A shape-partitioned statistical shape model for highly deformed femurs using X-ray images

To develop a patient-specific 3 D reconstruction of a femur modeled using the statistical shape model (SSM) and X-ray images, it is assumed that the target shape is not outside the range of variations allowed by the SSM built from a training dataset. We propose the shape-partitioned statistical shape model (SPSSM) to cover significant variations in the target shape. This model can divide a shape into several segments of anatomical interest. We break up the eigenvector matrix into the corresponding representative matrices for the SPSSM by preserving the relevant rows of the original matrix without segmenting the shape and building an independent SSM for each segment. To quantify the reconstruction error of the proposed method, we generated two groups of deformation models of the femur which cannot be easily represented by the conventional SSM. One group of femurs had an anteversion angle deformation, and the other group of femurs had two different scales of the femoral head. Each experiment was performed using the leave-one-out method for twelve femurs. When the femoral head was rotated by 30 degrees, the average reconstruction error of the conventional SSM was 5.34 mm, which was reduced to 3.82 mm for the proposed SPSSM. When the femoral head size was decreased by 20%, the average reconstruction error of the SSM was 4.70 mm, which was reduced to 3.56 mm for the SPSSM. When the femoral head size was increased by 20%, the average reconstruction error of the SSM was 4.28 mm, which was reduced to 3.10 mm for the SPSSM. The experimental results for the two groups of deformation models showed that the proposed SPSSM outperformed the conventional SSM.