Path-space algebra for constructing an average neuronal atlas from multi-class neuronal datasets

An open problem in biological image processing and analysis is the automated generation of neural atlases from image data. Such a neural atlas should be capable of representing typical neurons for each possible class. Further, the functioning atlas, called a neurome in this work, should enable the computation of neuron-to-neuron distances for the purposes of comparison and classification. Three technical roadblocks stand between the state of the art and the realization of a neural atlas. These three problems are the automated segmentation or tracing of 3-D neurons from image data, the computation of a neuron-to-neuron distance and the generation of a prototypical average neuron from the descriptions of multiple neurons. This paper concentrates on the latter problem - that of generating an average neuron. Our approach is hinged on the fundamental assumption that the individual paths of a neuron can be analyzed individually and used to describe the neuron as unit. In this path-based description, we account for path concurrence (the coexistence of multiple paths at given point), hierarchy (the importance of a path segment based on the position in a tree structure) and the actual 3-D position. This proof of concept is demonstrated by way of computing average neurons for three classes of neurons.