Phase correlation functions: FFT vs. FHT

Abstract

The ability to process an image is a crucial skill in many measurement activities. In image processing or pattern recognition, Fast Fourier Transform (FFT) is widely used. In particular, the Phase Only Correlation (POC) method demonstrates high robustness and subpixel accuracy in pattern matching. However, there is a disadvantage in the required memory machine because of the calculation of 2D-FFT. In applications in which the use of memory is a critical element, Fast Hartley Transform (FHT) seems to be a good substitute. In this context, the use of Hartley's transform can be of interest for apps implemented on portable systems e.g. smartphones. In this article, we present a comparison of the implementations of the phase correlation function using FFT and FHT. Particular attention is given to the analytical steps necessary to implement the POC by means of the Hartley transform.