CAREER: Shape Analysis in Submanifold Spaces: New Directions for Theory and Algorithms

职业:子流形空间中的形状分析:理论和算法的新方向

基本信息

  • 批准号:
    1945224
  • 负责人:
  • 金额:
    $ 45.12万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2020
  • 资助国家:
    美国
  • 起止时间:
    2020-02-01 至 2025-01-31
  • 项目状态:
    未结题

项目摘要

Shape analysis has now become an integral component of data science as it is key to modelling and analyzing quantitatively the geometric variability within datasets for applications as diverse as computer vision, speech/motion recognition, morphogenesis or computational anatomy. Among the variety of geometric structures that are studied in this field, curves, surfaces and more generally manifolds are both very natural objects but also particularly challenging to process and analyze due to the non-canonical structure of the corresponding shape spaces. This has in part hindered the development and effectiveness of shape analysis frameworks for such data, if compared for instance to the more widely studied case of images. This project attempts to bridge a few of these important gaps, both on the theoretical and computational side and develop new scalable algorithms for morphological analysis adapted to the growing size and complexity of real datasets. The project will also promote those research topics among students at various levels of the educational system, with the creation of an upper-level undergraduate course on differential and computational geometry, training of PhD students and K-12 outreach activities through the Women in Science and Engineering (WISE) program in particular.Building up on several prior works on shape spaces and metrics, the specific research objectives of this project are (1) to advance the analysis and comparison of relaxed shape matching problems deriving from Riemannian metrics on spaces of manifolds; (2) to investigate supervised and unsupervised deep learning approaches to improve the efficiency of manifold registration algorithms; and (3) to study novel extensions of those models to account for partial or incomplete data and model joint shape/topological variations across shapes. As part of this project's outcome, Python pipelines will be developed and made openly accessible to the scientific community with the long term goal of expanding the potential scope of applications of those methods.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.
形状分析现在已经成为数据科学的一个组成部分,因为它是建模和定量分析数据集内的几何变异性的关键,用于计算机视觉,语音/运动识别,形态发生或计算解剖学等各种应用。在该领域研究的各种几何结构中,曲线,曲面和更一般的流形都是非常自然的对象,但由于相应形状空间的非正则结构,处理和分析也特别具有挑战性。这在一定程度上阻碍了这些数据的形状分析框架的发展和有效性,如果与更广泛研究的图像相比。该项目试图弥合这些重要的差距,无论是在理论和计算方面,并开发新的可扩展算法的形态学分析适应日益增长的规模和复杂性的真实的数据集。该项目还将在教育系统的各个层次的学生中推广这些研究课题,特别是通过科学和工程妇女(WISE)计划,开设关于微分几何和计算几何的高水平本科课程,培训博士生和K-12外联活动。该项目的具体研究目标是(1)推进流形空间上黎曼度量的松弛形状匹配问题的分析和比较;(2)研究监督和无监督深度学习方法,以提高流形配准算法的效率;以及(3)研究这些模型的新扩展以说明部分或不完整的数据并对形状之间的关节形状/拓扑变化进行建模。作为该项目成果的一部分,Python管道将被开发并向科学界开放,其长期目标是扩大这些方法的潜在应用范围。该奖项反映了NSF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

期刊论文数量(9)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
On length measures of planar closed curves and the comparison of convex shapes
BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes
Diffeomorphic Registration with Density Changes for the Analysis of Imbalanced Shapes
用于不平衡形状分析的密度变化微分同胚配准
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
A Diffeomorphic Flow-Based Variational Framework for Multi-Speaker Emotion Conversion
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Nicolas Charon其他文献

A scalable framework for learning the geometry-dependent solution operators of partial differential equations
用于学习偏微分方程的几何依赖解算符的可扩展框架
  • DOI:
    10.1038/s43588-024-00732-2
  • 发表时间:
    2024-12-09
  • 期刊:
  • 影响因子:
    18.300
  • 作者:
    Minglang Yin;Nicolas Charon;Ryan Brody;Lu Lu;Natalia Trayanova;Mauro Maggioni
  • 通讯作者:
    Mauro Maggioni
PO-05-062 AI-BASED SHAPE ANALYSIS CORRELATES LEFT ATRIAL APPENDAGE MORPHOLOGY WITH STROKE RISK IN PATIENTS WITH ATRIAL FIBRILLATION
PO-05-062 基于人工智能的形状分析将左心耳附属结构形态与心房颤动患者的中风风险相关联
  • DOI:
    10.1016/j.hrthm.2025.03.1460
  • 发表时间:
    2025-04-01
  • 期刊:
  • 影响因子:
    5.700
  • 作者:
    Minglang Yin;Zan Ahmad;Emmanuel Hartman;Yashil Sukurdeep;Shiyi Chen;Jiwoo Noh;Nicolas Charon;David D. Spragg;Natalia A. Trayanova
  • 通讯作者:
    Natalia A. Trayanova
DH-482888-001 PREDICTING PERSONALIZED CARDIAC ELECTROPHYSIOLOGY USING DEEP LEARNING
DH-482888-001 使用深度学习预测个性化心脏电生理学
  • DOI:
    10.1016/j.hrthm.2024.03.261
  • 发表时间:
    2024-05-01
  • 期刊:
  • 影响因子:
    5.700
  • 作者:
    Minglang Yin;Nicolas Charon;Ryan Brody;Lu Lu;Mauro Maggioni;Natalia A. Trayanova
  • 通讯作者:
    Natalia A. Trayanova

Nicolas Charon的其他文献

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{{ truncateString('Nicolas Charon', 18)}}的其他基金

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:
    2402555
  • 财政年份:
    2024
  • 资助金额:
    $ 45.12万
  • 项目类别:
    Standard Grant
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
  • 财政年份:
    2020
  • 资助金额:
    $ 45.12万
  • 项目类别:
    Standard Grant
A General and Efficient Framework for Computational Shape Analysis Through Geometric Distributions
通过几何分布进行计算形状分析的通用且有效的框架
  • 批准号:
    1819131
  • 财政年份:
    2018
  • 资助金额:
    $ 45.12万
  • 项目类别:
    Standard Grant

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  • 批准号:
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Analysis of the effect of integral kernel shape on pattern formation in nonlocal reaction-diffusion equations
积分核形状对非局部反应扩散方程模式形成的影响分析
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  • 批准号:
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How Nutrients Shape Plant Roots: A Spatial Analysis of the Signaling Networks that Control Root Responses to Phosphorus
养分如何塑造植物根部:控制根部对磷反应的信号网络的空间分析
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