  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.
