A Fast and Deterministic Algorithm for Consensus Set Maximization

With the current booming applications of virtual reality, augmented reality, and robotics, efficiently extracting the maximum consensus set among large-scale corrupted data has become a critical challenge. However, existing methods typically focus on optimization and are rarely concerned about the running time. In this paper, we propose a new fast and deterministic algorithm to address the consensus set maximization problem. First, we propose a novel formulation that transforms the original problem into a sequence of decision problems (DPs). Second, we propose an efficient algorithm to assess the feasibility of these DPs. Comprehensive experiments on linear hyper-plane regression and non-linear homography matrix estimation show that our approach is fully deterministic and can effectively process large-scale and highly corrupted data without any special initialization. Under a pure MATLAB implementation and a laptop CPU, our method can successfully determine the maximum consensus set from 1000 input data points (with 70% of them being outliers) at 30 Hz.