Bridge Simulation and Metric Estimation on Landmark Manifolds

被引：12

作者：

Sommer, Stefan ^{[1
]}

Arnaudon, Alexis ^{[2
]}

Kuhnel, Line ^{[1
]}

Joshi, Sarang ^{[3
]}

机构：

[1] Univ Copenhagen, Dept Comp Sci DIKU, Copenhagen, Denmark

[2] Imperial Coll London, Dept Math, London, England

[3] Univ Utah, Dept Bioengn, Sci Comp & Imaging Inst, Salt Lake City, UT 84112 USA

来源：

GRAPHS IN BIOMEDICAL IMAGE ANALYSIS, COMPUTATIONAL ANATOMY AND IMAGING GENETICS | 2017年 / 10551卷

关键词：

Landmarks; Brownian motion; Brownian bridges; MLE; IMAGE REGISTRATION; DEFORMATION; DIFFEOMORPHISMS; DIFFUSION; FLOWS;

D O I：

10.1007/978-3-319-67675-3_8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：79 / 91

页数：13

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