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Neural Net Design Issues - Output Representations
Our initial neural network design had one output unit, providing a single
value on the range [0,1]: a low evaluation indicates a pixel is off to
the left of the contour, a high evaluation indicates off to the right,
and a value near 0.5 indicates the pixel is on the desired contour. The
network learns an evaluation function that produces a smoothly changing
value as a pixel and its neighbors change from left-of-contour values,
to on-contour values, and then to right-of-contour values.
An alternative network design we studied also has one output unit, but
this unit produces a low value for pixels centered on the contour, and
a high value for off-contour pixels. This style of output is a feature-detector
unit, where the output unit goes low on recognizing the contour, and stays
high in non-contour regions.
Neural Net Design Issues - Training
Our initial experiments demonstrated the smooth-evaluation-function output
unit works well when following a gradient, or ramp edge (for example, see
Figures 3 and 5). Unfortunately, this is unworkable if the network is trying
to learn to follow a thin line rather than a gradient. When following a
line, the local neighborhoods off to the left and right side of the line
are similar, and since they are expected to produce different outputs,
this is no longer a functional form and thus can't be learned.
Exemplars of the contour for training are easy to derive, given an established
contour in the image. Over the training set, the true extension of the
curve for several pixels ahead is known, and can be added to the training
set. A key issue, though, is the generation and spacing of negative exemplars.
The set of possible extensions considered for each point needs to be looked
at in the known training set, and appropriate non-contour training values
established.
Neural Net Design Issues - Input Representations
There are a variety of options for representing the input pixel space:
-
raw pixel values
-
filtered inputs (Laplacian, Sobel, ...)
-
masks based on neurologically-inspired models (center-surround, directed
gradient, ...)
Since neural nets can automatically extract high-order moments from the
data, it may seem best to just feed raw neighborhood pixel data into the
network, and let it automatically learn its best model. This is the strategy
used by the path-following system ALVINN [3].
However, in our application, efficient learning is also an issue, since
one goal of our systems is to keep pace with human operators. Appropriate
preprocessing of inputs should be able to accelerate the contour learning.
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Neural Networks for Boundary Tracing
stewart crawford-hines