3D anatomical shape atlas construction using mesh quality preserved deformable models

The construction of 3D anatomical shape atlas has been extensively studied in medical image analysis research for a variety of applications. Among the multiple steps of shape atlas construction, establishing anatomical correspondences across subjects is probably the most critical and challenging one. The adaptive focus deformable model (AFDM) [16] was proposed to tackle this problem by exploiting cross-scale geometry characteristics of 3D anatomy surfaces. Although the effectiveness of AFDM has been proved in various studies, its performance is highly dependent on the quality of 3D surface meshes. In this paper, we propose a new framework for 3D anatomical shape atlas construction. Our method aims to robustly establish correspondences across different subjects and simultaneously generate high-quality surface meshes without removing shape detail. Mathematically, a new energy term is embedded into the original energy function of AFDM to preserve surface mesh qualities during the deformable surface matching. Shape details and smoothness constraints are encoded into the new energy term using the Laplacian representation An expectation-maximization style algorithm is designed to optimize multiple energy terms alternatively until convergence. We demonstrate the performance of our method via two diverse applications: 3D high resolution CT cardiac images and rat brain MRIs with multiple structures.