  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.
