  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^2VR) to jointly estimate Cobb angles
and landmarks of the spine in X-rays in one single framework. The proposed
S^2VR 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 S2VR by kernel target
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, which
indicates its great potential in clinical use.
