Robust Group Synchronization via Quadratic Programming

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https://hdl.handle.net/11299/258619

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Robust Group Synchronization via Quadratic Programming

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Wyeth, Cole

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2023-06

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Thesis or Dissertation

Abstract

We review existing methods for the group synchronization problem and discuss ournovel quadratic programming formulation for estimating the corruption levels in group synchronization, and use these estimates to solve this problem. Our objective function exploits the cycle consistency of the group and we thus refer to our method as detection and estimation of structural consistency (DESC). This general framework can be extended to other algebraic and geometric structures. Our formulation has the following advantages: it can tolerate corruption as high as the information-theoretic bound, it does not require a good initialization for the estimates of group elements, it has a simple interpretation, and under some mild conditions the global minimum of our objective function exactly recovers the corruption levels. We demonstrate the competitive accuracy of our approach on both synthetic and real data experiments of rotation averaging.

Keywords

Computer vision

Group Synchronization

Inverse problem

Machine learning

Optimization

Description

University of Minnesota M.S. thesis. 2023. Major: Mathematics. Advisor: Gilad Lerman. 1 computer file (PDF); iii, 25 pages.

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Wyeth, Cole. (2023). Robust Group Synchronization via Quadratic Programming. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/258619.

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