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P-Count: Persistence-based Counting of White Matter Hyperintensities in Brain MRI

Xiaoling Hu, Annabel Sorby-Adams, Frederik Barkhof, W Taylor Kimberly, Oula Puonti, Juan Eugenio Iglesias

TL;DR

P-Count is presented, an algebraic WMH counting tool based on persistent homology that accounts for the topological features of WM lesions in a robust manner and is validated on the ISBI2015 longitudinal lesion segmentation dataset, where it produces significantly more accurate results than direct thresholding.

Abstract

White matter hyperintensities (WMH) are a hallmark of cerebrovascular disease and multiple sclerosis. Automated WMH segmentation methods enable quantitative analysis via estimation of total lesion load, spatial distribution of lesions, and number of lesions (i.e., number of connected components after thresholding), all of which are correlated with patient outcomes. While the two former measures can generally be estimated robustly, the number of lesions is highly sensitive to noise and segmentation mistakes -- even when small connected components are eroded or disregarded. In this article, we present P-Count, an algebraic WMH counting tool based on persistent homology that accounts for the topological features of WM lesions in a robust manner. Using computational geometry, P-Count takes the persistence of connected components into consideration, effectively filtering out the noisy WMH positives, resulting in a more accurate count of true lesions. We validated P-Count on the ISBI2015 longitudinal lesion segmentation dataset, where it produces significantly more accurate results than direct thresholding.

P-Count: Persistence-based Counting of White Matter Hyperintensities in Brain MRI

TL;DR

P-Count is presented, an algebraic WMH counting tool based on persistent homology that accounts for the topological features of WM lesions in a robust manner and is validated on the ISBI2015 longitudinal lesion segmentation dataset, where it produces significantly more accurate results than direct thresholding.

Abstract

White matter hyperintensities (WMH) are a hallmark of cerebrovascular disease and multiple sclerosis. Automated WMH segmentation methods enable quantitative analysis via estimation of total lesion load, spatial distribution of lesions, and number of lesions (i.e., number of connected components after thresholding), all of which are correlated with patient outcomes. While the two former measures can generally be estimated robustly, the number of lesions is highly sensitive to noise and segmentation mistakes -- even when small connected components are eroded or disregarded. In this article, we present P-Count, an algebraic WMH counting tool based on persistent homology that accounts for the topological features of WM lesions in a robust manner. Using computational geometry, P-Count takes the persistence of connected components into consideration, effectively filtering out the noisy WMH positives, resulting in a more accurate count of true lesions. We validated P-Count on the ISBI2015 longitudinal lesion segmentation dataset, where it produces significantly more accurate results than direct thresholding.
Paper Structure (6 sections, 3 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 6 sections, 3 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Persistence-based Counting
  4. Optimal threshold selection
  5. Experiments and Results
  6. Conclusion

Figures (4)

  • Figure 1: Motivation for P-Count: lesion counting from an MRI scan (a) based on direct thresholding of the soft probability map (b) is usually noisy and highly sensitive to the choice of the threshold (c,d).
  • Figure 2: Illustration of the proposed P-Count. (a) Illustration of the watershed algorithm in 1D. As basins fill up, each is associated with a "lifetime". (b) Changes in connected components are captured by the persistence diagram as the threshold increases.
  • Figure 3: Lesion count vs time for Subjects 2 and 4 of ISBI2015 using different thresholds (purple=more liberal; red=more conservative), for direct thresholding and P-Count. The thick red line corresponds to the ground truth count derived from manual segmentations.
  • Figure 4: 3D rendering of WMH for a sample subject. (a) Direct thresholding. (b) P-Count. (c) Ground truth. We note that a segmentation like (b) cannot be obtained by thresholding the probability map at any level, as it is based on persistence.