基于超图的鲁棒几何模型拟合的代表模式搜索
Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting
摘要：
本文提出了一种简单有效的{几何}模型拟合方法来拟合和分割多结构数据，即使在严重的离群值的存在。我们将几何模型拟合问题转化为超图上典型的模式搜索问题。具体地说，首先构造一个超图，其中顶点表示模型假设，超边表示数据点。超图涉及高阶相似性（而不是简单图上使用的成对相似性），它可以表征模型假设和数据点之间的复杂关系。{In此外，我们发展了一种超图简化技术，以去除超图中的“不重要”顶点，同时保留尽可能多的“重要”顶点。基于简化超图，我们提出了一种新的模式搜索算法，在合理的时间内搜索代表模式。最后，提出的模式搜索算法根据两个关键元素来检测模式，即，顶点的加权得分和顶点之间的相似性分析。总体而言，所提出的拟合方法能够高效地同时估计数据中模型实例的数量和参数。实验结果表明，该方法在合成数据和真实图像上均取得了明显优于{几}种最先进的模型拟合方法的效果。
英文摘要：
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.
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