AF: Small: Extending algorithms for topological notions of similarity
AF:小:相似性拓扑概念的扩展算法
基本信息
- 批准号:1614562
- 负责人:
- 金额:$ 29.7万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2016
- 资助国家:美国
- 起止时间:2016-09-01 至 2020-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
How would you measure the closeness of two signatures or two clayfigurines? This project explores the mathematics and computation ofmeasuring similarity between curves or 3-dimensional objects --whether to compare GPS tracking data to road maps, or medical scans of internal organs toreference models of healthy organs. While some well understood comparison methods simplylook at how close the objects are, this project aims to design moresophisticated measures that take into account the underlying structure(or topology) of the curves and surfaces. The PI plans to collaboratewith applications areas that use these measurement algorithms todevelop measures that best fit the areas, in addition to continuingher work in a larger network of shape analysis and computationaltopology communities, including organizing workshops focused atmentoring junior women in these areas.This project generalizes notions of similarity from curves to graphs, meshes, or3-manifolds. The primary problems and techniques come from theemerging field of computational topology, which combines algorithmsand computational geometry with mathematical foundations and toolsfrom the area of topology. In particular, the PI proposes to examinefundamental topological notions of similarity between curves andsurfaces in some ambient space, based on computing optimal homotopies, homologies, or isotopies. Eachpossibility offers a different notion of what it means for two thingsto be equivalent in the ambient space, and each can be optimized basedon the notions of area, "height," or "width." While several initialalgorithmic results on these measures have been published, there aremany open questions that remain. In addition, recent mathematicaldevelopments indicate many potentially tractable and feasible areasthat are yet to be explored from the algorithmic perspective. Some ofthese measures are likely to be hard to compute, which is of interestto the theoretical community, and approximation or fixed parametertractable algorithms may prove practical in applications areas. Theproject will also include collaborations in applications areas forthese measures, in order to better evaluate their utility.
你如何衡量两个签名或两个粘土雕像的接近程度?该项目探索了测量曲线或三维物体之间相似性的数学和计算——无论是将GPS跟踪数据与路线图进行比较,还是将内部器官的医学扫描与健康器官的参考模型进行比较。虽然一些比较方法只是简单地观察物体的距离,但该项目旨在设计更复杂的测量方法,考虑到曲线和表面的底层结构(或拓扑结构)。PI计划与使用这些测量算法的应用领域合作,开发最适合该领域的测量方法,此外,她还将继续在更大的形状分析和计算拓扑社区网络中开展工作,包括组织研讨会,重点指导这些领域的年轻女性。这个项目将相似性的概念从曲线推广到图形、网格或3流形。主要的问题和技术来自新兴的计算拓扑领域,它将算法和计算几何与拓扑领域的数学基础和工具相结合。特别地,PI建议在计算最优同伦、同构或同位素的基础上,检查一些环境空间中曲线和曲面之间相似性的基本拓扑概念。每种可能性都提供了一种不同的概念,即两种事物在环境空间中相等意味着什么,每种可能性都可以基于面积、“高度”或“宽度”的概念进行优化。虽然关于这些措施的一些初步算法结果已经公布,但仍有许多悬而未决的问题。此外,最近的数学发展表明,从算法的角度来看,许多潜在的可处理和可行的领域尚未被探索。其中一些测量可能难以计算,这是理论界感兴趣的,近似或固定参数可追踪算法可能在应用领域被证明是实用的。该项目还将包括在这些措施的应用领域的合作,以便更好地评估它们的效用。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Erin Chambers其他文献
Metric and Path-Connectedness Properties of the Fréchet Distance for Paths and Graphs
路径和图的 Fréchet 距离的度量和路径连通性属性
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Erin Chambers;Fasy, Brittany Terese;Holmgren, Benjamin;Majhi, Sushovan;Wenk, Carola - 通讯作者:
Wenk, Carola
The potential of a population register for addressing health inequities: an observational study using data linkage to improve breast cancer screening enrolment and participation in Indigenous Māori women in Aotearoa New Zealand
- DOI:
10.1186/s12913-024-12186-3 - 发表时间:
2025-01-13 - 期刊:
- 影响因子:3.000
- 作者:
Phyu Sin Aye;Karen Bartholomew;Michael Walsh;Kathy Pritchard;Maree Pierce;Jenny Richards;Erin Chambers;Aroha Haggie;Jesse Solomon;Gabrielle Lord;Tiffany Soloai;Lorraine Symons;Roimata Tipene;Rawiri McKree Jansen - 通讯作者:
Rawiri McKree Jansen
Clinical Significance of Quantitative Viral Load in Patients Positive for SARS-CoV-2
- DOI:
10.1016/j.ajmo.2023.100050 - 发表时间:
2023-12-01 - 期刊:
- 影响因子:
- 作者:
Shannon W. Finks;Edward Van Matre;William Budd;Elizabeth Lemley;N. Katherine Ray;Madeline Mahon;Erin Chambers;A. Lloyd Finks - 通讯作者:
A. Lloyd Finks
Publisher Correction: The potential of a population register for addressing health inequities: an observational study using data linkage to improve breast cancer screening enrolment and participation in Indigenous Māori women in Aotearoa New Zealand
- DOI:
10.1186/s12913-025-12376-7 - 发表时间:
2025-02-10 - 期刊:
- 影响因子:3.000
- 作者:
Phyu Sin Aye;Karen Bartholomew;Michael Walsh;Kathy Pritchard;Maree Pierce;Jenny Richards;Erin Chambers;Aroha Haggie;Jesse Solomon;Gabrielle Lord;Tiffany Soloai;Lorraine Symons;Roimata Tipene;Rawiri McKree Jansen - 通讯作者:
Rawiri McKree Jansen
Erin Chambers的其他文献
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{{ truncateString('Erin Chambers', 18)}}的其他基金
Travel: Third Workshop for Women in Computational Topology
旅行:第三届计算拓扑学女性研讨会
- 批准号:
2317401 - 财政年份:2023
- 资助金额:
$ 29.7万 - 项目类别:
Standard Grant
Collaborative Research: AF: Medium: A Unified Framework for Geometric and Topological Signature-Based Shape Comparison
合作研究:AF:Medium:基于几何和拓扑签名的形状比较的统一框架
- 批准号:
2106672 - 财政年份:2021
- 资助金额:
$ 29.7万 - 项目类别:
Continuing Grant
AF: Small: Collaborative Research: Reeb graph flows: Metrics, Drawings, and Analysis
AF:小型:协作研究:Reeb 图流:指标、绘图和分析
- 批准号:
1907612 - 财政年份:2019
- 资助金额:
$ 29.7万 - 项目类别:
Standard Grant
CGV: Small: Collaborative Research: Theories, algorithms, and applications of medial forms for shape analysis
CGV:小型:协作研究:形状分析的中间形式的理论、算法和应用
- 批准号:
1319944 - 财政年份:2013
- 资助金额:
$ 29.7万 - 项目类别:
Continuing Grant
CAREER: Generalizing Planar Algorithms
职业:推广平面算法
- 批准号:
1054779 - 财政年份:2011
- 资助金额:
$ 29.7万 - 项目类别:
Continuing Grant
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