The recurrent neural interaction in the primary visual cortex makes
its outputs complex nonlinear functions of its inputs. This nonlinear transform serves the
role of pre-attentive visual segmentation, i.e., the autonomous transformation from visual
inputs to processed outputs that selectively emphasize certain features (e.g., pop-out
features) for segmentation. Understanding the nonlinear dynamics of the neural
circuit is a key to appreciating the cortical computational potential and tasks.
However, the complex nonlinear dynamics of recurrent networks makes it extremely difficult
to build a well-behaved and computationally functional model of the cortex merely by
simulation trials. This paper describes an analytical study of the recurrent neural
dynamics. We derive requirements on the neural architecture, components, and
connection weights of a biologically plausible model of the cortex to achieve
simultaneously different components of pre-attentive segmentation: region segmentation,
figure-ground segregation, and contour enhancement. In addition, we analysis conditions
for behaviors such as neural oscillations, illusory contours, and visual
halluciations. Many of our analytical techniques can be applied to other recurrent
networks with translation invariant neural and connection structures.
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