Xivanki Share !!: One Part Basis to Rule them All: Steerable Part Models

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Last week, some of us vision hackers at MIT started an Object Recognition Reading Group.  The group is currently in stealth-mode, but our goal is to analyze, criticize, and re-synthesize ideas from the object detection/recognition community.  To inaugurate the group, I covered Hamed Pirsiavash's Steerable Part Models paper from the upcoming CVPR 2012 conference.  As background reading, I had to go over the mathematical basics of learning with tensors (i.e., multidimensional arrays) which were outlined in their earlier NIPS 2009 paper, Bilinear Classifiers for Visual Recognition.  After reading up on their work, I have a better grasp of what the trace operator actually does.  It is nothing more than a Hermitian inner product defined between the space of linear operators from C^N to C^M (see post here for geometric interpretations of the trace).

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Hamed Pirsiavash, Deva Ramanan, "Steerable part models", CVPR 2012

"Our representation can be seen as an approach to sharing parts." 
-- H. Pirisiavash and D. Ramanan

The idea behind this paper is relatively simple -- instead of learning category-specific part-models, learn a part-basis from which all category-specific part models come from.  Consider the different parts learned from a deformable part model (see Felzenszwalb's DPM page for more info about DPMs) and their depiction below.  If you take a close look you see that the parts are quite general, and it makes sense to assume that there is a finite basis from which these parts come from.

Parts from a Part-model

The model learns a steerable basis by factoring the matrix of all part models into the product of two low rank matrices, and because the basis is shared across categories, this performs both dimensionality reduction (like to help prevent over-fitting as well as speed up the final detectors) and sharing (likely to boost performance).

The learned steerable basis

While the objective function is not convex, it can be tackled via a simple alternating optimization algorithm where the resulting sub-objectives are convex and can be optimized using off-the-shelf Linear SVM solvers.  They call this property bi-convexity, and it doesn't guarantee finding the global optimum, just makes using standard tools easy.

While the results on PASCAL VOC2007, do not show an improvement in performance (VOC2007 is not a very good dataset for sharing as there are only a few category combinations which should in theory benefit significantly from sharing (e.g., bicycle and motorbike)), they show a significant computational speed up.  Below is a picture of the part-based car model from Felzenszwalb et al, as well as the one from their steerable basis approach.  Note that the HOG visualizations look very similar.

In conclusion, this is one paper worthy of checking out if you are serious about object recognition research.  The simplicity of the approach is a strong point, and if you are a HOG-hacker (like many of us these days) then you will be able to understand the paper without a problem.