The Unlabeled Correspondence Configuration Problem and Optimal Transport
Steven B. Damelin · 2024
The work presented in this chapter is motivated by the difficulty in trying to match point sets in the absence of labels in the sense that often one does not know which point to map to which. This is referred to commonly as the unlabeled problem. The authors discuss briefly optimal transport. In the paper [26], the authors investigate ways to align two point configurations by first finding a correspondence between points and then constructing a function which aligns the configurations. The terms reordering and relabeling are used interchangeably. The authors provide an example of question QU with two different 4-point configurations in R 2 which have the same distribution of distances.