Since the principles of proximity and smooth-continuation arise from local properties of the configuration of the edges, we can model them using only local information.

Both of these local properties are modeled by the distribution of smooth curves that pass through two given edges.

The distribution of curves is modeled by a smooth, stochastic motion of a particle. Given two edges, we determine the probability that a particle starts with the position and direction of the first edge and ends with the position and direction of the second edge.

The affinity from the first to the second edge is the sum of the probabilities of all paths that a particle can take between the two edges.

The change in direction of the particle over time is normally distributed with zero mean. Smaller the variance of the distribution, the smoother is the more probable curves that pass between two edges.

Thus the variance of the normal distribution models the principle of smooth-continuation. In addition each particle has a non-zero probability for decaying at any time.

Hence, edges that are farther apart are likely to have fewer curves that pass through both of them.

Thus the decay of the particles models the principle of proximity. The affinities between all pairs of edges form the affinity matrix.