Linear combinations of signals from two lines of the same or different orientations

Abstract

Whereas the influence on the elevation of visually perceived eye level (VPEL) by two bilaterally symmetric, long (64°-long), pitched-from-vertical lines in total darkness is only a little more than the average of the VPELs of the two lines measured separately [Matin & Li (1999). Vision Research, 39, 307–329], in the present experiments with 49 2-line combinations of seven orientations (−30° to +30° pitch), the VPEL for two short (12°-long) lines equals the additive sum of the separate influences of the two lines. With one line at a fixed orientation, the slope of the VPEL-versus-pitch function with the second line variable equals the slope of the function when viewing one line alone, but is shifted from the 1-line-alone function by the magnitude of the VPEL of the fixed line. Both the near-averaging and the additivity are summarized by V( θ l, θ r)= k 1+ k 2 [ V( θ l)+ V( θ r)], where V( θ l) and V( θ r) are the 1-line VPELs for the pitches of the left and right lines, and V(θ l, θ r) is the 2-line VPEL; the slope constant k 2 equals 0.5 for averaging, and 1.00 for simple additivity of the separate visual influences. Measured values are k 2=0.99 and k 2=0.61 for short and long lines, respectively. The shift of slope constant is determined by line length and not orientation: parallel and nonparallel lines follow the same rules of combination for short lines as they do for long lines. As for long lines, the short-line results are clear in showing that the visual influence on VPEL is controlled by an opponent-process mechanism. Although ‘saturation-near-an-asymptote’ along with opponency are required components of the interpretation for the basis of the combination of lines of different orientations and different lengths, they are not by themselves sufficient: All results conform to a neurophysiologically-based model [Matin and Li (1997b). Society for Neuroscience, 23, 175; Matin & Li, under review] that parallel processes feedforward signals from orientation-selective neural units in V1; the model accounts for the shift from additivity to near-averaging with increase in line length as a consequence of the increased contribution of shunting.