Quantitative study of perivascular spaces (PVSs) in brain magnetic resonance (MR) images is important for understanding the brain lymphatic system and its relationship with neurological diseases. One of major challenges is the accurate extraction of PVSs that have very thin tubular structures with various directions in three-dimensional (3D) MR images. In this paper, we propose a learning-based PVS segmentation method to address this challenge. Specifically, we first determine a region of interest (ROI) by using the anatomical brain structure and the vesselness information derived from eigenvalues of image derivatives. Then, in the ROI, we extract a number of randomized Haar features which are normalized with respect to the principal directions of the underlying image derivatives. The classifier is trained by the random forest model that can effectively learn both discriminative features and classifier parameters to maximize the information gain. Finally, a sequential learning strategy is used to further enforce various contextual patterns around the thin tubular structures into the classifier. For evaluation, we apply our proposed method to the 7T brain MR images scanned from 17 healthy subjects aged from 25 to 37. The performance is measured by voxel-wise segmentation accuracy, cluster- wise classification accuracy, and similarity of geometric properties, such as volume, length, and diameter distributions between the predicted and the true PVSs. Moreover, the accuracies are also evaluated on the simulation images with motion artifacts and lacunes to demonstrate the potential of our method in segmenting PVSs from elderly and patient populations. The experimental results show that our proposed method outperforms all existing PVS segmentation methods
