Improved Topological Preservation in 3D Axon Segmentation and Centerline Detection using Geometric Assessment-driven Topological Smoothing (GATS)

Automated axon tracing via fully supervised learning requires large amounts of 3D brain imagery, which is time consuming and laborious to obtain. It also requires expertise. Thus, there is a need for more efficient segmentation and centerline detection techniques to use in conjunction with automated annotation tools. Topology-preserving methods ensure that segmented components maintain geometric connectivity, which is especially meaningful for applications where volumetric data is used, and these methods often make use of morphological thinning algorithms as the thinned outputs can be useful for both segmentation and centerline detection of curvilinear structures. Current morphological thinning approaches used in conjunction with topology-preserving methods are prone to over-thinning and require manual configuration of hyperparameters. We propose an automated approach for morphological smoothing using geometric assessment of the radius of tubular structures in brain microscopy volumes, and apply average pooling to prevent over-thinning. We use this approach to formulate a loss function, which we call Geo-metric Assessment-driven Topological Smoothing loss, or GATS. Our approach increased segmentation and center-line detection evaluation metrics by 2%-5% across multiple datasets, and improved the Betti error rates by 9%. Our ablation study showed that geometric assessment of tubular structures achieved higher segmentation and centerline detection scores, and using average pooling for morphological smoothing in place of thinning algorithms reduced the Betti errors. We observed increased topological preservation during automated annotation of 3D axons volumes from models trained with GATS.