Conformal Geometry for Medical Imaging

在医学成像中，以高精度和保真度测量、比较、校准、登记和分析潜在变形的器官形状是至关重要的。然而，由于人体器官的复杂形状，这是极其困难的。不同的器官具有不同的拓扑结构和曲率分布，此外，由于疾病进展、运动、成像、手术和治疗，形状可能会变形。我们建议使用保形几何，这是一种理论上严谨，实际上有效和健壮的方法，来应对这一挑战。该项目的长远目标是发展保形几何，使其成为医学成像在生物医学领域广泛应用的主要工具。保形结构是一种自然结构，非常适合研究形状匹配和变形。一个强大的工具，里奇流，可以用来计算保形几何。它最近被应用于庞加莱猜想的证明中。我们已经开发了实用的计算算法来计算Ricci流，获得了有希望的初步结果，并计划将其与其他适形几何方法一起应用于结肠和大脑的各种临床病例研究中。该项目的健康相关性是显著改善临床应用的医学成像技术，从而改善诊断、手术计划、治疗、随访和临床研究。因此，医疗保健将大大改善，患者对筛查方案的参与将显著增加。该项目的具体目标是发展：(1)保形面扁平化；(2)保角映射用于体积参数化；(3)保角映射配准融合。研究设计和方法将包括开发和验证技术，以保形平面三维器官表面为规范参数表面，用于结肠息肉检测。我们将进一步扩展扁平化，实现基于Ricci流的体积参数化，然后将其应用于脑和结肠结构分割、肿瘤评估。此外，我们将使用一个通用的规范参数域实现形状配准和数据融合。大脑数据集将在受试者和模式之间和内部融合，以及结肠仰卧和俯卧将被登记，以改进癌症筛查。表演地点(S)（组织，城市，州）石溪大学（SUNY at Stony Brook）计算机科学与放射学系，NY石溪11794-4400

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 Poincaré 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: