Hypercomplex correlation techniques for vector images

Correlation techniques have been applied to almost every area of signal processing over the past century, yet their use has, in general, been limited to scalar signals. While there have been implementations in multichannel applications, these can be characterized as a combination of single channel processes. True vector correlation techniques, with global and interchannel measures, have only recently been demonstrated and are still in their infancy by comparison. This paper describes our work on vector correlation based on the use of hypercomplex Fourier transforms and presents, for the first time, a unified theory behind the information contained in the peak of a vector correlation response. By using example applications for color images, we also demonstrate some of the practical implications, together with our latest results.