Boundaries of objects in the real world almost always give rise to image edges. Therefore a section has been built into ASSET-2 which uses image edges found by the SUSAN edge detector [26] to ``fine-tune'' the cluster boundaries so that nearby edges can pull the boundaries into them. (Related here is the interesting work by Etoh, e.g., in [14], which also uses ``static'' image cues to aid motion segmentation.) This will of course not always be successful, as background edges may confuse the issue. However, this part of ASSET-2 has usually been a valuable addition to the core processes. In a situation where edge information is not relevant ASSET-2 can run without using the ``edge enhancement'' stage.
Edge correction of a cluster's boundary only takes place after it has been tracked for a certain number of frames. This is partly to prevent the wastage of computational effort on spurious clusters, but, more importantly, because, until the estimate of the cluster boundary is close to the actual object boundary, edge correction could degrade the object boundary instead of improving it.
This part of ASSET-2 works by taking the list of SUSAN edges and
creating a vector field from it which guides the object boundaries
towards image edges. A vector field is initialized to 
at
every point. Next each edge point is used to add to the existing field
a line of vectors pointing
Figure 7: The addition to the edge vector field caused by a single edge
point.
towards that edge point -- see Figure 7. This line of influence extends away from the edge in both directions perpendicular to it. The magnitudes of the vectors decrease in proportion to their distance from the original edge point.
Next the radial map describing the cluster outline is allowed to ``follow the forces'' which the vector field defines in the following way. The map boundary is split up into sections, centred at the end of one radius (say radius i) and running halfway towards the adjacent radii ends (radii i-1 and i+1). Thus each section will be made up of two line segments. Each section of the map boundary has the radial force on it calculated in the following way;
where 
is the ``force'' on 
, the ith radius,
is the edge vector field, the sum is taken over each
pixel in the two line segments making up the boundary section, and
is the unit vector in the direction of the ith radius.
The dot product finds the component of the sum of the ``forces'' on
the boundary section in the direction of the radius. The force 
is calculated for all i and then each 
is smoothed with its
neighbours. Next each radius is allowed to change its length by a
maximum of one pixel (in either direction), depending on the force on
it. This process is repeated several (typically ten) times. This
method was chosen instead of allowing a small number of larger changes
to the radii for the following reasons. Following this procedure the
shape is gradually allowed to change and the radii to affect each
other to find a best global fit to the edge influences. It also solves
the problem of the fact that the closer the section is to an image
edge the greater the force on it, which would give unstable (or at
least unpredictable) oscillations about the correct position if the
correction to the radius were made proportional to the force on it.
The method used gives a stable and accurate solution.
Finally, the corrected cluster shape is used to improve the original filtered radial map. To provide good temporal stability a weighted mean of the input to the edge correction algorithm and its output is taken.
This section of ASSET-2 is not implemented in the real-time version, as image data is not available to the main (PowerPC) processors with the current system architecture. However, this will soon be rectified with the release of the Parsytec TIP-Bus PowerPC boards.