# Bayesian Point Set Registration

## TL;DR

This paper introduces a Bayesian approach to simultaneously solve point set correspondence and transformation estimation, using MCMC sampling, with applications in materials science and synthetic data validation.

## Contribution

It presents a unified Bayesian framework for point set registration that handles noise and partial data, advancing beyond traditional separate optimization methods.

## Key findings

- Effective in noisy, sparse data scenarios
- Successfully applied to synthetic datasets
- Provides a probabilistic measure of transformation uncertainty

## Abstract

Point set registration involves identifying a smooth invertible transformation between corresponding points in two point sets, one of which may be smaller than the other and possibly corrupted by observation noise. This problem is traditionally decomposed into two separate optimization problems: (i) assignment or correspondence, and (ii) identification of the optimal transformation between the ordered point sets. In this work, we propose an approach solving both problems simultaneously. In particular, a coherent Bayesian formulation of the problem results in a marginal posterior distribution on the transformation, which is explored within a Markov chain Monte Carlo scheme. Motivated by Atomic Probe Tomography (APT), in the context of structure inference for high entropy alloys (HEA), we focus on the registration of noisy sparse observations of rigid transformations of a known reference configuration.Lastly, we test our method on synthetic data sets.