  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.
