Affinity Matrix
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 are 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 .
Shyjan Mahamud
Last modified: Tue Sep 8 14:15:50 EDT 1998