set consist of 200,000 patches.

  14. Distribution and Entropy

  15. Fast Matching Reference image Remaining Image (test) 3 3 3 3 3 3 3 3

  16. Fast Matching We create L = 16 hash tables to probe the 128-dimensional SIFT-feature space Each table is equipped with five 2-stable Projections , and the projected values are quantized into 15 segments, i.e., K = 5 and t = 15 For LSH, we use two threshold values of dot-product, θ =0.95and θ =0.97, to determine whether a pair of feature vectors in the same bucket yields a match LSH is 2 to 15 times faster than matching by exhaustive search a‧b = |a| |b| If a = b , then = 1

  17. Fast Matching DoGdetector + SIFT descriptor Hessian-affine detector + SIFT descriptor

  18. 2-stable LSH matching vs. exhaustive matching DoGdetector + SIFT descriptor

  19. 2-stable LSH matching vs. exhaustive matching Hessian-affine detector + SIFT descriptor

  20. Conclusion Using the approximate nearest-neighbor probing scheme derived from 2-stable Locality-Sensitive Hashing Make use of the efficient representation of the SIFT feature space, and present a fast feature-matching method for finding correspondences between two sets of interest points. And, Have been used by Whiteorange !!

  21. THANK YOU SO MUCH

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