A robust and accurate approach for reconstruction of patient-specific 3D bone models from sparse point sets

Abstract

Constructing an accurate patient-specific 3D bone model from sparse point sets is a challenging task. <i>A priori</i> information is often required to handle this otherwise ill-posed problem. Previously we have proposed an optimal approach for anatomical shape reconstruction from sparse information, which uses a dense surface point distribution model (DS-PDM) as the <i>a priori</i> information and formulates the surface reconstruction problem as a sequential three-stage optimal estimation process including (1) affine registration; (2) statistical morphing; and (3) kernel-based deformation. Mathematically, it is formulated by applying least-squares method to estimate the unknown parameters of linear regression models (the first two stages) and nonlinear regression model (the last stage). However, it is well-known that the least-squares method is very sensitive to outliers. In this paper, we propose an important enhancement that enables to realize stable reconstruction and robustly reject outliers. This is achieved by consistently employing least trimmed squares approach in all three stages of the reconstruction to robustly estimate unknown parameters of each regression model. Results of testing the new approach on a simulated data are shown.