Optimization- and learning-based algorithms for medical image computing

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1) Problems, difficulties and prior art: Finding automatically and efficiently meaningful regions in a numerical image, for instance an organ in a 3D medical scan or a person in a photograph, is a research problem of paramount importance within the computer vision and medical imaging communities for its theoretical and methodological challenges, and numerous useful applications. Current major application areas include medical image analysis, robotics, human-computer interaction, image retrieval and editing, security and surveillance, navigation, manufacturing, remote sensing and many others. For instance, in medical imaging, automatic detection and visualization of the 3D surfaces of anatomic structures is essential to efficient disease diagnosis/treatment/follow-up, surgery planning, radiologic reporting and health care practices at large. From a technical point of view, such detection problems are difficult and often application-dependent because of the various and complex appearances of medical scans. Mostly based on classical compute-vision techniques, the methods in the literature can handle only a small fraction of real-world problems because of the following reasons: (i) they do not take full advantage of the available prior knowledge, i.e., the contextual information that a machine can learn from a set of training structures/surfaces produced by a human expert. The mathematical descriptions used so far to model such knowledge are not complex enough to reflect human understanding of medical scans; and (ii) they may be very slow in many real-world scenarios. 2) Objectives: The overall objective of this research program is to develop fully trained, efficient (real-time) and theoretically sound algorithms for the automatic detection and visualization of the 3D surfaces of various organs from medical scans. Specific objectives include: (i) Theoretical objectives: We intend to define novel energy functionals based on information-theoretic measures and recent advances in machine learning. We further intend to design original and efficient optimization techniques for such functionals. The overall purpose is to determine solutions which embody important prior knowledge that has been either omitted or oversimplified in current algorithms; and (ii) Practical objectives: In practice, we plan to devise our technical investigations to solving various challenging and important problems, e.g., finding the 3D structures of the aorta, spine, heart, liver, prostate, brain tumors, as well as multiple abdominal organs, just to name a few examples. 3) Scientific approach: (i) Methodology: Our methodology is based on the following main steps: (a) building sophisticated functionals that describe contextual knowledge about the structures of interest (e.g., shape, geometric relations between several organs and high-level medical knowledge) using training data built by human experts; (b) investigating mathematically and solving numerically the minimization of the new functionals; and (d) evaluating experimentally the algorithms by comparisons to ground-truth data built by human experts. (ii) Technical and theoretical novelty/significance: We anticipate that our formulations lead to challenging optimization problems, which cannot be solved directly with standard techniques. We intend to derive original approximations or bounds, thereby designing novel and efficient optimization techniques that are still not in use in computer vision and medical imaging. We intend to focus on optimization-transfer and convex relaxation approaches. We anticipate the solutions we intend to develop will (a) be applicable to a breadth of problems; and (ii) yield state-of-the-art performances in regard to accuracy and speed.