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、配准和分析可能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，这一点极其困难。不同的器官具有不同的拓扑和曲率分布，而且由于疾病进展、运动、成像、手术和治疗等原因，其形状可能会变形。我们建议使用共形几何来解决这一挑战，这是一种理论上严格、实际有效和健壮的方法。这个项目的广泛的，长期的目标是发展保形几何学作为医学成像的广泛的生物医学应用的主要工具。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，Ricci流，可以用来计算共形几何。它最近被应用于Poincaré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，并计划将其与其他共形几何方法一起应用于各种临床案例-结肠和大脑。该项目与健康相关的是显著改进临床应用的医学成像技术，从而改善诊断、程序规划、治疗、随访和临床研究。因此，医疗保健将得到实质性改善，患者参与筛查计划的人数将显著增加。该项目的具体目标是开发：(1)保角曲面展平；(2)用于体积参数化的保角映射；以及(3)使用保角映射的配准和融合。研究设计和方法将包括开发和验证技术，将3D器官表面共形展平为用于结肠息肉检测的规范参数表面。我们将进一步扩展扁平化，实现基于Ricci Flow的体积参数化，并将其应用于脑和结肠结构分割，以及肿瘤评估。此外，我们还将使用一个通用的规范参数域来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之内进行融合，以及结肠仰卧和俯卧位将被登记为改进的癌症筛查。表演现场(S)(组织，城市，州)石溪大学计算机科学和放射学系(纽约州立大学石溪分校)石溪，NY 11794-4400组织缩写：

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: