Geometric and Combinatorial Algorithms for Optimal Surface Segmentation in Medical Images

有效地检测代表体积图像中对象边界的全局最优曲面是现代计算机辅助医疗诊断和治疗以及许多其他重要医疗应用中的基本问题和挑战。这项研究的具体问题是如何在体图像数据集中检测最优的单个和多个交互曲面。它允许识别地形形状、圆柱形形状和复杂形状的最佳表面。我们考虑的图像数据集具有各种不同的图像特征，如边缘、纹理和形状。这些问题的实质是解决一些属于计算几何基本问题的重要几何优化问题，如曲面识别、几何划分、几何k-均值聚类、度量标号等。这个项目的研究重点是开发高效的算法和新的技术来解决这些关键问题，并证明是全局最优的。几何和组合技术在医学问题中的应用在智力上是深刻的，可以导致理论计算机科学和医学的进步。所提出的图像分析方法允许以定量的方式客观地评估图像数据，有望对基于图像的临床护理产生重大影响。这项研究的一个重要目标是将软件中实现的算法传播到应用领域。在这方面，它有助于将计算机科学和医学界联系在一起。智力优点：我们期待这个项目做出一些理论贡献：(1)为解决当前医学研究和应用所面临的一系列关键计算问题提供新的算法技术；(2)将新的和理论上有趣的问题和算法引入几何和组合优化，丰富和推动该领域的进一步发展；(3)为图形算法和运筹学等其他理论领域提出新的具有挑战性的问题和新的方法，并为这些领域带来新的应用。广泛的影响：该项目的成功完成将导致极大地加快3-D和4-D医学图像处理的速度。自动图像分割软件将独立于平台，并将直接满足从基础研究到临床医学等广泛学科的广泛终端用户的需求。拟议的图像分析工具将为临床医生提供以3-D和4-D方式评估病变器官的手段，而不是像传统做法那样以2-D方式进行评估。此外，将研究成果注入课堂，为学生提供了在涉及计算机科学和现代医学的新兴重要交叉学科领域学习和实践的独特机会，促进了跨学科学习，并使更多多才多艺的科学家得以培养。

Efficient detection of globally optimal surfaces representing object boundaries in volumetric images is fundamental and remains challenging in modern computer-assisted medical diagnosis and treatment and many other important medical applications. This research deals with specific problems of detecting optimal single and multiple interacting surfaces in volumetric image datasets. It permits identification of optimal surfaces of terrain-like shapes, cylindrical shapes, and complex shapes. Image data sets we consider have various different image features, such as edge, texture, and shape. The essence of these problems is to solve a number of important geometric optimization problems belonging to the fundamental topics of computational geometry, such as surface identification, geometric partitioning, geometric k-means clustering, and metric labeling. The research focus of this project is on developing efficient algorithms and novel techniques for solving these crucial problems with a provably global optimality. The application of geometric and combinatorial techniques to medical problems is intellectually deep and can result in advances in both theoretical computer science and medicine. The proposed image analysis methods allow evaluating the image data objectively in a quantitative manner, promising to substantially impact image-based clinical care. An important goal of this research is dissemination of implemented algorithms in software to application domains. In doing this, it helps to bring together the computer science and the medical community.Intellectual Merit: We expect this project to make a number of theoretical contributions: (1) providing new algorithmic techniques for solving a set of crucial computational problems confronted by current medical research and applications; (2) introducing fresh and theoretically interesting problems and algorithms to geometric and combinatorial optimization, enriching and prodding further development of the field; (3) presenting new challenging problems and new approaches to other theoretical areas such as graph algorithms and operations research, and bringing new applications to these areas.Broader Impacts: The successful completion of this project will result in methodologies that greatly accelerate the pace of 3-D and 4-D medical image processing. The automated image segmentation software will be platform independent and will directly address the needs of a broad base of end users across a wide range of disciplines from basic research to clinical medicine. The proposed image analysis tools will provide clinicians with the means to assess diseased organs in 3-D and 4-D, rather than in 2-D as is typically done in conventional practice. In addition, infusion of the research results into the classroom provides students with a unique opportunity to study and practice in the emerging important interdisciplinary area involving computer science and modern medicine, promotes interdisciplinary learning, and enables the training of more versatile scientists.