Bounds on (Deterministic) Correlation Functions with Application to Registration

The auto/cross correlation of L2 functions are constrained by certain bounds which may often be used to advantage. These bounds apply to all the common cross correlation functions used for registration purposes (called ``deterministic'' correlation functions in this paper, as opposed to stochastic correlation based on non-L2 functions). It is shown that the envelopes of deterministic autocorrelations have essentially a cosine-like behavior but with jump discontinuities at points where the normalized relative displacement is the reciprocal of an integer. Several inequalities extending these results are given. It is shown how these can be applied toward obtaining improved registration algorithms.