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1995

David McG. Squire and Terry M. Caelli,
Shift, Rotation and Scale Invariant Signatures for
TwoDimensional Contours, in a Neural Network Architecture,
In Stephen W. Ellacott, John C. Mason and Iain J. Anderson eds., Mathematics of Neural Networks: Models Algorithms and
Applications,
Boston, Statistics and OR, pp. 344348, Kluwer Academic Publishers, July 1995.
A technique for obtaining shift, rotation and scale
invariant signatures for two dimensional contours is proposed and
demonstrated. An invariance factor is calculated at each point
by comparing the orientation of the tangent vector with vector fields
corresponding to the generators of Lie transformation groups for shift,
rotation and scaling. The statistics of these invariance factors over
the contour are used to produce an invariance signature.
This operation is implemented in a ModelBased Neural Network (MBNN),
in which the architecture and weights are parameterised by the
constraints of the problem domain. The end result after constructing
and training this system is the same as a traditional neural network: a
collection of layers of nodes with weighted connections. The design and
modeling process can be thought of as compiling an invariant
classifier into a neural network. We contend that these invariance
signatures, whilst not unique, are sufficient to characterise contours
for many pattern recognition tasks.
