This thesis documents the research into a method for object recognition in colour images based on a new method for coding the chromatic information for each pixel. It is based on the use of Fourier transforms where the outputs of the Fourier transforms are used to generate information about an object.

It is of use in situations where the monochromatic recognition of objects either fails or is not applicable. In addition, for the processing described in this thesis, it overcomes problems with Fourier transforming separate colour components which is the traditional method used in Fourier transforming colour images.

The research described in this thesis has used Fourier transforms to correlate two colour images. The colour is encoded so that the chromatic information is stored as a complex number for each pixel. This is made possible by storing the colour not as RGB values but as hue and saturation values so that only two components are required to describe the chromaticity, while intensity is kept separate. This enables the location of colour objects using phase correlation, where previously it would either have been impossible or would have required more Fourier transforms to have been calculated. This processing is combined with the use of the Fourier-Mellin transform to enable the quantification of the translation, rotation and scaling of an object in an image in comparison with an object in a reference image. This has obvious uses in industrial applications.

The Fourier-Mellin transform can be implemented using Fourier transforms and log-polar sampling of the pixels. Unfortunately, this non-linear sampling can reduce the accuracy of the phase correlation peak which is used to determine the scaling and rotation values so a novel spatially variable filter has been developed to reduce the possibility of the log-polar sampling ignoring pixels containing valuable data.

The use of the new representation for colour together with Fourier transform techniques has resulted in the use of quaternions for storing full colour. The supervisor of the author has developed a discrete Fourier transform (QDFT) which has been proven to convolve a colour image successfully. However, using the current QDFT with correlation produces a correct peak but also three other incorrect peaks. Much further work is needed if correlation is to be implemented using quaternions and other applications are to be explored.

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