Sarang Joshi
19/12/2019
Bio: Sarang is Professor of Bioengineering at the University of Utah.
Title: Riemannian Brownian Bridges and Metric Estimation on Landmark Manifolds.
Abstract: 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 non-linear PDE with no closed-form solution. 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.
