[A geometrical model for the perceived line of orientation based on subjective evaluations and human VEP data]

A geometric model in proposed based on subjective dissimilarity estimates among differently oriented line segments in the frontal plane and on visual evoked potentials (VEP) recorded in respond to abrupt changes in the orientation of such a line segment. The orientations are represented by points constituting a clised planar curve, with interpoint distances corresponding to interstimulus dissimilarities. The angle of the radius-vertor connecting the center of the configuration with its circumference encodes the orientation of the line stimuli in the visual field, and two Cartesian axes drawn through the center are interpreted as two orientation-opponent channels in the neuronal network processing line orientation. The first channel (the ordinate axis) gives maximal positive and maximal negative responses to, respectively, vertical and horizontal orientations, whereas the second channel (the abscissa axis) gives maximal positive and maximal negative responses to, respectively, 45 and 135 degrees orientations. The VEP analysis shows that the activity of the first channel affects the interpeak amplitudes of both the P1-N2 (P130-N180) and N2-P2 (N180-P230) components, whereas the second channel affects only the late component N180-P230. We propose the hypothesis according to which outputs of the two channels are connected linearly (which is reflected in the city-block metric obtained when distances are computed directly from neuronal activity), but the growth rate of the overall output is inhibited nonlinearly when it reaches large absolute values. This inhibition effectively transforms the "true" city-block metric of the line orientation space into the Euclidean metric one obtains when distances are computed from subjective dissimilarity estimates. VEP amplitudes as intermediate characteristics of visual processing between neuronal activity and subjective estimates represent intermediate metric (between city-block and Euclidean).