# Volume Visualization and 3D Image Processing on Optimal Lattices

The representation of data sets on a simple CC lattice is the most widespread standard in medical imaging and in other application areas of visualization. The root cause is that CC lattices are intuitive, easy to manage and are good in adapting to memory organization of computers. They also permit extremely simple calculations (eg. trilinear interpolation) due to their separability. Apart from their advantages there are several arguments against CC lattices. One of them is that they allow rather anisotropic sampling. By the same token the results are far from being optimal, so the question arises whether to use a lattice structure which is more isotropic and offers better quality sampling with the same grid density. The answer is actually offered by the BCC lattice therefore in 3D it is the optimal sampling grid. Numerically ~29,29% more efficient sampling might be accomplished by the BCC than by the CC lattice that is to say the same quality is feasible with less sample. On the one hand it results in smaller need of bandwidth since less data have to be stored and operated. On the other hand theoretically it allows the implementation of algorithms requiring less number of steps.

The aim of my research project is to verify the latter statement by developing a tomographic reconstruction framework. During the course of computer tomographic reconstruction, a model of the original three-dimensional object is constructed from two-dimensional projections by using iterative method. The data is evaluated in the discrete points of the space and interpolation is accomplished in the other points. The starting point is to require an appropriate quality. According to our assumption in case the discrete elements are overlapped with the points of the BCC grid, the reconstructed volumetric data will converge to the correct solution (to the original data) within less iterations, since the BCC lattice is able to represent the same spatial information in possession of ~29,29% less sample. In my thesis I am trying to test my hypothesis.