  The shape and connectivity of a neuron determine its function. Modern imaging
methods have proven successful at extracting such information. However, in
order to analyze this type of data, neuronal morphology needs to be encoded in
a graph-theoretic method. This encoding enables the use of high throughput
informatic methods to extract and infer brain function. The application of
graph-theoretic methods to neuronal morphological representation comes with
certain difficulties. Here we report a novel, effective method to accomplish
this task.
  The morphology of a neuron, which consists of its overall size, global shape,
local branch patterns, and cell-specific biophysical properties, can vary
significantly with the cell's identity, location, as well as developmental and
physiological state. Various algorithms have been developed to customize shape
based statistical and graph related features for quantitative analysis of
neuromorphology, followed by the classification of neuron cell types using the
features. Unlike the classical feature extraction based methods from imaged or
3D reconstructed neurons, we propose a model based on the rooted path
decomposition from the soma to the dendrites of a neuron and extract
morphological features on each path. We hypothesize that measuring the distance
between two neurons can be realized by minimizing the cost of continuously
morphing the set of all rooted paths of one neuron to another. To validate this
claim, we first establish the correspondence of paths between two neurons using
a modified Munkres algorithm. Next, an elastic deformation framework that
employs the square root velocity function is established to perform the
continuous morphing, which, in addition, provides an effective visualization
tool. We experimentally show the efficacy of NeuroPath2Path, NeuroP2P, over the
state of the art.
