A brief overview of the properties of the Gauss-Laguerre circular harmonic functions and the associated transform is given. Based on these properties, an efficient algorithm is developed for computing a normalized cross-correlation, in the full space of translation and rotation, between an image and template. The resulting algorithm is compared to standard spatial and frequency domain normalized cross-correlation in terms of computational complexity. The capabilities of the algorithm are illustrated in a complex scene.
A new resolution refinement method is introduced for template-matching. Fine-correlation uses sample replication to re ne match-accuracy to discrete inter-sample positions. Fine-correlation can be done in both the time and frequency domain. The achievable resolution-re finement is a function of signal-to-noise ratio; signal bandwidth; template-length and template information content. Templates can easily be described to a 10 times or higher time-resolution than the incoming signal. Fine-correlation provides a method of matching in such scenarios. Possible implementations are discussed. The preferred method is chosen. A noise-level- and templatelength analysis is done illustrating achievable resolution improvement. Two implementations of Fine-correlation conclude this paper. An appendix is devoted to the derivation of the resampling DFT and resampling DHT.