A Topological Nomenclature for 3D Shape Analysis in Connectomics

An essential task in nano-scale connectomics is the morphology analysis of neurons and organelles like mitochondria to shed light on their biological properties. However, these biological objects often have tangled parts or complex branching patterns, which makes it hard to abstract, categorize, and manipulate their morphology. Here we propose a topological nomenclature to name these objects like chemical compounds for neuroscience analysis. To this end, we convert the volumetric representation into the topology-preserving reduced graph, develop nomenclature rules for pyramidal neurons and mitochondria from the reduced graph, and learn the feature embedding for shape manipulation. In ablation studies, we show that the proposed reduced graph extraction method yield graphs better in accord with the perception of experts. On 3D shape retrieval and decomposition tasks, we show that the encoded topological nomenclature features achieve better results than state-of-the-art shape descriptors. To advance neuroscience, we will release a 3D mesh dataset of mitochondria and pyramidal neurons reconstructed from a 100{\mu}m cube electron microscopy (EM) volume. Code is publicly available at https://github.com/donglaiw/ibexHelper.