多结构几何模型拟合的超图优化
Hypergraph Optimization for Multi-structural Geometric Model Fitting
摘要：
近年来，基于超图的方法被提出来处理计算机视觉中的模型拟合问题，这主要是由于超图在表示数据点之间的复杂关系方面的优越能力。然而，当输入数据包括大量数据点（通常被噪声和离群值污染）时，超图变得极其复杂，这将显著增加计算负担。为了克服上述问题，我们提出了一种新的基于超图优化的模型拟合（HOMF）方法来构造一个简单而有效的超图。具体来说，HOMF包括两个主要部分：用于顶点优化的自适应内点估计算法和用于超边缘优化的迭代超边缘优化算法。该方法效率高，迭代次数少，能够得到精确的模型拟合结果。此外，HOMF可以直接应用谱聚类，以实现良好的拟合性能。大量的实验结果表明，HOMF优于几个国家的最先进的模型拟合方法对合成数据和真实图像，特别是在采样效率和处理严重的离群数据。
英文摘要：
Recently, some hypergraph-based methods have been proposed to deal with the problem of model fitting in computer vision, mainly due to the superior capability of hypergraph to represent the complex relationship between data points. However, a hypergraph becomes extremely complicated when the input data include a large number of data points (usually contaminated with noises and outliers), which will significantly increase the computational burden. In order to overcome the above problem, we propose a novel hypergraph optimization based model fitting (HOMF) method to construct a simple but effective hypergraph. Specifically, HOMF includes two main parts: an adaptive inlier estimation algorithm for vertex optimization and an iterative hyperedge optimization algorithm for hyperedge optimization. The proposed method is highly efficient, and it can obtain accurate model fitting results within a few iterations. Moreover, HOMF can then directly apply spectral clustering, to achieve good fitting performance. Extensive experimental results show that HOMF outperforms several state-of-the-art model fitting methods on both synthetic data and real images, especially in sampling efficiency and in handling data with severe outliers.
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