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Published byStefan Frayne Modified about 1 year ago

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Universidad Católica San Pablo Cristina Patricia Cáceres Jáuregui

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

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Nuisance parameters

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

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Local image features

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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

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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

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Pyramid match kernel optimal partial matching Optimal match: O(m 3 ) Pyramid match: O(mL) m = # features L = # levels in pyramid

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

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

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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.

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Locality Sensitive Hashing (LSH) Q h r 1 …r k XiXi N h << N Q Guarantee “approximate”- nearest neighbors in sub- linear time, given appropriate hash functions. Randomized LSH functions

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

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

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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

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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

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Fast Image Search for Learned Metrics 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( ) Learn a Malhanobis metric for LSH

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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 Summary

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