Alzheimer's disease (AD) is the most common progressive neurodegenerative disorder. Therefore, early detection and evaluation of prognosis of AD is an important issue in contemporary brain research. Magnetic Resonance Imaging (MRI) provides valuable diagnostic information about AD. In this work, brain tissue is extracted using phase-based level set method. Structure tensor analysis is used to visualize and quantify structural features of the brain from MRI. Further, quantitative measures are derived to classify different stages of AD. Normal and AD subjects were classified up to an accuracy of 88% using these features. It is observed that structural changes in brain can be characterized using this technique and therefore can be helpful in tracking the progression of AD and aid in classification between normal and AD subjects.