Degree: Doctor of Philosophy Abstract: Image texture is defined as visual patterns appearing in images. The powerful perceptive capability of texture features has made texture analysis a major research topic in computer vision and image processing. Texture features are used to detect defective products in factories, to understand human actions in surveillance systems, to identify people from biometric data (e.g., fingerprint, iris scan, and face photo), and to find abnormality in medical images. Indeed, many advanced applications take a direct or indirect advantage of texture analysis in their processing. An ideal texture feature should not only be discriminative but also be robust to imaging distortions. The developement of robust texture features is first motivated by applying texture analysis to Amyotrophic Lateral Sclerosis (ALS). ALS is a fatal neurodegenerative disease in which evidence of the disease is not perceptible in routine magnetic resonance images (MRI) of the brain even to a trained eye. Unlike brain tumors or multiple sclerosis, the lack of observable features possesses challenges to the detection and diagnosis of ALS. These challenges and the great need in the ALS research community to find a biomarker and to detect the patterns of degeneration in the brain have encouraged the author to study this disease using texture analysis. The results of this thesis suggest texture analysis is a potential biomarker for the disease and hence, open up new avenues towards understanding the disease. This thesis presents a useful approach for texture analysis of the brain. In contrast to the current methods, the proposed approach does not need a region of interest. It performs a voxel based texture analysis and provides a statistical map showing the regions in the brain statistically different between the groups of patients and healthy subjects. A Computer Aided Diagnosis (CAD) tool is developed for this purpose. This toolbox is called the Statistical MAp fRom Texture (SMART) and helps doctors make diagnoses and monitor the progression of diseases using texture analysis. Distortions and effects in real images (e.g., noise, illumination change, blurr effect) increase demand for developing robuts texture features. To address the robustness issues, a novel approach is presented called the Local Frequancy Descriptor (LFD). The LFD is the basis of several novel 2D and 3D texture features presented later in this thesis. It is also the basis of new image gradient operators for 2D and 3D images and a novel image matching method. All texture features, methods, and gradient operators defined based on the LFD show high accuracy and outperform the state-ofthe-art methods. In addition, they present remarkable robutness to imaging effects.