A Theory of Pattern Rejection

The e ciency of pattern recognition is critical when a large number of classes are to be discriminated, or when the recognition algorithm needs to be applied a large number of times. We propose and analyze a general technique, namely pattern rejection, that results in e cient pattern recognition. Rejectors are introduced as algorithms that can very quickly eliminate from further consideration most classes or inputs (depending on the setting). Rejectors may be combined to form composite rejectors, which are more e ective than any single rejector. Composite rejectors are analyzed and conditions derived which guarantee both e ciency and practicality. A general technique is proposed for the construction of composite rejectors, based on a single assumption about the classes. The generality of this assumption is shown through its connection with the Karhunen-Lo eve expansion. A relation of pattern rejection with Fisher's discriminant analysis is also shown. Composite rejectors were constructed for two applications, namely, object recognition and local feature detection. In both cases, a substantial improvement in e ciency over existing techniques was found.