adjusted to be even more similar to the incoming vec-
tor by the rule
dwik
dt
where y is a constant referred to the learning rate. In
this way, the network illustrated in Figure 4 can be
trained to classify input patterns I presented to F,
into mutually exclusive recognition categories separa-
ted by sharp categorical boundaries.
(6)
= yer (—wir + z;),
It has been, however, mathematically proved that
such learning process stabilizes only if the input pat-
terns form not too many clusters, relative to the num-
ber of coding nodes in F,; (GROSSBERG, 1976). A
competitive learning model does not always learn a
temporally stable code in response to an arbitrary in-
put environment. Certain instabilities may arise in the
competitive systems such that different nodes might
respond to the same input pattern on different oc-
casions. Moreover, later learning can wash away ear-
lier learning if the environment is not statically sta-
tionary or if novel inputs arise. All of these suggest
that the competitive learning can not deal with the so
called stability-plasticity dilemma (CARPENTER and
GROSSBERG, 1988).
4.4 The Stability-Plasticity Dilemma
To deal with the stability-plasticity dilemma, we need
systems which can remain plastic, or adaptive, in re-
sponse to significant events and yet remain stable in
response to irrelevant events, and which can preserve
its previously learned knowledge about group proper-
ties while continuing to learn new incoming patterns.
The stability-plasticity dilemma, faced by all intel-
ligent systems capable of autonomously adapting in
real time to unexpected changes in their world, can
be solved based on the so called adaptive resonance
theory (ART) developed by GROSSBERG (1976). A key
idea to solving this problem is to add a feedback me-
chanism between the competitive layer F'5 and the in-
put layer F,. This mechanism facilitates the learning
of new information without destroying old informa-
tion, automatic switching between stable and plastic
modes, and stabilization of the encoding of the classes
done by the nodes.
À simplified way to implement this idea is to make a
vigilance test of similarity before the weight vector is
adjusted. Suppose that an input pattern I activates
F,. Let F, in turn activate the node, or hypothesis,
vy at F5 which has the maxmum activity and whose
weight vector is therefore most similar to I. Now a
matching threshold e called vigilance is given. This
threshold determines how close a new input pattern
must be to a stored exemplar to be considered simi-
lar. If a bad match takes place, then a reset burst is
868
triggered. This reset burst shuts off the node v, for
the remainder of the weight adapting cycle and I is
stored as the weight vector of a previously uncom-
mitted node at F5. If a good match takes place, the
weight vector of v, is adapted by the rule
dwik s 1
dt ng + 1
(Li — wir), (7)
where n, denotes how many times the node v, has
been adapted till now.
5 A Novel Line Finder
Feature extraction, as mentioned earlier, is a multi-
level process of abstraction and representation, from
image representation (purely numeric) to object or
object-class models (highly abstracted). At the lowest
level of feature extraction, potentially useful image
events, such as homogeneous regions (collections of
contiguous image data points with similar properties),
lines, and curves, are extracted from the image data.
These image events can then be used as building ele-
ments to form more complex features like polylines
and polygons, in a bottom-up abstraction hierarchy.
In this section we only pay attention to finding and
describing lines in the image data. We want to demon-
strate our two-stage paradigm for feature extraction
by presenting its application in this limited domain.
5.1 Discovering Line Context
To facilitate the analysis let us first look at an image
illustrated in Figure 5a and try to find lines in it.
The first question we are facing is what a line means
in a numerical array of intensities. Actually, a line is
just an abstraction. It is a visual impression produ-
ced by a group of pixels and each pixel gives only a
very weak evidence for building this impression, even
if there were no stochastic component in this pixel.
This is quite intuitive if we focus our attention on a
region near the ridge of the roof (cf. the white line
in Figure. 5a) and extract this region from image (cf.
Figure 5b). It is clear that the ridge of the roof in
the image is only perceived owing to the combination
of weak evidence of all pixels in this so called line
support region (HANSON and RISEMAN, 1987). So, a
reasonable step for line finding is the perceptual orga-
nization of image pixels into a supporting line context
prior to making any decisions about any potential un-
derlying structures.
The perceptual laws are general grouping criteria du-
ring feature extraction. Among them, proximity, si-
milarity and continuity can be utilized to aggregate
image pixels into line support regions. As showed
