Uncertainty Estimation in Vascular Networks

Reconstructing vascular networks is a challenging task in medical image processing as automated methods have to deal with large variations in vessel shape and image quality. Recent methods have addressed this problem as constrained maximum a posteriori (MAP) inference in a graphical model, formulated over an overcomplete network graph. Manual control and adjustments are often desired in practice and strongly benefit from indicating the uncertainties in the reconstruction or presenting alternative solutions. In this paper, we examine two different methods to sample vessel network graphs, a perturbation and a Gibbs sampler, and thereby estimate marginals. We quantitatively validate the accuracy of the approximated marginals using true marginals, computed by enumeration.

[1]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[2]  Anand D. Sarwate,et al.  On Measure Concentration of Random Maximum A-Posteriori Perturbations , 2013, ICML.

[3]  E. Gumbel.  Statistical Theory of Extreme Values and Some Practical Applications : A Series of Lectures , 1954 .

[4]  Gábor Székely,et al.  Reconstructing cerebrovascular networks under local physiological constraints by integer programming , 2015, Medical Image Anal..

[5]  Bjoern H. Menze,et al.  Uncertainty quantification in brain tumor segmentation using CRFs and random perturbation models , 2016, 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI).

[6]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .

[7]  Tommi S. Jaakkola,et al.  On the Partition Function and Random Maximum A-Posteriori Perturbations , 2012, ICML.

[8]  Max A. Viergever,et al.  Ridge-based vessel segmentation in color images of the retina , 2004, IEEE Transactions on Medical Imaging.

[9]  Gregory Shakhnarovich,et al.  Diverse M-Best Solutions in Markov Random Fields , 2012, ECCV.

[10]  Mauricio Reyes,et al.  Perturb-and-MPM: Quantifying Segmentation Uncertainty in Dense Multi-Label CRFs , 2017, ArXiv.

[11]  Subhransu Maji,et al.  On Sampling from the Gibbs Distribution with Random Maximum A-Posteriori Perturbations , 2013, NIPS.

[12]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[13]  Michael Pienn,et al.  Automated integer programming based separation of arteries and veins from thoracic CT images , 2016, Medical Image Anal..

[14]  Kurt Mehlhorn,et al.  Engineering DFS-Based Graph Algorithms , 2017, ArXiv.

[15]  Pascal Fua,et al.  Reconstructing Curvilinear Networks Using Path Classifiers and Integer Programming , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Carsten Rother,et al.  Inferring M-Best Diverse Labelings in a Single One , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[17]  George Papandreou,et al.  Perturb-and-MAP random fields: Using discrete optimization to learn and sample from energy models , 2011, 2011 International Conference on Computer Vision.

[18]  Markus Rudin,et al.  Contrast-Enhanced Magnetic Resonance Microangiography Reveals Remodeling of the Cerebral Microvasculature in Transgenic ArcAβ Mice , 2012, The Journal of Neuroscience.

[19]  Isabelle Bloch,et al.  A review of 3D vessel lumen segmentation techniques: Models, features and extraction schemes , 2009, Medical Image Anal..

[20]  Pascal Fua,et al.  Simultaneous segmentation and anatomical labeling of the cerebral vasculature , 2016, Medical Image Anal..

[21]  Vincent Lepetit,et al.  Multiscale Centerline Detection , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Bjoern H. Menze,et al.  The Minimum Cost Connected Subgraph Problem in Medical Image Analysis , 2016, MICCAI.

[23]  Tommi S. Jaakkola,et al.  Learning with Maximum A-Posteriori Perturbation Models , 2014, AISTATS.

[24]  Ryan P. Adams,et al.  Randomized Optimum Models for Structured Prediction , 2012, AISTATS.