Spatial registration of neuron morphologies based on maximization of volume overlap

Morphological features are widely used in the study of neuronal function and pathology. Invertebrate neurons are often structurally stereotypical, showing little variance in gross spatial features but larger variance in their fine features. Such variability can be quantified using detailed spatial analysis, which however requires the morphologies to be registered to a common frame of reference. We outline here new algorithms - Reg-MaxS and Reg-MaxS-N - for co-registering pairs and groups of morphologies, respectively. Reg-MaxS applies a sequence of translation, rotation and scaling transformations, estimating at each step the transformation parameters that maximize spatial overlap between the volumes occupied by the morphologies. We test this algorithm with synthetic morphologies, showing that it can account for a wide range of transformation differences and is robust to noise. Reg-MaxS-N co-registers groups of more than two morphologies by iteratively calculating an average volume and registering all morphologies to this average using Reg-MaxS. We test Reg-MaxS-N using five groups of morphologies from the Droshophila melanogaster brain and identify the cases for which it outperforms existing algorithms and produce morphologies very similar to those obtained from registration to a standard brain atlas. We have described and tested algorithms for co-registering pairs and groups of neuron morphologies. We have demonstrated their application to spatial comparison of stereotypic morphologies and calculation of dendritic density profiles, showing how our algorithms for registering neuron morphologies can enable new approaches in comparative morphological analyses and visualization.