Invariance with respect to certain transformations is of great interest to pattern recognition, e.g. in many cases affine transformations do not affect the class membership of image object data. SIMARD et al. [1] introduced an effective means to compensate for small affine transformations in distance based classifiers called tangent distance (TD), which led to very good results in optical character recognition (OCR). In this paper we present results of experiments with this distance in a kernel density (KD) based classifier, proposing the usage of virtual test data in addition to virtual training data. On the original United States Postal Service (USPS) OCR-database we obtain an error rate of 2.2%. Furthermore, we propose a simple but effective image distortion model (IDM) and relate it to tangent distance. The IDM considerably increased performance of the classifier with and without tangent distance on a database of medical images containing 1617 radiographs coming from daily routine.
Many approaches to invariant pattern recognition are known [2] and TD has been used in a variety of settings, including neural networks and memory based techniques like (k-) nearest neighbor algorithms (k-NN) [3], while in our experiments KD based classifiers obtained better results. A number of solutions have been proposed for efficient implementation of such algorithms, e.g. usage of hierarchical confidence refinement [4] or models for representing large subsets of the prototypes [5]. An approach motivated by deformable models, which is related to the invariance approaches covered in this paper, was proposed in [6] and tested on a face database. In comparison to TD and IDM it uses different assumptions about the allowed transformations and their cost.