# Bridge Simulation and Metric Estimation on Landmark Manifolds

arXiv: https://arxiv.org/abs/1705.10943 · HTML: https://mlsanity.com/paper/1705.10943/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2017.

## Built on by (most cited first, 4 of 4)

- [Score matching for sub-Riemannian bridge sampling](https://mlsanity.com/paper/2404.15258/) (2024)
- [Neural Guided Diffusion Bridges](https://mlsanity.com/paper/2502.11909/) (2025)
- [Stochastics of shapes and Kunita flows](https://mlsanity.com/paper/2512.11676/) (2025)
- [A function space perspective on stochastic shape evolution](https://mlsanity.com/paper/2302.05382/) (2023)

## Abstract (arXiv)

We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric. The distribution possesses properties similar to the regular Euclidean normal distribution but its transition density is governed by a high-dimensional PDE with no closed-form solution in the nonlinear case. We show how the density can be numerically approximated by Monte Carlo sampling of conditioned Brownian bridges, and we use this to estimate parameters of the LDDMM kernel and thus the metric structure by maximum likelihood.