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Deterministic Approximate Methods for Maximum Consensus Robust Fitting

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Title: Deterministic Approximate Methods for Maximum Consensus Robust Fitting
Authors: Le, Huu, 1988, Chin, Tat Jun, Eriksson, Anders, Do, Thanh Toan, Suter, David
Source: IEEE Transactions on Pattern Analysis and Machine Intelligence. 43(3):842-857
Subject Terms: Maximum consensus, deterministic algorithm, approximate algorithm, robust fitting
Description: Maximum consensus estimation plays a critically important role in several robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify algorithms, which are cheap but can usually deliver only rough approximate solutions. On the other extreme, there are exact algorithms which are exhaustive search in nature and can be costly for practical-sized inputs. This paper fills the gap between the two extremes by proposing deterministic algorithms to approximately optimize the maximum consensus criterion. Our work begins by reformulating consensus maximization with linear complementarity constraints. Then, we develop two novel algorithms: one based on non-smooth penalty method with a Frank-Wolfe style optimization scheme, the other based on the Alternating Direction Method of Multipliers (ADMM). Both algorithms solve convex subproblems to efficiently perform the optimization. We demonstrate the capability of our algorithms to greatly improve a rough initial estimate, such as those obtained using least squares or a randomized algorithm. Compared to the exact algorithms, our approach is much more practical on realistic input sizes. Further, our approach is naturally applicable to estimation problems with geometric residuals. Matlab code and demo program for our methods can be downloaded from https://goo.gl/FQcxpi.
Access URL: https://research.chalmers.se/publication/522416
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  Data: Deterministic Approximate Methods for Maximum Consensus Robust Fitting
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  Data: <searchLink fieldCode="AR" term="%22Le%2C+Huu%22">Le, Huu</searchLink>, 1988<br /><searchLink fieldCode="AR" term="%22Chin%2C+Tat+Jun%22">Chin, Tat Jun</searchLink><br /><searchLink fieldCode="AR" term="%22Eriksson%2C+Anders%22">Eriksson, Anders</searchLink><br /><searchLink fieldCode="AR" term="%22Do%2C+Thanh+Toan%22">Do, Thanh Toan</searchLink><br /><searchLink fieldCode="AR" term="%22Suter%2C+David%22">Suter, David</searchLink>
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  Data: <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. 43(3):842-857
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  Data: <searchLink fieldCode="DE" term="%22Maximum+consensus%22">Maximum consensus</searchLink><br /><searchLink fieldCode="DE" term="%22deterministic+algorithm%22">deterministic algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22approximate+algorithm%22">approximate algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22robust+fitting%22">robust fitting</searchLink>
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  Label: Description
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  Data: Maximum consensus estimation plays a critically important role in several robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify algorithms, which are cheap but can usually deliver only rough approximate solutions. On the other extreme, there are exact algorithms which are exhaustive search in nature and can be costly for practical-sized inputs. This paper fills the gap between the two extremes by proposing deterministic algorithms to approximately optimize the maximum consensus criterion. Our work begins by reformulating consensus maximization with linear complementarity constraints. Then, we develop two novel algorithms: one based on non-smooth penalty method with a Frank-Wolfe style optimization scheme, the other based on the Alternating Direction Method of Multipliers (ADMM). Both algorithms solve convex subproblems to efficiently perform the optimization. We demonstrate the capability of our algorithms to greatly improve a rough initial estimate, such as those obtained using least squares or a randomized algorithm. Compared to the exact algorithms, our approach is much more practical on realistic input sizes. Further, our approach is naturally applicable to estimation problems with geometric residuals. Matlab code and demo program for our methods can be downloaded from https://goo.gl/FQcxpi.
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        Value: 10.1109/TPAMI.2019.2939307
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      – Text: English
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        PageCount: 16
        StartPage: 842
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      – SubjectFull: Maximum consensus
        Type: general
      – SubjectFull: deterministic algorithm
        Type: general
      – SubjectFull: approximate algorithm
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      – SubjectFull: robust fitting
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      – TitleFull: Deterministic Approximate Methods for Maximum Consensus Robust Fitting
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            NameFull: Le, Huu
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            NameFull: Chin, Tat Jun
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            NameFull: Do, Thanh Toan
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              M: 01
              Type: published
              Y: 2021
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