A cell model in the ventral visual pathway for the detection of circles of curvature constituting figures

Abstract

The contour of an arbitrary figure can be represented as a group of circles of curvature in contact with it, with each curvature circle represented by its center OC and radius r. We propose a series of cell models for detecting this circle, which is composed of a lateral geniculate nucleus (LGN) cell, nondirectionally selective (NDS) simple cell, and curvature-circle detection cell (CDC). The LGN and NDS simple cells were previously modeled. The CDC has been modeled as follows. Each tangent in contact with this circle is detected by an NDS simple cell that performs the Hough transformation of LGN cell responses, and then this tangent is transformed to a three-dimensional (3D) normal line in a CDC column. This transformation has been named a 3D normal-line transform. Performing this transformation for all tangents causes a CDC at the intersection of these normal lines to fire most intensively, and thus the OC and r of the circle is detected as the coordinates of this intersection. Therefore, the CDC has been modeled as this 3D normal-line transform. Based on this CDC, we model two types of constancy CDC: a position-invariant CDC and a curvature-invariant CDC. These three types of CDC reflect the response to various stimuli in actual area V4 cells. In order to validate these CDC types neurophysiologically, we propose an experimental method using microelectrodes. Cell models previously reported correspond to this hierarchy: the S1, S2, and C2 cells correspond to the NDS simple cell, CDC, and position-invariant CDC, respectively.