The rest of the thesis is organized as follows. Chapter 2 presents a tutorial on general probability theory and statistical inference. It describes the important mathematical concepts, and the notation, concerning nonparametric statistics, information theory, and MRFs that form the foundation of many of the key ideas in this dissertation. The next five chapters give the new ideas and algorithms in this dissertation for several applications. We present the related work from literature concerning each of these approaches as a part of each of those chapters. Chapter 3 presents the theoretical and engineering aspects of the adaptive-MRF image model. All subsequent chapters present adaptive image-processing methods that rely on this image model. The next two chapters, i.e., Chapters 4 and 5, present algorithms for image restoration in the absence and presence of the knowledge of the degradation process, respectively. Chapter 5 specifically concerns denoising MR images. Chapter 6 presents a method for classifying brain tissues in MR images. The optimality criteria for segmentation in this chapter are applied to texture segmentation in Chapter 7. Chapter 8 summarizes the dissertation and discusses a few directions for extending the work.