Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting

In this paper, we propose a simple and effective {geometric} model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking problem on hypergraphs. Specifically, a hypergraph is firstly constructed, where the vertices represent model hypotheses and the hyperedges denote data points. The hypergraph involves higher-order similarities (instead of pairwise similarities used on a simple graph), and it can characterize complex relationships between model hypotheses and data points. {In addition, we develop a hypergraph reduction technique to remove "insignificant" vertices while retaining as many "significant" vertices as possible in the hypergraph}. Based on the {simplified hypergraph, we then propose a novel mode-seeking algorithm to search for representative modes within reasonable time. Finally, the} proposed mode-seeking algorithm detects modes according to two key elements, i.e., the weighting scores of vertices and the similarity analysis between vertices. Overall, the proposed fitting method is able to efficiently and effectively estimate the number and the parameters of model instances in the data simultaneously. Experimental results demonstrate that the proposed method achieves significant superiority over {several} state-of-the-art model fitting methods on both synthetic data and real images.