Orientation, scale, and discontinuity as emergent properties of illusory contour shape

A recent neural model of illusory contour formation is based on a distribut ion of natural shapes traced by particles moving with constant speed in dir ections given by Brownian motions. The input to that model consists of pair s of position and direction constraints, and the output consists of the dis tribution of contours joining all such pairs. In general, these contours wi ll not be closed, and their distribution will not be scaleinvariant. In thi s article, we show how to compute a scale-invariant distribution of closed contours given position constraints alone and use this result to explain a well-known illusory contour effect.