Efficiently searching for similar images ( Kristen Grauman )

1. Efficiently searching for similar images (KristenGrauman) Universidad Católica San Pablo Cristina Patricia Cáceres Jáuregui cristina.caceres.jauregui@ucsp.edu.pe

2. Motivation Fast image search is a useful component for a number of vision problems. Plenty of nuisance parameters (lighting, pose, background clutter, etc.)

3. Nuisance parameters

4. Outline Scalable image search • Fast correspondence-based search with local features • Fast similarity search for learned metrics

5. Local image features

6. How to handle sets of features? • Want to compare, index, cluster, etc. local • representations, but: • • Each instance is unordered set of vectors • • Varying number of vectors per instance

7. Comparing sets of local features Previous strategies: • Match features individually, vote on small sets to verify • Explicit search for one-to-one correspondences • Bag-of-words: Compare frequencies of prototype features

8. optimal partial matching Pyramid match kernel Optimal match: O(m3) Pyramid match: O(mL) m = # features L = # levels in pyramid

9. Pyramid match: main idea Feature space partitions serve to “match” the local descriptors within successively wider regions. descriptor space

10. Pyramid match: main idea Histogram intersection counts number of possible matches at a given partitioning.

11. Image search with matching- sensitive hash functions • Main idea: – Map point sets to a vector space in such a way that a dot product reflects partial match similarity (normalized PMK value). – Exploit random hyperplane properties to construct matching-sensitive hash functions. – Perform approximate similarity search on hashed examples.

12. Locality Sensitive Hashing (LSH) N Xi h h r1…rk r1…rk Q Guarantee “approximate”-nearest neighbors in sub-linear time, given appropriate hash functions. Randomized LSH functions << N 110101 110111 Q 111101

13. LSH functions for dot products The probability that a randomhyperplane separates two unit vectors depends on the angle between them: Corresponding hash function: A) High dot product: unlikely to split B) Lower dot product: likely to split

14. Metric learning There are various ways to judge appearance/shape similarity… but often we know more about (some) data than just their appearance.

15. Metric learning • Exploit partially labeled data and/or (dis)similarity constraints to construct more useful distance function • Can dramatically boost performance on clustering, indexing, classification tasks. • Various existing techniques

16. Fast similarity search for learned metrics • Goal: – Maintain query time guarantees while performing approximate search with a learned metric • Main idea: – Learn Mahalanobis distance parameterization – Use it to affect distribution from which random hash functions are selected • LSH functions that preserve the learned metric • Approximate NN search with existing methods

17. Fast Image Search for Learned Metrics Learn a Malhanobis metric for LSH It should be unlikely that a hash function will split examples like those having similarity constraints… …but likely that it splits those having dissimilarity constraints. h( ) = h( ) h( ) ≠h( )

18. Summary • Local image features useful, important to handle efficiently • Introduced scalable methods to allow fast similarity search methods with – Local feature matching – Learned Mahalanobis metrics • Key idea: design hash functions that encode matching process, or the constraints provided