# A Closest Point Proposal for MCMC-based Probabilistic Surface Registration

arXiv: https://arxiv.org/abs/1907.01414 · HTML: https://mlsanity.com/paper/1907.01414/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2019.

## Built on by (most cited first, 6 of 6)

- [A Review of Uncertainty Estimation and its Application in Medical Imaging](https://mlsanity.com/paper/2302.08119/) (2023)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Approximating Intersections and Differences Between Linear Statistical Shape Models Using Markov Chain Monte Carlo](https://mlsanity.com/paper/2211.16314/) (2022)
- [Dynamic multi feature-class Gaussian process models](https://mlsanity.com/paper/2112.04495/) (2021)
- [GiNGR: Generalized Iterative Non-Rigid Point Cloud and Surface Registration Using Gaussian Process Regression](https://mlsanity.com/paper/2203.09986/) (2022)
- [Posterior shape models revisited: Improving 3D reconstructions from partial data using target specific models](https://mlsanity.com/paper/2509.05776/) (2025)

## Abstract (arXiv)

We propose to view non-rigid surface registration as a probabilistic inference problem. Given a target surface, we estimate the posterior distribution of surface registrations. We demonstrate how the posterior distribution can be used to build shape models that generalize better and show how to visualize the uncertainty in the established correspondence. Furthermore, in a reconstruction task, we show how to estimate the posterior distribution of missing data without assuming a fixed point-to-point correspondence. We introduce the closest-point proposal for the Metropolis-Hastings algorithm. Our proposal overcomes the limitation of slow convergence compared to a random-walk strategy. As the algorithm decouples inference from modeling the posterior using a propose-and-verify scheme, we show how to choose different distance measures for the likelihood model. All presented results are fully reproducible using publicly available data and our open-source implementation of the registration framework.