Automatic Extraction of a Piecewise Symmetry Surface of a 3D Mesh: Application to Scoliosis

Symmetry analysis of the surface of anatomical structures offers good promise for diagnosis, follow-up and therapy planning of pathologies causing abnormal deformities. This paper addresses the problem of detecting and modelling symmetry of bilateral structures, even in cases where the transformation between the two lateral parts is not a simple planar reflection but a symmetry with respect to a curved symmetry surface. We describe a new method to compute a piecewise curved symmetry surface for 3D objects. The algorithm is based on the computation of a 3D symmetry line, which defines strips by orthogonal slicing. A local symmetry plane is computed for each strip by an ICP-like method. The set of all local symmetry planes forms a piecewise symmetry surface. The method is first validated on parametric objects. Then, we show its potential as a non-invasive technique for the study of patients affected by scoliosis. Finally, our approach is generic enough that it could be extended to other medical applications such as facial dysplasia.