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.

利用持续同调的代数学方法，P-Count基于WM损伤的拓扑特征，过滤出噪音性的WMH阳性结果，从而更准确地计数真实病灶。在ISBI2015纵向病灶分割数据集上验证了P-Count的准确性优于直接阈值法。

基于持久性的白质高信号计数方法在脑部MRI中的应用