Large Deviations for Stochastic Flows of Diffeomorphisms

Budhiraja, Amarjit; Dupuis, Paul; Maroulas, Vasileios

doi:10.21236/ada476254

Cited by 1 publication

(1 citation statement)

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“…They do not estimate the registration parameters. There has been some work on stochastic flows of diffeomorphics [6], which are Brownian motions, i.e., small perturbations integrated along a time-dependent flow. This differs from the prior distribution in our work, which is on the tangent space of initial velocity fields, rather than on the entire time-dependent flow.…”

Section: Related Workmentioning

confidence: 99%

Bayesian Estimation of Regularization and Atlas Building in Diffeomorphic Image Registration

Zhang

Singh

Fletcher

2013

Lecture Notes in Computer Science

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This paper presents a generative Bayesian model for diffeomorphic image registration and atlas building. We develop an atlas estimation procedure that simultaneously estimates the parameters controlling the smoothness of the diffeomorphic transformations. To achieve this, we introduce a Monte Carlo Expectation Maximization algorithm, where the expectation step is approximated via Hamiltonian Monte Carlo sampling on the manifold of diffeomorphisms. An added benefit of this stochastic approach is that it can successfully solve difficult registration problems involving large deformations, where direct geodesic optimization fails. Using synthetic data generated from the forward model with known parameters, we demonstrate the ability of our model to successfully recover the atlas and regularization parameters. We also demonstrate the effectiveness of the proposed method in the atlas estimation problem for 3D brain images.

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Section: Related Workmentioning

confidence: 99%