Understanding bone morphology is essential for successful computer assisted orthopaedic surgery, where definition of normal anatomical variations and abnormal morphological patterns can assist in surgical planning and evaluation of outcomes. The proximal femur was the anatomical target of the study described here. Orthopaedic surgeons have studied femoral geometry using 2D and 3D radiographs for precise fit of bone-implant with biological fixation. The use of a Statistical Shape Model (SSM) is a promising venue for understanding bone morphologies and for deriving generic description of normal anatomy. A SSM uses measures of statistics on geometrical descriptions over a population. Current SSM construction methods, based on Principal Component Analysis (PCA), assume that shape morphologies can be modeled by pure point translations. Complicated morphologies, such as the femoral head-neck junction that has non-rigid components, can be poorly explained by PCA. In this work, we showed that PCA was impotent for processing complex deformations of the proximal femur and propose in its place our Principal Tangent Component (PTC) analysis. The new method used the Lie algebra of affine transformation matrices to perform simple computations, in tangent spaces, that corresponded to complex deformations on the data manifold.INTRODUCTION
METHOD
