In this article, we introduce the ongoing research in modeling and mapping for heterogeneous, customizable, parallel systems, as part of the effort in the newly established Center for Domain-Specific Computing (CDSC). This research combines the diverse backgrounds from multiple disciplines, including computer science and engineering, electrical engineering, medicine, and applied mathematics. The goal of this project is to look beyond parallelization and to focus on domain-specific customization as the next disruptive technology to bring orders-of-magnitude power-performance efficiency improvement to important application domains. The project initially focuses on medical imaging applications, which provide an important tool in diagnosis and treatment of most medical problems, but many advances in this field have been constrained to the research environment due to a lack of computational power. Orders of magnitude in power-performance efficiency improvement that this project is expected...