Consensus Maximisation Using Influences of Monotone Boolean Functions

TL;DR

This paper introduces a novel approach to robust data fitting in computer vision by connecting consensus maximisation with Monotone Boolean Functions, enabling efficient outlier detection and near-optimal solutions.

Contribution

It establishes a theoretical link between MaxCon and MBFs, and proposes an iterative algorithm leveraging influences for improved outlier handling.

Findings

The MBF-based algorithm achieves near-optimal solutions quickly.

Effective in datasets with many outliers.

Applicable to both synthetic and real visual data.

Abstract

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.