Deterministic Approximate Methods for Maximum Consensus Robust Fitting

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...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence Vol. 43; no. 3; pp. 842 - 857
Main Authors: Le, Huu, Chin, Tat-Jun, Eriksson, Anders, Do, Thanh-Toan, Suter, David
Format: Journal Article
Language:English
Published: United States IEEE 01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
approximate algorithm
Approximation
Approximation algorithms
Computational modeling
Computer vision
Data models
deterministic algorithm
Estimation
Mathematical model
Maximization
Maximum consensus
Optimization
robust fitting
Robustness
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
Online Access:Get full text
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Summary: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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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2019.2939307