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Quantifying Registration Uncertainty With Sparse Bayesian Modelling.

Loic Le Folgoc, Herve Delingette, Antonio Criminisi

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    This study compares uncertainty estimates from approximate Bayesian modeling and exact Markov Chain Monte Carlo sampling for medical image registration. The exact method validates the approximate model, showing reasonable uncertainty quantification in image regions with varying texture and gradients.

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    Area of Science:

    • Medical Image Analysis
    • Computational Biology
    • Statistical Modeling

    Background:

    • Bayesian modeling automates hyperparameter tuning in medical image registration.
    • Sparsity-inducing priors enable adaptive, data-driven parametrization of transformations.
    • Variational Bayes (VB) offers an efficient approximate inference framework.

    Purpose of the Study:

    • To evaluate the accuracy of uncertainty quantification from approximate (VB) vs. exact (MCMC) Bayesian inference in sparse medical image registration models.
    • To compare the performance of VB and MCMC methods in characterizing the posterior distribution of transformations.
    • To assess the clinical relevance and reliability of uncertainty estimates in medical image registration.

    Main Methods:

    • Implementation of an exact inference scheme using reversible jump Markov Chain Monte Carlo (MCMC) sampling.
    • Characterization of the posterior distribution of transformation parameters.
    • Comparison of uncertainty predictions between VB and MCMC-based methods.

    Main Results:

    • The true posterior distribution under the sparse Bayesian model is found to be meaningful and quantitatively reasonable.
    • Uncertainty estimates are higher in textureless image regions.
    • Uncertainty estimates are lower in areas with strong image intensity gradients.

    Conclusions:

    • The sparse Bayesian model provides meaningful uncertainty quantification for medical image registration.
    • Approximate inference (VB) yields reliable uncertainty estimates comparable to exact methods (MCMC).
    • Uncertainty maps accurately reflect image characteristics, highlighting areas of lower confidence in textureless regions.