Summaries of craters on terrestrial bodies, such as the number and size distribution, are essential for understanding the history of the Solar System. Identifying craters, however, has not been automated and thus relies on expert crater-counters marking static images. Robbins et al. (2014) (hereafter R14) showed that, contrary to previously held assumptions, there exists large variability across expert crater-counters' identified crater lists. How best to combine identified crater lists across multiple experts for the purposes of learning about the Solar System is an open and consequential question. R14 combined identified crater lists via clustering through a modification of the popular DBSCAN clustering method. Their approach did not, however, make use of all the constraining information available nor did it provide an estimate of clustering uncertainty. To address the shortcomings of the DBSCAN method, we present a novel clustering approach that can combine multiple lists of identified objects of interest from the same image. The key innovation is incorporating a dysfunctional family constraint into the Bayesian nonparametric clustering approach, the Chinese restaurant process (CRP), which naturally takes into account information about the crater identifier. The dysfunctional family Chinese restaurant process (DFCRP) provides an estimate of clustering uncertainty. In this work, we provide guidance on hyperparameter specification, present a Gibbs sampler, and perform a simulation study to compare the performance of the DFCRP to the CRP. Finally, we apply the DFCRP to the crater identification problem of R14, comparing results, and also demonstrate the types of analyses that can be performed with posterior draws of cluster assignments.

翻译：对类地天体上陨石坑的总结（如数量与尺寸分布）对于理解太阳系历史至关重要。然而，陨石坑的识别尚未实现自动化，目前仍依赖专家陨石坑计数员对静态图像进行标注。Robbins等人（2014，以下简称R14）的研究表明，与先前假设相反，不同专家陨石坑计数员识别的陨石坑清单之间存在显著差异。如何有效整合多个专家的识别结果以推进太阳系研究，仍是一个开放且关键的问题。R14通过改进流行的DBSCAN聚类方法，对多份识别清单进行了聚类整合。然而，该方法既未充分利用所有约束信息，也未提供聚类不确定性的估计。为解决DBSCAN方法的不足，我们提出了一种新型聚类方法，能够整合同一图像中多个识别清单的目标对象。其核心创新在于将“功能紊乱家族”约束引入贝叶斯非参数聚类方法——中国餐馆过程（CRP）中，天然地利用了陨石坑标识符信息。功能紊乱家族中国餐馆过程（DFCRP）可提供聚类不确定性的估计值。本研究给出了超参数设定指南，提出了Gibbs采样器，并通过仿真研究对比了DFCRP与CRP的性能。最后，我们将DFCRP应用于R14的陨石坑识别问题，对比了分析结果，并展示了如何利用后验聚类分配的抽样结果进行各类分析。