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Triadic Split-Merge Sampler

机译：Triadic拆分合并采样器

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In machine vision typical heuristic methods to extract parameterized objects out of raw data points are the Hough transform and RANSAC. Bayesian models carry the promise to optimally extract such parameterized objects given a correct definition of the model and the type of noise at hand. A category of solvers for Bayesian models are Markov chain Monte Carlo methods. Naive implementations of MCMC methods suffer from slow convergence in machine vision due to the complexity of the parameter space. Towards this blocked Gibbs and split-merge samplers have been developed that assign multiple data points to clusters at once. In this paper we introduce a new split-merge sampler, the triadic split-merge sampler, that perform steps between two and three randomly chosen clusters. This has two advantages. First, it reduces the asymmetry between the split and merge steps. Second, it is able to propose a new cluster that is composed out of data points from two different clusters. Both advantages speed up convergence which we demonstrate on a line extraction problem. We show that the triadic split-merge sampler outperforms the conventional split-merge sampler. Although this new MCMC sampler is demonstrated in this machine vision context, its application extend to the very general domain of statistical inference.
机译：在机器视觉中，从原始数据点中提取参数化对象的典型启发式方法是Hough变换和RANSAC。贝叶斯模型具有在正确定义模型和手头噪声类型的前提下最佳提取此类参数化对象的承诺。贝叶斯模型的一种求解器是马尔可夫链蒙特卡罗方法。由于参数空间的复杂性，MCMC方法的简单实现在机器视觉中收敛缓慢。为此，已经开发了Gibbs和拆分合并采样器，可以一次将多个数据点分配给群集。在本文中，我们介绍了一种新的拆分合并采样器，即三重拆分拆分采样器，它可以在两个和三个随机选择的簇之间执行步骤。这有两个优点。首先，它减少了拆分和合并步骤之间的不对称性。其次，它能够提出一个新的集群，该集群由来自两个不同集群的数据点组成。这两个优点都加快了收敛速度，我们在行提取问题上证明了这一点。我们显示三元组拆分合并采样器的性能优于常规拆分合并采样器。尽管在这种机器视觉环境中演示了这种新型MCMC采样器，但其应用范围已扩展到非常广泛的统计推断领域。

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