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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在超图上搜索代表性模式以进行鲁棒的几何模型拟合

在本文中，我们提出了一种简单有效的几何模型拟合方法，即使在存在严重异常值的情况下，也可以拟合和分割多结构数据。我们将几何模型拟合的任务作为超图上的代表性模式寻求问题。具体来说，首先构造一个超图，其中顶点表示模型假设，而超边表示数据点。超图涉及更高阶的相似性（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归约技术，以在保留超图中尽可能多的“重要”顶点的同时，删除“无关紧要”的顶点。基于简化的超图，然后，我们提出了一种新颖的寻模算法，以在合理的时间内搜索代表模式。最后，提出的寻模算法根据两个顶点的权重得分和顶点之间的相似度分析这两个关键要素对模式进行检测。总体而言，所提出的拟合方法能够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，在合成数据和真实图像上，该方法均比几种最新模型拟合方法具有明显的优越性。提出的拟合方法能够同时有效地估计数据中模型实例的数量和参数。实验结果表明，在合成数据和真实图像上，该方法均比几种最新模型拟合方法具有明显的优越性。提出的拟合方法能够同时有效地估计数据中模型实例的数量和参数。实验结果表明，在合成数据和真实图像上，该方法均比几种最新模型拟合方法具有明显的优越性。