The Recognition of Shapes In Binary Images Using a Gradient Classifier

A prototype-based shape classifier that makes comparisons based on blurred representations of binary images is considered. The blurring induces a metric on the space of all images that varies continuously under continuous deformation of the image plane. This blurred representation is suitable for direct implementation of a nearest neighbor classifier. However, it is still desirable to have a representation that is invariant under certain spatial deformations, such as rotation, translation, and scaling of the image plane. A representation that is invariant under these transformations is produced by transforming an input to a local minimum of its distance from each prototype simultaneously. These minima are found by performing a gradient descent on an appropriate error surface defined over the transformation parameters. The error functional is the $$2-norm of the difference between the blurred prototype and the blurred input. The resulting classifier makes more efficient use of prototypes than the nearest neighbor classifier.