Shape is represented in the visual system by patterns of activity across populations of neurons. We studied the population code for shape in area V4 of macaque monkeys, which is part of the ventral (object-related) pathway in primate visual cortex. We have previously found that many macaque V4 neurons are tuned for the curvature and object-centered position of boundary fragments (such as 'concavity on the right'). Here we tested the hypothesis that populations of such cells represent complete shapes as aggregates of boundary fragments. To estimate the population representation of a given shape, we scaled each cell's tuning peak by its response to that shape, summed across cells and smoothed. The resulting population response surface contained 3-8 peaks that represented major boundary features and could be used to reconstruct (approximately) the original shape. This exemplifies how a multi-peaked neural population response can represent a complex stimulus in terms of its constituent elements.