Non-smooth M-estimator for maximum consensus estimation

Huu Le, Anders Eriksson, Michael Milford, Thanh-Toan Do, Tat-Jun Chin, David Suter

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publication29th British Machine Vision Conference, BMVC 2018
EditorsHubert P. H. Shum, Timothy Hospedales
Place of PublicationLondon UK
PublisherBritish Machine Vision Association and Society for Pattern Recognition
Number of pages12
Publication statusPublished - 2018
Externally publishedYes
EventBritish Machine Vision Conference 2018 - Newcastle, United Kingdom
Duration: 3 Sep 20186 Sep 2018
Conference number: 29th


ConferenceBritish Machine Vision Conference 2018
Abbreviated titleBMVC 2018
CountryUnited Kingdom
Internet address

Cite this