This thesis describes a number of approaches to the problems of automatic defect detection in ultrasonic Time of Flight Diffraction (TOFD) and X-ray radioscopic images of butt welds in steel plate. A number of novel image segmentation techniques are developed, two of which feature the use of backpropagation artificial neural networks. Two new methods for defect detection in ultrasonic TOFD images are described - the first uses thresholding of individual one-dimensional A-scans, and the second uses a neural network to classify pixels using two dimensional local area statistics. In addition, three new methods for defect detection in radioscopic images are described - the first is based on the use of two conventional spatial filters, the second uses grey level morphology to replace the 'blurring' stage of conventional "blur and subtract' procedures, and the third uses a neural network to classify pixels using raw grey level data at the input layer. It is considered that all five methods which have been developed show novelty in their methodology, design and implementation, most specifically in that (1) no previous methods for automatic defect detection in TOFD images, (2) very few successful implementations of grey level data processing by neural networks, and (3) few examples of local area segmentation of 'real' textured images for automatic inspection have been reported in the literature. The methods developed were tested against data interpreted by skilled NDT inspectors. In the case of the ultrasonic TOFD image processing, both automatic methods performed exceptionally well, producing results comparable to that of a human inspector. In the case of the radioscopic image processing, the ANN method also produced results comparable to that achieved by a human inspector and also gave comparable or consistently better results than those obtained using a number of existing techniques.