Tetrahedral Mesh Modeling of Density Data for Anatomical Atlases and Intensity-Based Registration

In this paper, we present the first phase of our effort to build a bone density atlas. We adopted a tetrahedral mesh structure to represent anatomical structures. We propose an efficient and automatic algorithm to construct the tetrahedral mesh from contours in CT images corresponding to the outer bone surfaces and boundaries between compact bone, spongy bone, and medullary cavity. We approximate bone density variations by means of continuous density functions in each tetrahedron of the mesh. Currently, our density functions are second degree polynomial functions expressed in terms of barycentric coordinates associated with each tetrahedron. We apply our density model to efficiently generate Digitally Reconstructed Radiographs. These results are immediately applicable as means of speeding up 2D-3D and 3D-3D intensity based registration and will be incorporated into our future work on construction of atlases and deformable intensity-based registration.