Segmentation of vertebrae from 3D spine images by applying concepts from transportation and game theories

Abstract

We describe a landmark-based three-dimensional (3D) segmentation framework, in which the shape representation of the object of interest is based on concepts from transportation theory. Landmark-based shape representation relies on a premise that considering spatial relationships for every pair of landmarks is redundant, therefore landmarks are first separated into clusters. Landmarks within each cluster form a complete graph of connections, while landmarks within any two clusters are connected in a one-to-one manner by applying a concept from transportation theory called the optimal assignment. The resulting optimal assignment-based shape representation captures the most descriptive shape properties and therefore represents an adequate balance among rigidity, elasticity and computational complexity, and is combined with a 3D landmark detection algorithm that is based on concepts from game theory. The framework was applied to segment 50 lumbar vertebrae from 3D computed tomography images, and the resulting symmetric surface distance of 0.76}0.10mm and Dice coefficient of 93.5}1.0% indicate that accurate segmentation can be obtained by the described framework. Moreover, when compared to the complete graph, the computational time was reduced by a factor of approximately nine in the case of optimal assignment-based shape representation.