Mammalian primary visual cortex (V1) is topographically organized such that the pattern of neural activation in V1 reflects the location and spatial extent of visual elements in the retinal image, but it is unclear whether this organization contributes to visual perception. We combined computational modeling, voltage-sensitive dye imaging (VSDI) in behaving monkeys and behavioral measurements in humans to investigate whether the large-scale topography of V1 population responses influences shape judgments. Specifically, we used a computational model to design visual stimuli that had the same physical shape, but were predicted to elicit variable V1 response spread. We confirmed these predictions with VSDI. Finally, we designed a behavioral task in which human observers judged the shapes of these stimuli and found that their judgments were systematically distorted by the spread of V1 activity. This illusion suggests that the topographic pattern of neural population responses in visual cortex contributes to visual perception.