  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.
