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.

本文提出了一种简单而高效的几何模型适应方法，该方法利用超图的典型性寻求问题以适应并分割多重结构数据，同时在存在严重的异常值情况下。

基于超图的鲁棒几何模型拟合中代表性模式的搜索

Searching for Representative Modes on Hypergraphs for Robust Geometric  Model Fitting

Quick Shift is a popular mode-seeking and clustering algorithm. We present
finite sample statistical consistency guarantees for Quick Shift on mode and
cluster recovery under mild distributional assumptions. We then apply our
results to construct a consistent modal regression algorithm.

利用 Quick Shift 算法，根据较为温和的分布假设，提出了在模式和聚类恢复方面的有限样本统计一致性保证，然后应用这一结果来构建一致的模式回归算法。