Abstract:
This thesis is concerned with the development of a practical framework for the processing of images sampled on a hexagonal lattice. Processing of images on a hexagonal lattice is generally considered beneficial for several reasons. Firstly, the lattice has a greater packing density allowing more samples per unit area. This allows more information to be extracted from the visual stimuli. Secondly, each point in a hexagonal lattice has a uniform distance from its neighbours. This uniform connectivity is particularly useful when dealing with images which contain curved structures. Finally, due to the oblique nature of hexagonal pixels, images appear perceptibly less blocky than square images of equivalent resolution. The proposed framework addressed four issues which are considered crucial to the development of a viable and practical hexagonal image processing system. These are addressing, sampling, processing, and display. In this thesis an addressing scheme is developed which is hierarchical, spatiotopic, and computationally efficient. Additionally, the scheme only requires a single digit index to address every point in the hexagonal lattice. The proposed sampling scheme reorders square images to produce hexagonal images. It does this by converting hexagonal addresses to Euclidean coordinates and using a bi-linear sampling kernel. Many image processing applications were developed within the framework using the addressing scheme. These include, but are not limited to, morphology, edge detection, fast Fourier transform, and pyramidal decomposition. Additionally, several applications were developed to further illustrate the utility of the proposed scheme. Display was achieved using graphics hardware to render the hexagons. The proposed framework for hexagonal image processing was found to be very computationally efficient. This is primarily due to the addressing scheme. A detailed comparison with square image processing found it to be more computationally efficient in most regards. This is even considering the additional overhead due to sampling and display of image data. This advantage along with the qualitative benefits lead to a strong argument that the time is ripe to consider hexagonal image processing in earnest.