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Presented by Relja Arandjelović The Power of Comparative Reasoning University of Oxford 29 th November 2011 Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung Lin @ Google ICCV 2011
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Overview Ordinal embedding of features based on partial order statistics Non-linear embedding Simple extension for polynomial kernels Data independent Very easy to implement
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Idea Compare feature vectors based on the order of dimensions, sorted by magnitude Ranking is invariant to constant offset, scaling, small noise Use local ordering statistics; example pair-wise measure: WTA (Winner Takes All) hashing scheme produces vectors comparable via Hamming distance. The distance approximates: For K=2,
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Similarity function
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Winner Takes All (WTA)
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K parameter Increasing K biases the similarity towards the top of the list
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WTA with polynomial kernel Simple to do WTA on the polynomial expansion of the feature space Computed in O(p), where p is the polynomial kernel degree
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Results: Descriptor matching (SIFT / DAISY) Descriptor matching task, Liberty dataset K=2, 10k binary codes RAW: +11.6% SIFT: +10.4% DAISY: +11.2% Note: SIFT is 128-D so there are 8128 possible pairs, might as well compute PO exactly in this case; similar for 200-D DAISY I tried briefly for SIFT on a different task: works
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Results: VOC VOC 2010 Bag-of-words of their descriptor based on Gabor wavelet responses K=4 Linear SVM χ 2 for 1000-D: 40.1% WTA for 1000-D: +2%
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Results: Image retrieval LabelMe dataset: 13,500 images; 512-D Gist descriptor K=4, p=4
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Conclusions Partial order statistics could be a good way to compare vectors Data independent: no training stage Non-linear embedding: could use a linear SVM in this space Simple to implement and try out My note for SIFT/DAISY: Can just discard all this hashing stuff and encode all pair-wise relations
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