Unlabelled landmark matching via Bayesian data selection, and application to cell matching across imaging modalities

TL;DR

This paper introduces a Bayesian method for landmark matching between unlabelled point sets, handling differences in point counts and correspondences, with applications in cell matching across imaging modalities.

Contribution

It presents a novel Bayesian data selection technique for joint inference of transformations and correspondences in unlabelled point cloud matching.

Findings

Validated with in silico tests and biological experiments

Successfully matched cells across different imaging modalities

Demonstrated broad applicability of Bayesian data selection

Abstract

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.