3D Cobb Angle Measurements from Scoliotic Mesh Models with Varying Face-Vertex Density

Abstract

To evaluate spinal deformities, the Cobb angle is the main diagnostic parameter that is usually measured on two-dimensional coronal radiographic (X-ray) images. In this paper, we propose a method for the evaluation of the three-dimensional (3D) Cobb angle from 3D spine mesh models with varying face-vertex density. For the upper-end and lower-end vertebra mesh models, the location of the vertebral body center and mesh faces that belong to the vertebral body surface are identified by unsupervised classification of mesh faces of the vertebral body, which serve only as training data, and subsequent supervised classification of all mesh faces. Adjacent mesh faces are then labeled with the same class, and after comparison to mesh faces in the training data, we label the mesh faces of the superior and inferior vertebral endplate. Finally, planes are fitted to the superior endplate of the upper-end vertebra and the inferior endplate of the lower-end vertebra, which define the 3D Cobb angle. The method was tested on 60 triangular mesh models of the scoliotic spine, and each mesh model was generated at 17 different face-vertex densities. For meshes with the mean face edge length below 6 mm, the proposed method was accurate, with the mean absolute error of $3.0^\circ$ and the corresponding standard deviation of $2.2^\circ$ when compared to reference measurements.