CRII: ACI: 4D Dynamic Anisotropic Meshing and Applications

在医疗保健、交通和仿真领域中，需要实时地从复杂场景中逼真地重建、可视化和捕获时空（4D）模型/图像（动态对象）。例如，实时地对器官及其周围组织的4D可变形形状和变化进行高保真动态建模和可视化对于构建用于放射治疗的有效4D模型规划/捕获（例如，4D-Doctor系统）。它需要动态各向异性建模和多模态成像技术，以实现准确的配准、分割和可视化。该项目的目标是开发一种工具，用于高效地计算具有大规模体积图像数据中的特征和细节的复杂4D对象的高质量4D动态各向异性网格模型。该项目涉及几何建模、计算机图形学和医学图像处理等多个学科，有可能为跨学科研究和教育整合提供一个高质量的平台。该项目旨在丰富韦恩州立大学本科和研究生阶段的计算机科学和工程课程。因此，本文的研究符合NSF推动科学进步和促进国民健康、繁荣和福利的使命，建立高质量和高效率的4D动态各向异性网格划分的理论和计算框架对于有效地表示和捕获4D数据是必不可少的。该项目的主要优势在于基于粒子的黎曼度量网格建模方法的变革性研究思想和方法，为几何引导的3D/4D成像信息学奠定基础。建议的探索性研究活动将针对以下主要主题和目标：（1）开发一种新的基于粒子的高质量三维和四维各向异性四面体网格划分方法;（2）评估网格质量并将所提出的理论网格化方法应用于医学成像，并开发测试床系统以评估其在4D-Doctor系统中的能力和潜力，包括4D图像配准和分割。统一的理论基于粒子的网格框架，集成高斯能量，动态黎曼度量，和高维嵌入理论，可以从一个全新的角度，使高效生成动态各向异性网格。这项研究计划是创新的，因为它将建立一个新的几何建模框架，支持3D/4D成像信息。

There is an emerging need in healthcare, transportation, and simulation areas to realistically reconstruct, visualize, and capture space-time (4D) models/images (dynamic objects) from a complicated scenario in real-time. For example, high-fidelity dynamically modeling and visualizing 4D deformable shapes and variations of organs and their surrounding tissues in real-time become important for building an effective 4D model planning/capturing for radiation therapy (e.g., 4D-Doctor system). It requires dynamic anisotropic modeling and multi-modality imaging techniques for accurate registration, segmentation, and visualization. The goal of this project is to develop a tool for efficiently computing high-quality 4D dynamic anisotropic meshing models for complicated 4D objects with features and details in the large-scale volume image data. This project involves several disciplines, such as geometric modeling, computer graphics, and medical image processing, and has a potential to provide a high-quality platform for both interdisciplinary research and education integration. This project will aim to enrich the computer science and engineering curriculum at Wayne State University in both the undergraduate and graduate levels. Therefore, this research aligns with the NSF mission to promote the progress of science and to advance the national health, prosperity and welfare.A theoretical and computational framework for 4D dynamic anisotropic meshing with high quality and efficiency is essential for tackling challenges in efficiently representing and capturing the 4D data. The key strength of this project focuses on the transformative research ideas and approaches in particle-based approach for Riemannian metric mesh modeling, serving as a foundation for geometry-guided 3D/4D imaging informatics. The proposed exploratory research activities will address the following major themes and objectives: (1) to develop a novel particle-based method for high-quality 3D and 4D anisotropic tetrahedral meshing; (2) to evaluate the mesh quality and apply the proposed theoretical meshing approaches in applications to medical imaging, and develop a testbed system to evaluate its capability and potential in 4D-Doctor system, including 4D image registration and segmentation. The unified theoretical particle-based meshing framework, integrating Gaussian energy, dynamic Riemannian metrics, and high-dimensional embedding theory, can enable efficient generation of dynamic anisotropic meshes from a brand new perspective. This research initiative is innovative as it will establish a novel geometric modeling framework supporting 3D/4D imaging informatics.