Presented by Relja Arandjelović

The Power of Comparative Reasoning

University of Oxford 29th November 2011

Jay Yagnik, Dennis Strelow, David Ross, Ruei-sung Lin

@ Google

ICCV 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