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This paper proposes a novel approach for uncertainty quantification in denseConditional Random Fields (CRFs). The presented approach, calledPerturb-and-MPM, enables efficient, approximate sampling from dense multi-labelCRFs via random perturbations. An analytic error analysis was performed whichidentified the main cause of approximation error as well as showed that theerror is bounded. Spatial uncertainty maps can be derived from thePerturb-and-MPM model, which can be used to visualize uncertainty in imagesegmentation results. The method is validated on synthetic and clinicalMagnetic Resonance Imaging data. The effectiveness of the approach isdemonstrated on the challenging problem of segmenting the tumor core inglioblastoma. We found that areas of high uncertainty correspond well towrongly segmented image regions. Furthermore, we demonstrate the potential useof uncertainty maps to refine imaging biomarkers in the case of extent ofresection and residual tumor volume in brain tumor patients.

Perturb-and-MPM: Quantifying Segmentation Uncertainty in Dense Multi-Label CRFs