On Optimum Recognition Error and Reject Tradeoff

The performance of a pattern recognition system is characterized by its error and reject tradeoff. This paper describes an optimum rejection rule and presents a general relation between the error and reject probabilities and some simple properties of the tradeoff in the optimum recognition system. The error rate can be directly evaluated from the reject function. Some practical implications of the results are discussed. Examples in normal distributions and uniform distributions are given.