Shift, Rotation and Scale Invariant Signatures for Two-Dimensional Contours, in a Neural Network Architecture

A technique for obtaining shift, rotation and scale invariant signatures for two dimensional contours in images is proposed and demonstrated. The technique is based upon a measure of the degree to which the local tangent estimate at each point in the contour is consistent with having been generated by a shift, rotation or scale invariant function. An invariance factor is calculated at each point by comparing the orientation of the tangent vector with each of the vector elds corresponding to the Lie generators of the transformation groups for shift, rotation and scaling. The statistics of these invariance factors over all points in the contour are used to produce an invari-ance signature for the contour. The operations described above are implemented in a Model-Based Neural Network: a network in which the structure of layers and nodes and the values of the weights are parameterised by constraints of the problem domain. This speciic network calculates the invariance signature for a contour in an input image, and uses this as the input to hidden layers which form a traditional neural network classiier. It should be noted that the end result after constructing and training this system, is exactly the same as a traditional neural network: a collection of layers of nodes with weighted connections. The design and model-ing process can thus be thought of as \compiling" a shift, rotation and scale invariant classiier into a neural network. The nal product could be used at run-time on hardware or software designed solely for traditional neural networks. We contend that these invariance signatures, whilst David Squire was funded by an Australian Postgraduate Award not uniquely characterising any given contour, are suucient to characterise contours for many two-dimensional pattern recognition tasks. Results are presented demonstrating the utility of this technique for invariant pattern recognition.