In this section
@article{Arnaudon:2017,
author = {Arnaudon, A and Holm, DD and Sommer, S},
journal = {Foundations of Computational Mathematics},
title = {A Geometric Framework for Stochastic Shape Analysis},
url = {http://arxiv.org/abs/1703.09971v2},
year = {2017}
}
TY - JOUR
AB - We introduce a stochastic model of diffeomorphisms, whose action on a varietyof data types descends to stochastic evolution of shapes, images and landmarks.The stochasticity is introduced in the vector field which transports the datain the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework forshape analysis and image registration. The stochasticity thereby models errorsor uncertainties of the flow in following the prescribed deformation velocity.The approach is illustrated in the example of finite dimensional landmarkmanifolds, whose stochastic evolution is studied both via the Fokker-Planckequation and by numerical simulations. We derive two approaches for inferringparameters of the stochastic model from landmark configurations observed atdiscrete time points. The first of the two approaches matches moments of theFokker-Planck equation to sample moments of the data, while the second approachemploys an Expectation-Maximisation based algorithm using a Monte Carlo bridgesampling scheme to optimise the data likelihood. We derive and numerically testthe ability of the two approaches to infer the spatial correlation length ofthe underlying noise.
AU - Arnaudon,A
AU - Holm,DD
AU - Sommer,S
PY - 2017///
SN - 1615-3375
TI - A Geometric Framework for Stochastic Shape Analysis
T2 - Foundations of Computational Mathematics
UR - http://arxiv.org/abs/1703.09971v2
UR - http://hdl.handle.net/10044/1/50241
ER -