Fast computed tomography and volume rendering using the body-centered cubic lattice

Two main tasks in the field of volumetric image processing are acquisition and visualization of 3D data. The main challenge is to reduce processing costs, while maintaining high accuracy. To achieve these goals for volume rendering (visualization), we demonstrate that non-separable box splines for body-centered cubic (BCC) lattices can be adapted to fast evaluation on graphics hardware. Thus, the BCC lattice can be used for interactive volume rendering leading to better image quality than comparable methods. Leveraging this result, we study volumetric reconstruction methods based on the Expectation Maximization (EM) algorithm. We show the equivalence of the standard implementation of the EM-based reconstruction with an implementation based on hardware-accelerated volume rendering for nearest-neighbor interpolation to achieve fast reconstruction times. Accuracy is improved by adapting the EM algorithm for the BCC lattice, leading to superior accuracy, more compact data representation, and better noise reduction compared to the Cartesian one.