  This paper proposes a novel approach for uncertainty quantification in dense
Conditional Random Fields (CRFs). The presented approach, called
Perturb-and-MPM, enables efficient, approximate sampling from dense multi-label
CRFs via random perturbations. An analytic error analysis was performed which
identified the main cause of approximation error as well as showed that the
error is bounded. Spatial uncertainty maps can be derived from the
Perturb-and-MPM model, which can be used to visualize uncertainty in image
segmentation results. The method is validated on synthetic and clinical
Magnetic Resonance Imaging data. The effectiveness of the approach is
demonstrated on the challenging problem of segmenting the tumor core in
glioblastoma. We found that areas of high uncertainty correspond well to
wrongly segmented image regions. Furthermore, we demonstrate the potential use
of uncertainty maps to refine imaging biomarkers in the case of extent of
resection and residual tumor volume in brain tumor patients.
