Accepted for Publication in Ieee Transactions on Medical Imaging (preprint) Quantifying Registration Uncertainty with Sparse Bayesian Modelling
Accepted for Publication in Ieee Transactions on Medical Imaging (preprint) Quantifying Registration Uncertainty with Sparse Bayesian Modelling
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接受发表在 IEEE Transactions on Medical Imaging（预印本）中使用稀疏贝叶斯模型量化配准不确定性
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通讯作者：
N. Ayache
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作者：
Lo¨ıc Le Folgoc;H. Delingette;A. Criminisi;N. Ayache
我们研究了稀疏贝叶斯模型下医学图像配准的不确定性量化。贝叶斯建模在自动调优配准超参数（如数据和正则化函数之间的权衡）方面已经被证明是强大的。稀疏诱导先验最近被用来使参数化本身自适应和数据驱动。变换参数的稀疏先验有效地支持使用粗基函数来捕获可见运动的全局趋势，而只有在存在相干图像信息和运动的情况下才引入更精细、高度局部化的基函数。在早期的工作中，稀疏贝叶斯模型下的近似推理是在一个高效的变分贝叶斯（VB）框架中解决的。在本文中，我们感兴趣的是在这种近似方案下与在精确模型下得出的不确定性估计的理论和经验质量。我们实现了一种基于可逆跳跃马尔可夫链蒙特卡罗（MCMC）采样的（渐近）精确推理方案来表征变换的后验分布，并比较了基于VB和MCMC的方法的预测结果。发现稀疏贝叶斯模型下的真实后验分布是有意义的：估计不确定性的数量级在数量上是合理的，在无纹理区域的不确定性较高，在强度梯度强的方向上不确定性较低。
—We investigate uncertainty quantification under a sparse Bayesian model of medical image registration. Bayesian modelling has proven powerful to automate the tuning of registration hyperparameters, such as the trade-off between the data and regularization functionals. Sparsity-inducing priors have recently been used to render the parametrization itself adaptive and data-driven. The sparse prior on transformation parameters effectively favors the use of coarse basis functions to capture the global trends in the visible motion while finer, highly localized bases are introduced only in the presence of coherent image information and motion. In earlier work, approximate inference under the sparse Bayesian model was tackled in an efficient Variational Bayes (VB) framework. In this paper we are interested in the theoretical and empirical quality of uncertainty estimates derived under this approximate scheme vs. under the exact model. We implement an (asymptotically) exact inference scheme based on reversible jump Markov Chain Monte Carlo (MCMC) sampling to characterize the posterior distribution of the transformation and compare the predictions of the VB and MCMC based methods. The true posterior distribution under the sparse Bayesian model is found to be meaningful: orders of magnitude for the estimated uncertainty are quantitatively reasonable, the uncertainty is higher in textureless regions and lower in the direction of strong intensity gradients.