Robust model fitting is a core algorithm in several computer vision applications. Despite being studied for decades, solving this problem efficiently for datasets that are heavily contaminated by outliers is still challenging: due to the underlying computational complexity. A recent focus has been on learning-based algorithms. However, most of these approaches are supervised (which require a large amount of labelled training data). In this paper, we introduce a novel unsupervised learning framework: that learns to directly (without labelled data) solve robust model fitting. Moreover, unlike other learning-based methods, our work is agnostic to the underlying input features, and can be easily generalized to a wide variety of LP-type problems with quasi-convex residuals. We empirically show that our method outperforms existing (un)supervised learning approaches, and also achieves competitive results compared to traditional (non-learning-based) methods. Our approach is designed to try to maximise consensus (MaxCon), similar to the popular RANSAC. The basis of our approach, is to adopt a Reinforcement Learning framework. This requires designing appropriate reward functions, and state encodings. We provide a family of reward functions, tunable by choice of a parameter. We also investigate the application of different basic and enhanced Q-learning components.

Maximisation of Consensus (MaxCon) is one of the most widely used robust criteria in computer vision. Tennakoon et al. (CVPR2021), made a connection between MaxCon and estimation of influences of a Monotone Boolean function. In such, there are two distributions involved: the distribution defining the influence measure; and the distribution used for sampling to estimate the influence measure. This paper studies the concept of weighted influences for solving MaxCon. In particular, we study the Bernoulli measures. Theoretically, we prove the weighted influences, under this measure, of points belonging to larger structures are smaller than those of points belonging to smaller structures in general. We also consider another “natural” family of weighting strategies: sampling with uniform measure concentrated on a particular (Hamming) level of the cube. One can choose to have matching distributions: the same for defining the measure as for implementing the sampling. This has the advantage that the sampler is an unbiased estimator of the measure. Based on weighted sampling, we modify the algorithm of Tennakoon et al., and test on both synthetic and real datasets. We show some modest gains of Bernoulli sampling, and we illuminate some of the interactions between structure in data and weighted measures and weighted sampling.

Community detection in random graphs or hypergraphs is an interesting fundamental problem in statistics, machine learning and computer vision. When the hypergraphs are generated by a {\em stochastic block model}, the existence of a sharp threshold on the model parameters for community detection was conjectured by Angelini et al. 2015. In this paper, we confirm the positive part of the conjecture, the possibility of non-trivial reconstruction above the threshold, for the case of two blocks. We do so by comparing the hypergraph stochastic block model with its Erd{\"o}s-R{\'e}nyi counterpart. We also obtain estimates for the parameters of the hypergraph stochastic block model. The methods developed in this paper are generalised from the study of sparse random graphs by Mossel et al. 2015 and are motivated by the work of Yuan et al. 2022. Furthermore, we present some discussion on the negative part of the conjecture, i.e., non-reconstruction of community structures.

Consensus maximisation (MaxCon), which is widely used for robust fitting in computer vision, aims to find the largest subset of data that fits the model within some tolerance level. In this paper, we outline the connection between MaxCon problem and the abstract problem of finding the maximum upper zero of a Monotone Boolean Function (MBF) defined over the Boolean Cube. Then, we link the concept of influences (in a MBF) to the concept of outlier (in MaxCon) and show that influences of points belonging to the largest structure in data would generally be smaller under certain conditions. Based on this observation, we present an iterative algorithm to perform consensus maximisation. Results for both synthetic and real visual data experiments show that the MBF based algorithm is capable of generating a near optimal solution relatively quickly. This is particularly important where there are large number of outliers (gross or pseudo) in the observed data.

Robust model fitting is a core algorithm in a large number of computer vision applications. Solving this problem efficiently for datasets highly contaminated with outliers is, however, still challenging due to the underlying computational complexity. Recent literature has focused on learning-based algorithms. However, most approaches are supervised (which require a large amount of labelled training data). In this paper, we introduce a novel unsupervised learning framework that learns to directly solve robust model fitting. Unlike other methods, our work is agnostic to the underlying input features, and can be easily generalized to a wide variety of LP-type problems with quasi-convex residuals. We empirically show that our method out-performs existing unsupervised learning approaches, and achieves competitive results compared to traditional methods on several important computer vision problems1.