Construction and Simplification of Bone Density Models

This paper presents a hierarchical tetrahedral mesh model to represent the bone density atlas. We propose and implement an efficient and automatic method to construct hierarchical tetrahedral meshes from CT data sets of bony anatomy. The tetrahedral mesh is built based on contour tiling between CT slices. The mesh is then smoothed using an enhanced Laplacian algorithm. And we approximate bone density variations by means of continuous density functions written as smooth Bernstein polynomial spline expressed in terms of barycentric coordinates associated with each tetrahedron. We further perform the tetrahedral mesh simplification by collapsing the tetrahedra and build hierarchical structure with multiple resolutions. Both the shape and density error bound are preserved during the simplification. Furthermore a deformable prior model is computed from a collection of training models. Point Distribution Model is used to compute the variability of the prior model. Both the shape information and the density statistics are parameterized in the prior model. Our model demonstrates good accuracy, high storage efficiency and processing efficiency. We also compute the Digitally Reconstructed Radiographs from our model and use them to evaluate the accuracy and efficiency of our model. Our method has been tested on femur and pelvis data sets. This research is part of our effort of building density atlases for bony anatomies and applying them in deformable density based registrations. Keyword: Hierarchical Tetrahedral Mesh, Density Function, Mesh Simplification, Prior Model