[Paper Review] Perturb-and-MPM: Quantifying Segmentation Uncertainty in Dense Multi-Label CRFs

Raphael Meier, Urspeter Knecht+3 more|arXiv (Cornell University)|Mar 1, 2017

Radiomics and Machine Learning in Medical Imaging30 references3 citations

TL;DR

This paper introduces Perturb-and-MPM, a computationally efficient method for quantifying segmentation uncertainty in dense multi-label Conditional Random Fields (CRFs) by applying random perturbations to approximate sampling from the Gibbs distribution. The approach generates spatial uncertainty maps that accurately localize segmentation errors, particularly at tissue boundaries, and improves the reliability of imaging biomarkers like extent of resection and residual tumor volume in glioblastoma patients.

ABSTRACT

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.

Motivation & Objective

• To address the lack of uncertainty quantification in dense multi-label CRFs, which are widely used in medical image segmentation but lack probabilistic sampling capabilities.
• To develop a computationally efficient method for generating spatial uncertainty maps that reflect confidence in segmentation results.
• To validate the method on challenging glioblastoma tumor core segmentation and demonstrate its clinical utility in improving imaging biomarker estimation.
• To enable uncertainty-aware segmentation workflows that support human expert review and enhance reliability in radiotherapy and neurosurgery.

Proposed method

• Proposes Perturb-and-MPM, a perturbation-based sampling method that applies random perturbations to the energy function of a dense multi-label CRF to approximate samples from the Gibbs distribution.
• Uses a variant of the MAP inference framework, replacing exact MAP with a perturbed version to enable sampling without requiring full MCMC or ILP solving.
• Employs st-cut-based min-marginal estimation for uncertainty computation, which is feasible in the context of the perturbed energy function.
• Derives spatial uncertainty maps from the frequency of voxel label changes across multiple perturbed samples, reflecting local confidence in segmentation.
• Applies the method to 3D MR images of glioblastoma patients, using synthetic data for error analysis and clinical data for validation.
• Validates the method using ground truth from expert raters and evaluates uncertainty maps against segmentation errors and biomarker accuracy.

Experimental results

Research questions

• RQ1 Can perturbation-based sampling effectively quantify uncertainty in dense multi-label CRFs where exact sampling is infeasible?
• RQ2 How well do the resulting uncertainty maps localize segmentation errors, particularly at tissue boundaries?
• RQ3 Can uncertainty maps improve the accuracy of volumetric imaging biomarkers such as extent of resection and residual tumor volume?
• RQ4 Does the method remain robust and efficient when applied to large-scale 3D medical image volumes?

Key findings

• Uncertain regions identified by Perturb-and-MPM correspond closely to areas with segmentation errors, especially at tissue boundaries where labeling is most ambiguous.
• The method produces stable uncertainty maps after a small number of samples, indicating convergence and computational efficiency.
• Excluding uncertain voxels from volume estimation significantly improved the accuracy of extent of resection and residual tumor volume biomarkers compared to ground truth from four expert raters.
• The uncertainty maps are most informative in regions of high boundary complexity, while overconfident models may fail to reflect errors in central regions of misclassified areas.
• Perturb-and-MPM enables reliable uncertainty quantification without requiring MCMC or ILP solving, making it suitable for clinical deployment.
• The approach enhances the reliability of automated segmentation in high-throughput radiomics by providing data quality measures through uncertainty estimation.