F. Attneave (1954) famously suggested that information along visual contours is concentrated in regions of high magnitude of curvature, rather than being distributed uniformly along the contour. Here the authors give a formal derivation of this claim, yielding an exact expression for information, in C. Shannon's (1948) sense, as a function of contour curvature. Moreover, they extend Attneave's claim to incorporate the role of sign of curvature, not just magnitude of curvature. In particular, the authors show that for closed contours, such as object boundaries, segments of negative curvature (i.e., concave segments) literally carry greater information than do corresponding regions of positive curvature (i.e., convex segments). The psychological validity of this informational analysis is supported by a host of empirical findings demonstrating the asymmetric way in which the visual system treats regions of positive and negative curvature.
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