A two-step hypergraph reduction based fitting method for unbalanced data

In this paper, we propose a two-step hypergraph reduction based fitting for unbalanced data. A hypergraph effectively characterizes the relationship between model hypotheses and data points for model fitting. However, a hypergraph-based fitting method often suffers from the problem of high computational cost due to the complex relationship between hyperedges and vertices. Hypergraph reduction algorithms are used to alleviate this problem, but they cannot work well for unbalanced data. To deal with the unbalanced model fitting problem, we first locally remove hyperedges corresponding to the same model instances in data, and then globally remove hyperedges corresponding to the bad model hypotheses. Moreover, we extend the binary incident matrix of a normal hypergraph to a continuous (soft) generalization, to improve the accuracy of hypergraph partition for model fitting. Experimental results on both synthetic data and real images demonstrate that the proposed method has significant superiority over several other state-of-the-art fitting methods. (C) 2018 Elsevier B.V. All rights reserved.