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

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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.