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 first 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.

中文翻译：

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搜索超图上的代表性模式以实现稳健的几何模型拟合


在本文中，我们提出了一种简单有效的几何模型拟合方法，即使存在严重异常值，也可以拟合和分割多结构数据。我们将几何模型拟合任务视为超图上的代表性模式搜索问题。具体来说，首先构建超图，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），并且它可以表征模型假设和数据点之间的复杂关系。此外，我们开发了一种超图缩减技术来删除“不重要”的顶点，同时在超图中保留尽可能多的“重要”顶点。基于简化的超图，我们提出了一种新颖的模式搜索算法，以在合理的时间内搜索代表性模式。最后，所提出的模式搜索算法根据两个关键要素检测模式，即顶点的权重分数和顶点之间的相似性分析。总的来说，所提出的拟合方法能够高效且有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，所提出的方法在合成数据和真实图像上都比几种最先进的模型拟合方法具有显着的优越性。