CAREER: High-order Tensor Analysis for Groupwise Correspondence: Theory, Algorithms, and Applications

职业：分组对应的高阶张量分析：理论、算法和应用

• 批准号: 1350521
• 负责人: Haibin Ling
• 金额: $ 47.97万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-02-01 至 2019-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1350521&HistoricalAwards=false
• 关键词: CAREER; order; Tensor; Analysis; Groupwise

Visual matching is a fundamental problem in computer vision (CV) and intensive research efforts have been devoted to building correspondence between a pair of visual objects. By contrast, finding correspondence among an ensemble of objects remains challenging. This project develops a unified framework for this problem and to apply the framework to different applications. The research establishes a close correlation between the classical multi-dimensional assignment (MDA) problem and low-rank tensor approximation. Such correlation paves a way of using high-order tensor analysis for groupwise visual matching that assumes an MDA formulation. Along the way, a series of algorithms are developed to address challenging issues such as computational efficiency and context modeling. These algorithms are then deployed to different tasks including simultaneous tracking of multiple targets, tracking of deformable structures, and batch alignment of visual ensembles. This project can generate broad impact on areas of computer vision, computer graphics, combinatorial optimization, oral and maxillofacial radiology, image-guided intervention, physical therapy, security and defense, education research, etc. On the one hand, the fundamental importance of visual matching makes the project transformative to many other CV problems. On the other hand, the project benefits a wide range of fields outside the CV community through the use of interdisciplinary applications as test beds. This project also integrates tightly research and education with highlights on supervising students from underrepresented groups, combining computer vision and education research, and involving undergraduates in research.

视觉匹配是计算机视觉（CV）中的一个基本问题，人们一直致力于在一对视觉对象之间建立对应关系。相比之下，寻找一组对象之间的对应关系仍然具有挑战性。该项目针对这个问题开发了一个统一的框架，并将该框架应用于不同的应用程序。该研究建立了经典多维分配（MDA）问题和低秩张量近似之间的密切相关性。这种相关性为使用高阶张量分析进行假设 MDA 公式的分组视觉匹配铺平了道路。在此过程中，开发了一系列算法来解决计算效率和上下文建模等具有挑战性的问题。然后将这些算法部署到不同的任务，包括同时跟踪多个目标、跟踪可变形结构以及批量对齐视觉集合。该项目可以对计算机视觉、计算机图形学、组合优化、口腔颌面放射学、图像引导干预、物理治疗、安全与防御、教育研究等领域产生广泛影响。一方面，视觉的根本重要性匹配使该项目能够解决许多其他 CV 问题。另一方面，该项目通过使用跨学科应用程序作为测试平台，使 CV 社区以外的广泛领域受益。该项目还将研究和教育紧密结合起来，重点是监督弱势群体的学生，将计算机视觉和教育研究结合起来，并让本科生参与研究。