Parameter isolating transforms and admissible distortions

An often encountered pattern recognition problem is that of identifying a given image as related to one of a set of prototypes even though they may differ by virtue of the action of a non-linear mapping of image points. Certain parameterized distortions are such that a transform may be found that has the property of isolating the distortion effect as a factor in the transform space allowing subsequent identification and removal of the distortion. Herein the most general form of distortion is found that allows a related transform with such properties to be constructed. Furthermore a test for the admissibility of a distortion is given as well as the general form of the required parameter isolating transform.