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.
翻译:共识最大化(MaxCon)被广泛用于计算机视野的强力配置,目的是找到符合模型的最大数据子集。 在本文中,我们概述了MaxCon问题与寻找波伦立方体上定义的单体波列因函数最大末位的抽象问题之间的联系。然后,我们将影响概念(在MBF中)与外端概念(在MaxCon中)联系起来,并表明属于数据中最大结构的点的影响在某些条件下一般会较小。根据这一观察,我们提出了一个迭代算法来进行共识最大化。合成和真实视觉数据实验的结果显示,基于MBF的算法能够较快地产生近乎最佳的解决方案。在观测到的数据中有大量外端(毛值或伪值)的情况下,这一点尤其重要。