Collaborative Research: Data-Driven Elastic Shape Analysis with Topological Inconsistencies and Partial Matching Constraints

协作研究：具有拓扑不一致和部分匹配约束的数据驱动的弹性形状分析

• 批准号: 1953267
• 负责人: Nicolas Charon
• 金额: $ 15万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2024-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1953267&HistoricalAwards=false
• 关键词: Collaborative; Research; Data; Driven; Elastic

This research project focuses on data structures that are represented as curves or surfaces. Such structures occur in applications ranging from brain anatomy, computer vision, and molecular biology to meteorological and financial data. Data can be either directly acquired by devices such as laser scans or indirectly reconstructed from microscopy or magnetic resonance imaging. Such images and analyses appear for example in the study of human anatomy and motion or in applications to computer graphics and motion. The project lies in the broad area of statistical shape analysis, in which one tries to quantify geometric and/or topological variability within and across populations. The work aims to develop practical methods to characterize the shape of data objects in order to ascertain their roles in larger systems. The project will involve graduate students and produce open source software. The project relies on the paradigms of elastic shape analysis, which is traditionally concerned with analyzing the variability in the geometries of the objects under consideration. At its core is the notion of a distance between two shapes, which stems from a Riemannian setting using a metric that is invariant to the action of certain shape-preserving transformations and embeds both the global nonlinearity of the space as well as its local linearity. The first goal is to develop a comprehensive theoretical and numerical framework for elastic shape analysis of curves and surfaces that allows for topological inconsistencies and partial matching constraints. This framework combines elastic shape analysis with methods from geometric measure theory and topological data analysis. The second goal is to apply the framework to a wide variety of synthetic and real data, in particular to morphological analysis of high-resolution orthopedic surface complexes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个研究项目的重点是用曲线或曲面表示的数据结构。这种结构的应用范围从脑解剖学、计算机视觉、分子生物学到气象和金融数据。数据既可以通过激光扫描等设备直接获取，也可以通过显微镜或磁共振成像间接重建。这样的图像和分析出现在人体解剖学和运动的研究中，或者在计算机图形学和运动的应用中。该项目属于统计形状分析的广泛领域，其中试图量化人口内部和人口之间的几何和/或拓扑变化。这项工作旨在开发实用的方法来表征数据对象的形状，以便确定它们在更大的系统中的角色。该项目将涉及研究生，并生产开源软件。该项目依赖于弹性形状分析的范例，弹性形状分析传统上关注于分析所考虑的物体几何形状的可变性。其核心是两个形状之间距离的概念，该概念源于黎曼设置，该度量对某些形状保持变换的作用是不变的，并且嵌入了空间的全局非线性和局部线性。第一个目标是为允许拓扑不一致和部分匹配约束的曲线和曲面的弹性形状分析开发一个全面的理论和数值框架。该框架将弹性形状分析与几何测量理论和拓扑数据分析方法相结合。第二个目标是将该框架应用于各种各样的合成和真实数据，特别是高分辨率骨科表面复合物的形态分析。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

A Diffeomorphic Flow-Based Variational Framework for Multi-Speaker Emotion Conversion

• DOI: 10.1109/taslp.2022.3209948
• 发表时间: 2022-11
• 期刊: IEEE/ACM Transactions on Audio, Speech, and Language Processing
• 作者: Ravi Shankar;Hsi-Wei Hsieh;N. Charon;A. Venkataraman

Body mass classification from skeletal elements using landmark-free morphological atlas estimation with diffeomorphic shape mapping

使用具有微分同形形状映射的无地标形态图谱估计对骨骼元素进行体重分类

• DOI: 10.1117/12.2655795
• 发表时间: 2023
• 期刊: Medical Imaging 2023
• 作者: Li, Heyuan;Shi, Gengxin;Meckel, Lauren;Cunningham, Deborah;Wescott, Daniel J.;Sylvester, Adam D.;Charon, Nicolas;Zbijewski, Wojciech
• 通讯作者: Zbijewski, Wojciech

Supervised Deep Learning of Elastic SRV Distances on the Shape Space of Curves

曲线形状空间上弹性 SRV 距离的监督深度学习

• DOI: 10.1109/cvprw53098.2021.00499
• 发表时间: 2021
• 期刊: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR
• 作者: Hartman, Emmanuel;Sukurdeep, Yashil;Charon, Nicolas;Klassen, Eric;Bauer, Martin
• 通讯作者: Bauer, Martin

A New Variational Model for Shape Graph Registration with Partial Matching Constraints

具有部分匹配约束的形状图配准的新变分模型

• DOI: 10.1137/21m1418587
• 发表时间: 2022
• 期刊: SIAM Journal on Imaging Sciences
• 影响因子: 2.1
• 作者: Sukurdeep, Yashil;Bauer, Martin;Charon, Nicolas
• 通讯作者: Charon, Nicolas