Non-smooth M-estimator for maximum consensus estimation

Abstract

This paper revisits the application of M-estimators for a spectrum of robust estimation problems in computer vision, particularly with the maximum consensus criterion. Current practice makes use of smooth robust loss functions, e.g. Huber loss, which enables M-estimators to be tackled by such well-known optimization techniques as Iteratively Re-weighted Least Square (IRLS). When consensus maximization is used as loss function for M-estimators, however, the optimization problem becomes non-smooth. Our paper proposes an approach to resolve this issue. Based on the Alternating Direction Method of Multiplier (ADMM) technique, we develop a deterministic algorithm that is provably convergent, which enables the maximum consensus problem to be solved in the context of M-estimator. We further show that our algorithm outperforms other differentiable robust loss functions that are currently used by many practitioners. Notably, the proposed method allows the sub-problems to be solved efficiently in parallel, thus entails it to be implemented in distributed settings.

Document Type

Conference Proceeding

Funding Information

Australian Research Council

School

School of Science

RAS ID

30763

Grant Number

ARC Number : FT170100072, ARC Number : FT140101229, ARC Number : DP160103490

Copyright

subscription content

Publisher

BMVA Press

Identifier

David Suter

https://orcid.org/0000-0001-6306-3023

Comments

Le, H., Eriksson, A., Milford, M., Do, T. T., Chin, T. J., & Suter, D. (2018). Non-smooth M-estimator for maximum consensus estimation supplementary material. In British Machine Vision Conference 2018. Newcastle, United Kingdom: Northumbria University. Available here

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