One of the fundamental issues in image processing and machine vision is texture, specifically texture feature extraction, classification and abnormality detection. This thesis is concerned with the analysis and classification of natural and random textures, where the building elements and the structure of texture are not clearly determinable, hence statistical and signal processing approaches are more appropriate. We investigate the advantages of multi-scale/multidirectional signal processing methods, higher order statistics-based schemes, and computationally low cost texture analysis algorithms. Consequently these advantages are combined to form novel algorithms. We develop a multi-scale/multi-directionalWalsh-Hadamard transform for fast and robust texture feature extraction, where scale and angular decomposition properties are integrated into an ordinary Walsh-Hadamard transform, to increase its texture classification performance. We also introduce a highly accurate Gabor Composition method for texture abnormality detection which is a combination of a signal processing and a statistical method, namely Gabor filters and co-occurrence matrices. Furthermore, to overcome the practical drawbacks of traditional classification approaches, that require an extensive training stage, we introduce a method based on restructured eigenfilters for texture abnormality detection within a novelty detection framework. This demands only a minimal training stage using a few normal samples. The proposed schemes are compared with commonly used texture classification methods on different image sets, including a high resolution outdoor scene database, samples of the VisTex colour texture suite, and randomly textured normal and abnormal tiles. The results are then analysed in order to evaluate texture classification performance, based upon accuracy, generality and computational costs.