Conformal Geometry for Medical Imaging

State University New York Stony Brook, Stony Brook NY

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Abstract

It is paramount in medical imaging to measure, compare, calibrate, register and analyze potentially deformed organ shapes with high accuracy and fidelity. However, this is extremely difficult due to the complicated shape of human organs. Different organs have different topologies and curvature distributions, and furthermore, the shape may deform due to disease progression, movement, imaging, surgery and treatment. We propose to use conformal geometry, a theoretically rigorous and practically efficient and robust method, to tack this challenge. The broad, long-term objective of this project is to develop conformal geometry as a primary tool in the vast biomedical applications of medial imaging. Conformal structure is a natural structure, ideally suited to study shape matching and deformation. A powerful tool, Ricci flow, can be used to compute conformal geometry. It has been applied recently in the proof of the Poincar[unreadable] conjecture. We have developed practical computational algorithms to compute Ricci flow, obtained promising preliminary results, and plan to apply it with other conformal geometric methods in a variety of clinical case-studies for the colon and brain. The health relatedness of the project is to dramatically improve medical imaging techniques for clinical applications, thereby improving the diagnosis, procedure planning, treatment, follow-ups and clinical research. Consequently, health care will be substantially improved, as well as patients'participation in screening programs will be noticeably increased. The specific aims of this project are to develop: (1) conformal surface flattening;(2) conformal mapping for volumetric parameterization;and (3) registration and fusion using conformal mapping. The research design and methodology will include developing and validating techniques to conformally flatten 3D organ surfaces to canonical parametric surfaces for colonic polyp detection. We will further extend flattening to implement volumetric parameterization based on Ricci flow and then apply it to brain and colon structure segmentation, and tumor evaluation. In addition, we will implement shape registration and data fusion using a common canonical parameter domain. Brain data sets will be fused between and within subjects and modalities, as well as colon supine and prone will be registered for improved cancer screening. PERFORMANCE SITE(S) (organization, city, state) Departments of Computer Science and Radiology Stony Brook University (SUNY at Stony Brook) Stony Brook, NY 11794-4400 Organization abbreviation: