The recognition of shapes in binary images using a gradient classifier

The authors consider a prototype-based binary image classifier that makes comparisons based on blurred representations of the images. 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 which is invariant under certain spatial deformations, such as rotation, translation, and scaling of the image plane. A representation which is invariant under these transformation 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 over the transformation parameters. The error functional is the L₂-norm of the difference between the blurred prototype and the blurred input. The resulting classifier makes more efficient use of prototypes than does the nearest-neighbor classifier