Computational Methods for Image Rotation and Computer Aided Tomography Volume I: Theoretical Basi. Volume II: Computer Software

Abstract

This thesis, describes work whose principal goal has been to research and identify an optimum algorithm for computing the Radon transform - optimum in the sense of minimum CPU time for maximum image fidelity. This transform is the basis for a wide range of applications which are either directly or indirectly associated with Computer Aided Tomography. It has therefore been important to try and identify an optimum computational technique for the evaluation of this transform. A central theme to the computational techniques reported in this thesis has been the digital image rotation for which a new algorithm has been designed based entirely on integer arithmetic. This algorithm has been used for the evaluation of the forward and inverse Radon transforms (in particular, forward and back-projection). The relationship between the interpolation methods used for image rotation and the filtering techniques required to compute the inverse Radon transform has been studied in detail. The result of this study has been to identify a specific data processing path which provides an algorithm whose 'computational energy' is approximately half that of previously published algorithms. With an optimum algorithm identified, research has been undertaken into the use of the Radon transform for two-dimensional array processing. It is shown that the Radon transform can be used to reduce the dimensionality of a problem from two-dimensions to a one-dimensional problem. By applying signal processors to the set of projections obtained by taking the Radon transform of an image, the inverse Radon transform can be used to reconstruct the processed image. The value of this approach lies in the fact that some useful one-dimensional signal processing algorithms do not have a two-dimensional extension or else the implementation of the two-dimensional algorithm is computationally intensive. An example of the latter case is reported.