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：
Nicolas Charon
金额：
$ 45.12万
依托单位：
Johns Hopkins University
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

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1945224&HistoricalAwards=false
关键词：
CAREER Shape Analysis Submanifold Spaces

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.

形状分析现在已成为数据科学的组成部分，因为它是对数据集中的几何变异性进行建模和分析的关键，以构成计算机视觉，语音/运动识别，形态发生或计算解剖结构等多样化的应用。在该领域所研究的各种几何结构中，曲线，表面和更普遍的歧管都是非常自然的对象，但由于相应形状空间的非经典结构，在处理和分析方面尤其具有挑战性。如果将图像更广泛地研究的情况进行比较，则这部分阻碍了形状分析框架的发展和有效性。该项目试图在理论和计算方面弥合其中的一些重要差距，并开发出新的可扩展算法，以适应形态学分析，以适应实际数据集的规模和复杂性的增长。该项目还将在教育系统的各个层面的学生中促进这些研究主题，并通过科学和科学妇女的妇女和K-12尤其是工程（明智）计划。建立在形状空间和指标上的几项先前的作品，该项目的特定研究目标是（1）提高对歧管空间上从里曼尼亚指标得出的放松形状匹配问题的分析和比较; （2）调查受监督和无监督的深度学习方法，以提高流形登记算法的效率；（3）研究这些模型的新扩展，以解释跨形状的部分或不完整的数据以及模型的关节形状/拓扑变化。作为该项目结果的一部分，科学界将开发和公开访问Python管道，并以长期的目标是扩大这些方法的潜在应用范围。该奖项反映了NSF的法定任务，并被认为是值得通过的支持。使用基金会的智力优点和更广泛的影响评估标准进行评估。

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

DOI：
10.1007/s10455-021-09795-0
发表时间：
2020-10
期刊：
Annals of Global Analysis and Geometry
影响因子：
0.7
作者：
N. Charon;T. Pierron
通讯作者：
N. Charon;T. Pierron

BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes

DOI：
10.1109/iccv51070.2023.01304
发表时间：
2022-11
期刊：
2023 IEEE/CVF International Conference on Computer Vision (ICCV)
影响因子：
0
作者：
Emmanuel Hartman;E. Pierson;Martin Bauer;N. Charon;M. Daoudi
通讯作者：
Emmanuel Hartman;E. Pierson;Martin Bauer;N. Charon;M. Daoudi

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

DOI：
10.1007/978-3-030-78191-0_3
发表时间：
2021
期刊：
Information Processing in Medical Imaging
影响因子：
0
作者：
Hsieh, Hsi-Wei;Charon, Nicolas.
通讯作者：
Charon, Nicolas.

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
影响因子：
0
作者：
Hartman, Emmanuel;Sukurdeep, Yashil;Charon, Nicolas;Klassen, Eric;Bauer, Martin
通讯作者：
Bauer, Martin

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