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Deterministic Approximate Methods for Maximum Consensus Robust Fitting.

Huu Le, Tat-Jun Chin, Anders Eriksson

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |September 9, 2019
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    Summary
    This summary is machine-generated.

    This study introduces new deterministic algorithms for maximum consensus estimation, offering a practical middle ground between fast but imprecise randomized methods and slow but exact approaches for robust fitting in computer vision.

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    Area of Science:

    • Computer Vision
    • Optimization
    • Robust Fitting

    Background:

    • Maximum consensus estimation is crucial for robust fitting in computer vision.
    • Current methods include approximate randomized algorithms and costly exact algorithms.
    • A gap exists between approximate and exact solutions for practical applications.

    Purpose of the Study:

    • To bridge the gap between approximate and exact consensus maximization algorithms.
    • To propose novel deterministic algorithms for approximate maximum consensus optimization.
    • To provide practical solutions for robust fitting problems.

    Main Methods:

    • Reformulation of consensus maximization using linear complementarity constraints.
    • Development of two novel deterministic algorithms: a non-smooth penalty method with Frank-Wolfe optimization and an Alternating Direction Method of Multipliers (ADMM).
    • Both algorithms leverage convex subproblems for efficient optimization.

    Main Results:

    • The proposed algorithms significantly improve rough initial estimates from methods like least squares or randomized approaches.
    • Demonstrated practicality on realistic input sizes, outperforming exact algorithms.
    • The methods are well-suited for estimation problems involving geometric residuals.

    Conclusions:

    • The developed deterministic algorithms offer a practical and efficient approach to approximate maximum consensus estimation.
    • These methods provide a valuable alternative to existing approximate and exact techniques in computer vision.
    • The algorithms are applicable to a range of robust fitting problems, particularly those with geometric constraints.