Direct Estimation of Spinal Cobb Angles by Structured Multi-output Regression

The Cobb angle that quantitatively evaluates the spinal curvature plays an important role in the scoliosis diagnosis and treatment. Conventional measurement of these angles suffers from huge variability and low reliability due to intensive manual intervention. However, since there exist high ambiguity and variability around boundaries of vertebrae, it is challenging to obtain Cobb angles automatically. In this paper, we formulate the estimation of the Cobb angles from spinal X-rays as a multi-output regression task. We propose structured support vector regression (S\(^2\)VR) to jointly estimate Cobb angles and landmarks of the spine in X-rays in one single framework. The proposed S\(^2\)VR can faithfully handle the nonlinear relationship between input images and quantitative outputs, while explicitly capturing the intrinsic correlation of outputs. We introduce the manifold regularization to exploit the geometry of the output space. We propose learning the kernel in S\(^2\)VR by kernel alignment to enhance its discriminative ability. The proposed method is evaluated on the spinal X-rays dataset of 439 scoliosis subjects, which achieves the inspiring correlation coefficient of \(92.76\%\) with ground truth obtained manually by human experts and outperforms two baseline methods. Our method achieves the direct estimation of Cobb angles with high accuracy, indicating its great potential in clinical use.