Fast 2-D Hartley transform in 3-D object representation and recognition

In image processing or computer vision, Fourier transform is widely used for frequency-domain analysis. However, Hartley transform can be a very good substitute for more commonly used Fourier transform when the real input data are concerned. A two-dimensional butterfly algorithm for fast Fourier transform has been modified to calculate the Hartley transform faster than that of using row-column decomposition. This paper presents three different frequency-domain registration techniques, power cepstrum, complex cepstrum and phase correlation. These techniques not only are capable of precise registration of images but also lead to three-dimensional (3-D) reconstruction of real objects by finding the corresponding points and disparities of an image pair. Use of these recently developed techniques allows one to obtain a precise displacement between two images and a quantitative measurement of 3-D information in a relatively faster computation time. Hartley transform can be used to implement all of these three techniques instead of using complex number computation required by Fourier transform. An additional 35 percent saving of the computation time is achieved by implementing the two-dimensional butterfly algorithm for computing Hartley transform. This reduction in computation time makes the use of Hartley transform in frequency-domain analysis more attractive.