Fast Contour Matching Using Approximate Earth Mover's Distance

Weighted graph matching is a good way to align a pair of shapes represented by a set of descriptive local features; the set of correspondences produced by the minimum cost of matching features from one shape to the features of the other often reveals how similar the two shapes are. However, due to the complexity of computing the exact minimum cost matching, previous algorithms could only run efficiently when using a limited number of features per shape, and could not scale to perform retrievals from large databases. We present a contour matching algorithm that quickly computes the minimum weight matching between sets of descriptive local features using a recently introduced low-distortion embedding of the Earth Mover's Distance (EMD) into a normed space. Given a novel embedded contour, the nearest neighbors in a database of embedded contours are retrieved in sublinear time via approximate nearest neighbors search. We demonstrate our shape matching method on databases of 10,000 images of human figures and 60,000 images of handwritten digits.

A Detailed Look at Scale and Translation Invariance in a Hierarchical Neural Model of Visual Object Recognition

The HMAX model has recently been proposed by Riesenhuber & Poggio as a hierarchical model of position- and size-invariant object recognition in visual cortex. It has also turned out to model successfully a number of other properties of the ventral visual stream (the visual pathway thought to be crucial for object recognition in cortex), and particularly of (view-tuned) neurons in macaque inferotemporal cortex, the brain area at the top of the ventral stream. The original modeling study only used ``paperclip'' stimuli, as in the corresponding physiology experiment, and did not explore systematically how model units' invariance properties depended on model parameters. In this study, we aimed at a deeper understanding of the inner workings of HMAX and its performance for various parameter settings and ``natural'' stimulus classes. We examined HMAX responses for different stimulus sizes and positions systematically and found a dependence of model units' responses on stimulus position for which a quantitative description is offered. Interestingly, we find that scale invariance properties of hierarchical neural models are not independent of stimulus class, as opposed to translation invariance, even though both are affine transformations within the image plane.