We propose a method for improving the quality of cone-beam tomographic reconstruction done with a C-arm. C-arm scans frequently suffer from incomplete information due to image truncation, limited scan length, or other limitations. Our proposed "hybrid reconstruction" method injects information from a prior anatomical model, derived from a subject-specific computed tomography (CT) or from a statistical database (atlas), where the C-arm X-ray data is missing. This significantly reduces reconstruction artifacts with little loss of true information from the X-ray projections. The methods consist of constructing anatomical models, fast rendering of digitally reconstructed radiograph (DRR) projections of the models, rigid or deformable registration of the model and the X-ray images, and fusion of the DRR and X-ray projections, all prior to a conventional filtered back-projection algorithm. Our experiments, conducted with a mobile image intensifier C-arm, demonstrate visually and quantitatively the contribution of data fusion to image quality, which we assess through comparison to a "ground truth" CT. Importantly, we show that a significantly improved reconstruction can be obtained from a C-arm scan as short as 90° by complementing the observed projections with DRRs of two prior models, namely an atlas and a preoperative same-patient CT. The hybrid reconstruction principles are applicable to other types of C-arms as well.

This paper presents a novel method for volume rendering of unstructured grids. Previously, we introduced an algorithm for perspective-correct interpolation of barycentric coordinates and computing polynomial attenuation integrals for a projected tetrahedron using graphics hardware. Here, we enhance the algorithm by providing a simple and efficient method to compute the projected shape (silhouette) and tessellation of a tetrahedron, in perspective and orthographic projection models. Our tessellation algorithm is published here for the first time. Compared with works of other groups on rendering unstructured grids, the main contributions of this work are: 1) A new algorithm for finding the silhouette of a projected tetrahedron. 2) A method for interpolating barycentric coordinates and thickness on the faces of the tetrahedron. 3) Visualizing higher-order attenuation functions using GPU without preintegration. 4) Capability of applying shape deformations to a rendered tetrahedral mesh without significant performance loss. Our visualization model is independent of depth-sorting of the cells. We present imaging and timing results of our implementation, and an application in time-critical "2D-3D" deformable registration of anatomical models. We discuss the impact of using higher-order functions on quality and performance.

This paper presents a novel method for computing simulated x-ray images, or DRRs (digitally reconstructed radiographs), of tetrahedral meshes with higher-order attenuation functions. DRRs are commonly used in computer assisted surgery (CAS), with the attenuation function consisting of a voxelized CT study, which is viewed from different directions. Our application of DRRs is in intra-operative "2D-3D" registration, i.e., finding the pose of the CT dataset given a small number of patient radiographs. We register 2D patient images with a statistical tetrahedral model, which encodes the CT intensity numbers as Bernstein polynomials, and includes knowledge about typical shape variation modes. The unstructured grid is more suitable for applying deformations than a rectilinear grid, and the higher-order polynomials provide a better approximation of the actual density than constant or linear models. The infra-operative environment demands a fast method for creating the DRRs, which we present here. We demonstrate this application through the creation and use of a deformable atlas of human pelvis bones. Compared with other works on rendering unstructured grids, the main contributions of this work are: 1) Simple and perspective-correct interpolation of the thickness of a tetrahedral cell. 2) Simple and perspective-correct interpolation of front and back barycentric coordinates with respect to the cell. 3) Computing line integrals of higher-order functions. 4) Capability of applying shape deformations and variations in the attenuation function without significant performance loss. The method does not depend on for pre-integration, and does not require depth-sorting of the visualized cells. We present imaging and timing results of implementing the algorithm, and discuss the impact of using higher-order functions on the quality of the result and the performance.