As the use of medical imaging starts to reach beyond the diagnosis of structural abnormalities of relatively focal character, the need for computer-based methods and algorithms that detect spatio-temporally complex patterns of structure and function becomes more imperative. This talk discusses the development of such methods, which combine image analysis, shape statistics and pattern recognition principles, in order to extract pertinent information from medical images, and use it for diagnostic or prognostic purposes. Several current challenges in dealing with high-dimensional medical image data will be discussed, which could potentially be overcome using mathematical models and analysis developed by the applied math community.