Robust and Accurate Reconstruction of Patient-Specific 3D Surface Models from Sparse Point Sets: A Sequential Three-Stage Trimmed Optimization Approach

Abstract

Constructing an accurate patient-specific three-dimensional (3D) bone model from sparse point sets is a challenging task. A priori 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 [1], which uses a dense surface point distribution model (DS-PDM) as the a priori information and formulates the surface reconstruction problem as a three-stage optimal estimation process including (1) affine registration; (2) statistical extrapolation; and (3) kernel-based deformation. In this paper, we propose an important enhancement that enables to realize stable reconstructions and robustly reject outliers. Handling of outliers is a very crucial requirement especially in the surgical scenario. This is achieved by consistently employing the Least Trimmed Squares (LTS) approach with a roughly estimated outlier rate in all three stages of the reconstruction process. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically determine it. Results of testing the new approach on dry cadaveric femurs with different outlier rates are shown.