Articulated Spine Models for 3-D Reconstruction From Partial Radiographic Data

Three-dimensional models of the spine are extremely important to the assessment of spinal deformities. However, it could be difficult in practical situations to obtain enough accurate information to reconstruct complete 3-D models. This paper presents a set of methods to rebuild complete models either from partial 3-D models or from 2-D landmarks. The spine was modeled as an articulated object to take advantage of its natural anatomical variability. A statistical model of the vertebrae and spine shape was first derived. Then, complete models were computed by finding the articulated spine descriptions that were consistent with the observations while optimizing the prior probability given by the statistical model. The observations used were the absolute positions, orientations, and shapes of the vertebrae when a partial 3-D model was available. The reconstruction of 3-D spine models from 2-D landmarks identified on radiograph(s) was performed by minimizing the Mahalanobis distance and the landmarks reprojection error. The vertebrae estimated from partial models were within 2 mm of the measured values (which is comparable to the accuracy of currently used methods) if at least 25% of the vertebrae were available. Experiments also suggest that the reconstruction from posterior-anterior and lateral radiographs using the proposed method is more accurate than the conventional triangulation method.