Department of Bioengineering, Imperial College, London, UK
The Map Seeking Circuit of Arathorn [1] is a biologically inspired mechanism which offers a generic solution to the complex task of estimating chains of image transformations by proposing a model for the forward/backward projections in the neural circuitry of the brain. For the majority of object recognition problems, the consideration of all the possible combinations for a non-trivial number of transformations introduces a combinatorial explosion in computational complexity. The MSC has a layered architecture representing different parameters to be explored and implements an ordered sequence of comparisons of transformed images using forward/backward superimpositions at each layer in an iterative process. The entire search space is given uniform weighting initially and the mechanism operates by culling unlikely combinations considering one parameter at a time. Although the search is partitioned into 1D sub-spaces, the superimpositions allow several likely combinations of the parameters in the sequence to be taken into account at once, allowing a combinatorial dimension to the search. The complexity in this scheme, therefore, grows additively as the number of different parameters in the sequence is increased rather than exponentially as an initial expectation from the nature of the problem.
In this work, we first provide a statistical interpretation of the MSC in a Bayesian framework. The superimpositions in this scheme are explained as marginalisations that remove the effect of all the other parameters except for one at a time. Then we introduce Monte Carlo Map Seeking Circuits (MC-MSC) that improve the performance of the MSC by representing the likelihoods of the parameters by a set of samples which are initially placed at fixed intervals and keep only the ‘important’ characteristics of the likelihoods as the iterations proceed for an accurate estimation of marginalisations. A major drawback of the dimensionality reduction through marginalisations is that of ‘collusions’, i.e. combinations of patterns create new illusory patterns in the superimpositions, in the presence of clutter as might be expected for practical problems. This is addressed by adopting a serial/parallel search scheme inspired by the biological visual search in the form of a ‘queuing’ procedure. Our preliminary results illustrate the performance of MC-MSC and ‘queuing’ (79% correct detection rate for 135 cases – cluttered input image with similar objects present) in comparison to fully parallel MSC (21% success rate) scheme in the case of translation, rotation, and scaling parameter search.
[1] D.W.Arathorn, Map-Seeking Circuits in Visual Cognition, Stanford Uni. Press, ’02