Colour information as a third dimension in Fourier transform and correlation

Image processing is carried out in general with monochromatic information. So it does not consider the colour information of the objects. However, the human visual system is very sensitive to the colour information, so it seems logical to introduce this information to increase the capacity of computer-based systems. Obtaining all the spectral information for each pixel of an image could between expensive but the image acquisition systems may provide several images each one corresponding to a special sub-band. In this paper we introduce the colour as the third dimension of images and extend the definition of Fourier transform and correlation to these signals. Firstly, we study the Fourier transform properties of these 3D images, paying special attention to the third dimension, which contains the colour information. Then, the correlation operation is studied. As an application, we extend the pattern recognition method based in correlation to these signals and we show the advantages of introducing the colour information