In natural environments, objects are viewed under a wide variety of lighting conditions, poses, backgrounds, and juxtapositions with other objects. Artificial vision systems that are sufficiently invariant to accommodate such variations are never sufficiently selective. The rich structure of real images offers a multitude of chance arrangements, many of which cause systems to falsely detect an object that is not there. On the other hand, systems that are highly selective are at the same time highly prone to missed detections in the face of natural variability. The visual systems of humans and animals, in contrast, are able to see accurately under a wide range of viewing conditions--how is it that biological systems are both selective and invariant?

The pursuit of this question leads to an analogous question about complex cells and other invariant cell types that are ubiquitous in the ventral visual pathway. Their strength would appear to be their weakness: How is it possible for the visual system to build selectivity out of invariance? Models of complex cells suggest an explanation. Complex and other invariant cell types, by virtue of their nonlinear response characteristics, necessarily possess a functional connectivity whereby these cells become functionally connected to a generally small subset of their inputs. This commitment is circumstantial, inasmuch as it depends on the particular pattern in the receptive field. Functional connectivity is a demonstrable mathematical property of virtually all of the non-linear models put forward to date for complex-cell receptive-field properties. What is more, these observations lead to the conclusion that pairs of such cells that possess overlapping receptive fields will demonstrate a functional common input. This too is circumstantial, and in fact functional common input is high exactly when the patterns in the respective receptive fields "fit together"---correspond to pieces of a larger whole.

These observations suggest a solution to the dilemma of invariance versus selectivity: pieces that fit properly together generate a high degree of functional common input, which manifests itself by a statistical dependence between otherwise invariant representations, most likely in the form of partial synchrony, thereby signaling a composition of parts to cells deeper in the visual pathway.

In search of experimental confirmation of this proposed answer to the selectivity/invariance dilemma, the investigators employ new statistical and methodological techniques to study new questions about the receptive-field properties of invariant cells, and to measure new variables in the joint statistics of invariant cells with overlapping receptive fields.

National Science Foundation (NSF)
Division of Information and Intelligent Systems (IIS)
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Kenneth C. Whang
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Brown University
United States
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