Population coding of complex shapes in macaque area V4

We recently reported that many V4 neurons encode sections of complex shape boundaries in terms of their curvature and relative position (Pasupathy & Connor, 2001). For example, one neuron may be tuned for concave curvature to the right (of object center), another'tuned for convex curvature at the top, etc. These tuning properties can be described with two-dimensional Gaussian functions on a curvature x angular position domain. In the current study, we estimated V4 population activity by summing the response-weighted Gaussian tuning functions. We found that, while individual V4 cells encode boundary sections, the V4 population response represents complete shapes. To derive the population response to a given shape, we weighted each cell's tuning peak (in the curvature x position domain) by its response to that shape. We then summed the weighted tuning peaks and smoothed the resulting surface. This produced a multi-peaked function on the 2-dimensional curvature x position domain. The peaks in this function corresponded closely to the major boundary features in the original shape. The strongest peaks in the population response were those corresponding to sharper convex and concave boundary features. Shallow boundary curvature was represented more weakly. We quantified overall correspondence by calculating average distance (on the curvature x position domain) between population surface peaks and closest matching boundary features. Across 49 complex shape stimuli, the median average distance was 4.04° in the angular position dimension and 0.07 in the curvature dimension (which ranges from -1.0 (sharp concave) to 1.0 (sharp convex)). Thus, the V4 population signal represents complete shapes in terms of the curvatures and positions of their constituent boundary features.