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The talks are about 30 minutes long. There is also time for questions and after PM for free discussions as well. Some snacks and refreshments will be served bring your mug, if possible. Topology preservation is a crucial issue in parallel reductions that transform binary pictures by changing only a set of black points to white at a time. We present three sufficient conditions for topology-preserving parallel reductions on the three types of pictures of the unconventional 3D face-centered cubic FCC grid.
One of them provides methods of verifying that a given parallel reduction always preserves the topology. The remaining ones directly provide deletion rules of topology-preserving parallel reductions, and make us possible to generate topologically correct thinning algorithms.
Furthermore, we construct a kernel-thinning algorithm from our last sufficient condition. In computed tomography and several related scientific domains, the Fourier slice theorem is a powerful mathematical tool to solve the problem of image reconstruction.
Although this theorem is well understood in the continuous case, a detailed quantitative analysis of artifacts caused by discretization is rarely found in the computed tomographic literature. Assuming a practical Fourier Domain Reconstruction FDR algorithm, which performs resampling by interpolation or approximation in the frequency domain, artifacts have two main sources.