This paper addresses the problem of registering multiple point sets. Solutions to this problem are often approximated by repeatedly solving for pairwise registration, which results in an uneven treatment of the sets forming a pair: a model set and a data set. The main drawback of this strategy is that the model set may contain noise and outliers, which negatively affects the estimation of the registration parameters. In contrast, the proposed formulation treats all the point sets on an equal footing. Indeed, all the points are drawn from a central Gaussian mixture, hence the registration is cast into a clustering problem. We formally derive batch and incremental EM algorithms that robustly estimate both the GMM parameters and the rotations and translations that optimally align the sets. Moreover, the mixture's means play the role of the registered set of points while the variances provide rich information about the contribution of each component to the alignment. We thoroughly test the proposed algorithms on simulated data and on challenging real data collected with range sensors. We compare them with several state-of-the-art algorithms, and we show their potential for surface reconstruction from depth data.

中文翻译：

---

具有批处理和增量期望最大化的多点集的联合对齐

本文解决了注册多个点集的问题。通常通过反复求解成对配准来近似解决该问题的解决方案，这导致对形成成对的集合（模型集和数据集）的处理不均。该策略的主要缺点是模型集可能包含噪声和异常值，这会对配准参数的估计产生负面影响。相反，建议的公式将所有点集均等对待。实际上，所有的点都是从中央高斯混合中得出的，因此配准就变成了聚类问题。我们正式导出了批处理和增量EM算法，这些算法可稳健地估计GMM参数以及最佳对齐集合的旋转和平移。而且，混合物' s表示已注册点集的作用，而方差提供了有关每个成分对路线的贡献的丰富信息。我们在模拟数据和用距离传感器收集的具有挑战性的真实数据上彻底测试了所提出的算法。我们将它们与几种最先进的算法进行了比较，并展示了它们根据深度数据进行表面重建的潜力。