Deep Laplacian Coordinates: End-to-end deeply guided anisotropic diffusion for COVID-19 pulmonary lesion segmentation

Despite notable advances in deep learning, accurately segmenting lung lesions in computed tomography remains a significant challenge due to the scarcity of annotated data and the high diversity in lesion appearance. To address these issues, seeded image segmentation stands out as a flexible and accurate approach, adapting to diverse image contexts and target definitions. Building on this perspective, we introduce the Deep Laplacian Coordinates Neural Network (DLCNN): a novel framework that integrates deep boundary detection, anisotropic diffusion and seed-driven labeling to segment lung lesions caused by COVID-19. DLCNN employs a semantically enriched deep contour network that predicts edge weights for a graph-based image representation. These weights are then incorporated into our label propagation model, which is built upon the Laplacian Coordinates diffuser, leveraging many attractive properties such as global optimality, robust boundary delineation and directionally adaptive diffusion. By combining the representational power of deep boundary learning with the generalizability of a seed-driven anisotropic diffusion model, the proposed framework accurately captures lung lesions, even when boundaries are poorly defined. DLCNN consistently outperforms both recent and state-of-the-art marker-based segmentation methods, as confirmed by extensive quantitative and qualitative analyses, particularly in complex scenarios involving low contrast and irregular lesion shapes.