Globally optimal spinal cord segmentation using a minimal path in high dimensions

Spinal cord segmentation is an important step to empirically quantify spinal cord atrophy that can occur in neurological diseases such as multiple sclerosis (MS). In this work, we propose a novel method to find the globally optimal segmentation of the spinal cord using a high dimensional minimal path search. The spinal cord cross-sectional shapes are represented using principal component analysis (in the probability simplex) which captures most of spinal cord's axial cross-sectional variation and partial volume effects. We propose modifications to the A* minimal path search algorithm that drastically reduce the required memory and run-time to make our high dimensional minimal path optimization computationally feasible. Finally, we validate our results over five vertebrae levels of both healthy and MS clinical MR volumes (20 volumes total) and show improvements on volume agreement with expert segmentations and less user interaction when compared to current state-of-the-art methods.