Bayesian characterization of uncertainty in intra-subject non-rigid registration

Petter Risholm,Isaiah Norton,Alex J Golby,Firdaus Janoos,William M Wells

doi:10.1016/j.media.2013.03.002

Petter Risholm, Isaiah Norton + Show 3 more

Open Access

https://doi.org/10.1016/j.media.2013.03.002

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Abstract

In settings where high-level inferences are made based on registered image data, the registration uncertainty can contain important information. In this article, we propose a Bayesian non-rigid registration framework where conventional dissimilarity and regularization energies can be included in the likelihood and the prior distribution on deformations respectively through the use of Boltzmann's distribution. The posterior distribution is characterized using Markov Chain Monte Carlo (MCMC) methods with the effect of the Boltzmann temperature hyper-parameters marginalized under broad uninformative hyper-prior distributions. The MCMC chain permits estimation of the most likely deformation as well as the associated uncertainty. On synthetic examples, we demonstrate the ability of the method to identify the maximum a posteriori estimate and the associated posterior uncertainty, and demonstrate that the posterior distribution can be non-Gaussian. Additionally, results from registering clinical data acquired during neurosurgery for resection of brain tumor are provided; we compare the method to single transformation results from a deterministic optimizer and introduce methods that summarize the high-dimensional uncertainty. At the site of resection, the registration uncertainty increases and the marginal distribution on deformations is shown to be multi-modal.

Highlights

The vast majority of non-rigid registration methods only report a single transformation result without any estimate of the registration uncertainty, which could provide valuable information whenever important clinical decisions, or high-level analysis, are based on registered data
If the registration result was associated with some uncertainty measure, or confidence limits, it could be possible to detect that the method had difficulty in finding a proper alignment of the images in certain locations, and the surgical risk involved with making decisions based on the registered data could be evaluated
We introduce a Bayesian nonrigid registration framework where the posterior distribution on deformation parameters is characterized by Markov Chain Monte Carlo (MCMC)

Summary

Introduction

The vast majority of non-rigid registration methods only report a single transformation (i.e. a point-estimate) result without any estimate of the registration uncertainty, which could provide valuable information whenever important clinical decisions, or high-level analysis, are based on registered data. Various factors such as the ill-posed nature of non-rigid registration, the stochastic nature of the images, the large variability of anatomy, the presence of homogeneous intensity regions, and imaging artifacts like distortion and biasfield, may negatively affect the registration uncertainty. It should be noted that a highly uncertain (low precision) registration result does not necessarily mean that the result is inaccurate and vice versa, so systematic errors (bias) of the registration model should be evaluated before placing trust in precise registration results

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