A statistical shape model of femoral head-neck cross sections using principal tangent components

Diagnosis of orthopedic conditions, such as femoroacetabular impingement, is difficult to automate. Current methods rely on human analysis of contours that are derived from planar cross-sections of volumetric data. We propose a statistical shape model for analyzing proximal femoral contours. Current frameworks, based on principal component analysis, appear inadequate for analyzing femoral contours because of the complex deformations in diseased patients. We present an analysis based on principal tangent components as a new method for shape description. This model represents deformations as a flow on a manifold, then performs calculations on the associated tangent spaces through exponential mapping, which is appealing because computations on the tangent spaces are Euclidean even if the actual deformations are highly nonlinear. The new model recovered 98% of the contour shapes using only two components, whereas the conventional method needed 48 components to achieve the same reconstruction.