Formulation of Border-Ownership Assignment in Area V2 as an Optimization Problem

Abstract

Border-ownership (BO) assignment, or the assignment of borders to an occluding object, is a primary step in visual perception. Physiological experiments have revealed the existence of neurons in area V2 that respond selectively to objects placed on a specific side of their response field. Although existing models can reproduce this phenomenon, they are not based on a clear computational theory. For this study, we formulated BO assignment as a well-defined optimization problem. We hypothesize that information related to BO assignment can be expressed as a conservative vector field. This conservative vector field is proposed as the gradient of a scalar field that carries information related to the depth order of the overlapping object. Conservative vector fields have zero curl (rotation). Using this theorem, we construct and solve an optimization problem. Numerical simulations demonstrate that a model based on our derived algorithm solves BO assignment for problems of perceived order and occlusion. Deduced neural networks provide insight into possible characteristics of lateral connections in area V2.