Report

The Power of Comparative Reasoning Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung Lin @ Google ICCV 2011 Presented by Relja Arandjelović University of Oxford 29th November 2011 Overview Ordinal embedding of features based on partial order statistics Non-linear embedding Simple extension for polynomial kernels Data independent Very easy to implement 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, Similarity function Winner Takes All (WTA) K parameter Increasing K biases the similarity towards the top of the list 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 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 Results: VOC VOC 2010 Bag-of-words of their descriptor based on Gabor wavelet responses K=4 Linear SVM χ2 for 1000-D: 40.1% WTA for 1000-D: +2% Results: Image retrieval LabelMe dataset: 13,500 images; 512-D Gist descriptor K=4, p=4 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