We study how the quality of an image reconstructed by a binary tomographic algorithm depends on the direction of the observed object in the scanner, if only a few projections are available. To do so we conduct experiments on a set of software phantoms by reconstructing them form different projection sets using an algorithm based on D.C. programming (a method for minimizing the difference of convex functions), and compare the accuracy of the corresponding reconstructions by two suitable approaches. Based on the experiments, we discuss consequences on applications arising from the field of non-destructive testing, as well.

\

}, isbn = {978-3-642-12711-3}, doi = {10.1007/978-3-642-12712-0_22}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy}, editor = {Reneta P Barneva and Valentin E Brimkov and Herbert A Hauptman and Renato M Natal Jorge and Jo{\~a}o Manuel R S Tavares} } @inbook {866, title = {Topology Preserving Parallel Smoothing for 3D Binary Images}, booktitle = {Proceedings of the Computational Modeling of Objects Represented in Images (CMORI)}, volume = {6026}, year = {2010}, note = {ScopusID: 77952401887doi: 10.1007/978-3-642-12712-0_26}, month = {May 2010}, pages = {287 - 298}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Buffalo, USA}, abstract = {This paper presents a new algorithm for smoothing 3D binary images in a topology preserving way. Our algorithm is a reduction operator: some border points that are considered as extremities are removed. The proposed method is composed of two parallel reduction operators. We are to apply our smoothing algorithm as an iteration-by-iteration pruning for reducing the noise sensitivity of 3D parallel surface-thinning algorithms. An efficient implementation of our algorithm is sketched and its topological correctness for (26,6) pictures is proved. {\textcopyright} 2010 Springer-Verlag.

}, doi = {10.1007/978-3-642-12712-0_26}, author = {G{\'a}bor N{\'e}meth and P{\'e}ter Kardos and K{\'a}lm{\'a}n Pal{\'a}gyi}, editor = {Reneta P Barneva and Valentin E Brimkov and Herbert A Hauptman and Renato M Natal Jorge and Jo{\~a}o Manuel R S Tavares} } @inbook {1138, title = {On the number of hv-convex discrete sets}, booktitle = {Combinatorial Image Analysis}, series = {Lecture Notes in Computer Science}, number = {4958}, year = {2008}, note = {UT: 000254600100010ScopusID: 70249110264doi: 10.1007/978-3-540-78275-9_10}, month = {Apr 2008}, pages = {112 - 123}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Buffalo, NY, USA}, abstract = {One of the basic problems in discrete tomography is thereconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfills some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. The class of hv-convex discrete sets and its subclasses have a well-developed theory. Several reconstruction algorithms as well as some complexity results are known for those classes. The key to achieve polynomial-time reconstruction of an hv- convex discrete set is to have the additional assumption that the set is connected as well. This paper collects several statistics on hv-convex discrete sets, which are of great importance in the analysis of algorithms for reconstructing such kind of discrete sets. {\textcopyright} 2008 Springer-Verlag Berlin Heidelberg.

}, isbn = {978-3-540-78274-2}, doi = {10.1007/978-3-540-78275-9_10}, author = {P{\'e}ter Bal{\'a}zs}, editor = {Valentin E Brimkov and Reneta P Barneva and Herbert A Hauptman} }