An optimal three-stage method for anatomical shape reconstruction from sparse information using a dense surface point distribution model

摘要

Constructing anatomical shape from sparse information is a challenging task. A priori information is often required to handle this otherwise ill-posed problem. In this paper, the problem is formulated as a three-stage optimal estimation process using an a priori dense surface point distribution model (DS-PDM). The dense surface point distribution model itself is constructed from an already-aligned training shape set using Loop subdivision. It provides a dense and smooth description of all a priori training shapes. Its application in anatomical shape reconstruction facilitates all three stages as follows. The first stage, registration, is to iteratively estimate the scale and the 6-dimensional (6D) rigid registration transformation between the mean shape of DS-PDM and the input points using the iterative closest point (ICP) algorithm. Due to the dense description of the mean shape, a simple point-to-point distance is used to speed up the searching for closest point pairs. The second stage, morphing, optimally and robustly estimates a dense patient-specific template surface from DS-PDM using Mahalanobis distance based regularization. The estimated dense patient-specific template surface is then fed to the third stage, deformation, which uses a newly formularized kernel-based regularization to further reduce the reconstruction error. The proposed method is especially useful for accurate and stable surface reconstruction from sparse information when only a small number of a priori training shapes are available. It has been successfully tested on anatomical shape reconstruction of femoral heads using only dozens of sparse points, yielding very promising results.