We consider the problem of landmark matching between two unlabelled point sets, in particular where the number of points in each cloud may differ, and where points in each cloud may not have a corresponding match. We invoke a Bayesian framework to identify the transformation of coordinates that maps one cloud to the other, alongside correspondence of the points. This problem necessitates a novel methodology for Bayesian data selection; simultaneous inference of model parameters, and selection of the data which leads to the best fit of the model to the majority of the data. We apply this to a problem in developmental biology where the landmarks correspond to segmented cell centres, where potential death or division of cells can lead to discrepancies between the point-sets from each image. We validate the efficacy of our approach using in silico tests and a microinjected fluorescent marker experiment. Subsequently we apply our approach to the matching of cells between real time imaging and immunostaining experiments, facilitating the combination of single-cell data between imaging modalities. Furthermore our approach to Bayesian data selection is broadly applicable across data science, and has the potential to change the way we think about fitting models to data.
翻译:我们考虑了两个未贴标签的点组之间的标志性匹配问题,特别是每个云中点数可能不同,每个云中点数可能没有相应的匹配点。我们援引一个巴伊西亚框架来确定绘制一个云的坐标的转换,以及各个点的对应点。这个问题需要一种新颖的方法来选择巴伊西亚数据;同时推断模型参数,以及选择数据,使模型最适合大多数数据。我们将此应用于发展生物学中的一个问题,在那里,每个云中点数可能不同,每个云中点数可能没有相应的匹配点数。我们援引一个巴伊西亚框架来确定绘制一个云的坐标的坐标转换,以及各个点的对应点的对应点。我们验证了我们在硅测试和微注入荧光标记实验中使用的方法的功效。我们随后运用了我们的方法来将实际时间成像和免疫性实验之间的细胞匹配,便利将单细胞数据组合到成像模式之间。此外,我们选择贝伊数据的方法在数据科学中广泛适用,并有可能改变我们对数据进行模型的思维方式。