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

Abstract

AbstractConstructing 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.KeywordsSurface reconstructiondense surface point distribution modelleast trimmed squares estimationhypothesis test