PSGMM++: Pulmonary Segment Segmentation with Anatomical Insights

The lung has a complex hierarchical structure comprising lobes and pulmonary segments. Pulmonary segments are not segmented based on visual features, but rather on anatomical knowledge that each segment is centered on a bronchus or artery, far from the intersegmental borders. In this paper, we propose PSGMM++, an extension of PSGMM, for pulmonary segment segmentation with anatomical insights. PSGMM leverages spatial information of bronchial and vascular structures and generates probability maps using Gaussian Mixture Models (GMMs) for each pulmonary segment's location, addressing the limitation of existing image-based segmentation models that lack the understanding of positional priors. Building upon PSGMM, PSGMM++ further enhances segmentation performance by explicitly incorporating anatomical relationships and utilizing local geometric features effectively. The centroids of each GMM component are located on the bronchus or artery, ensuring that the intersegmental borders are positioned away from these central structures. The covariance and weight are defined by local features extracted around each centroid, making them sensitive to local structural variations. As the training approach shifts from voxel-wise classification to classwise probability distribution generation, we introduce a novel loss function designed to maximize likelihood while satisfying the constraint of each GMM parameter through the expectation-maximization (EM) algorithm, named EM loss. Built on a solid theoretical foundation, it provides explainability when applied to pre-surgical navigation. Furthermore, PSGMM++ demonstrates effective and flexible performance due to its efficient design.