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

A recent neural model of illusory contour formation is based on a distribution of natural shapes traced by particles moving with constant speed in directions given by Brownian motions. The input to that model consists of pairs of position and direction constraints, and the output consists of the distribution of contours joining all such pairs. In general, these contours will not be closed, and their distribution will not be scale-invariant. In this 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.