Javid, Shawn Farhang; (1991) Three-dimensional image processing using voxels. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis investigates the differences between results obtained by applying two- dimensional operators to sequences of slices through three-dimensional image data, and by applying three-dimensional operators to the same data. Emphasis is placed on the differing results for surface extraction which are obtained when the surfaces are generated from two- dimensional edge operators or directly from three-dimensional surface operators. In particular, three-dimensional surface detection operators are shown to perform better than the concatenation of edges derived from their two-dimensional analogues. Several new contributions to the fields of pixel and voxel processing are made. Dodecahedral connectivity is presented as a solution to the three-dimensional connectivity paradox. The problem of edge and surface detection is examined in detail. Derivations and proofs of new morphological properties of arbitrary dimension Laplacian operators and zero-crossing detection algorithms are provided, as are the conditions under which they can be successfully applied, and what form is most appropriate for a desired resultant topology. New, more accurate approximations of the three-dimensional Laplacian are also derived and applied. The performance of a small class of fundamental, yet well established, differentiation based local neighbourhood edge and surface detection operators is examined in the presence of noise and under varying slicing conditions. This simple class of operators has been chosen to provide an initial framework for an investigation which could be extended to more sophisticated operations. A survey of binary digital topology in two and three dimensions is provided giving a theoretical basis for the comparison between differences in output of edge and surface detection operators. Also, a survey of many of the types of operators one is typically interested in applying to pixels is provided where the operators are extended to operate on voxels, and numerous examples are provided which demonstrate the differences between them with regards to resultant topology. Operators such as spatial and frequency transforms, filtering, and the like are described, extended to three-dimensions, and applied to real world data. Edge and surface detection operators arc applied to real world data sets consisting of MRI slices through regions of the human body and serial section microscopy slices through organs of a rat, and a simple approach to the use of the output of edge and surface detection operators is described. The image and volumetric processing algorithms are implemented within a new interpreted software environment. A description is provided of the design and implementation of this software which is divided into several layers in order to meet the needs of different levels of users. The environment is simple yet powerful, hides the complexity often associated with interacting with image processing devices, and is device independent, extensible, and portable. It has proved useful in both the 'rapid prototyping' of image processing algorithms as well as the analysing of such algorithms. Since the visualisation of three-dimensional data is inherently more difficult than that of two-dimensional data, a survey of different solutions to the display of voxel data is presented. Demonstrations of some of the methods are given on segmented real world objects and a new pattern recognition approach to the fitting of polygons to surfaces is presented and compared with other known methods. Given that acquisition of voxel data sets has become commonplace, the analysis performed in this thesis is expected to be applicable in many disciplines.

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