Multiplication rather than addition of neural signals is believed to underpin a variety of sensory processes, yet the evidence for multiplication is rare. Here we provide psychophysical evidence for neural multiplication in human visual processing of shape. We show that the curvature of a contour is likely detected by a mechanism that multiplies rather than adds the signals from afferent sub-units that detect parts of the curve. Using a novel perceptual after-effect, in which the perceived shape of a sinusoidal-shaped contour is altered following adaptation to a contour of slightly different sinusoidal shape, a pronounced 'dip' in the size of the after-effect is found when the adapting contour is broken into segments of a particular length and spacing. Simulations reveal that the presence and shape of the dip is only expected if the afferent sub-units to curvature detectors are multiplied. The after-effect itself is then best explained in terms of the population response of a range of such curvature detectors tuned to different curvatures.