In binary tomography, the goal is to reconstruct binary images from a small set of their projections. However, especially when only two projections are used, the task can be extremely underdetermined. In this paper, we show how to reduce ambiguity by using the morphological skeleton of the image as a priori. Three different variants of our method based on Simulated Annealing are tested using artificial binary images, and compared by reconstruction time and error. © 2012 Springer-Verlag.

%B Combinatorial Image Analysis %S Lecture Notes in Computer Science %I Springer Verlag %C Berlin; Heidelberg; New York; London; Paris; Tokyo %P 263 - 273 %8 Nov 2012 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-34732-0_20 %0 Book Section %B Computational Modeling of Objects Represented in Images %D 2010 %T Direction-dependency of a binary tomographic reconstruction algorithm %A László Gábor Varga %A Péter Balázs %A Antal Nagy %E Reneta P Barneva %E Valentin E Brimkov %E Herbert A Hauptman %E Renato M Natal Jorge %E João Manuel R S Tavares %XWe 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.

%B Computational Modeling of Objects Represented in Images %S Lecture Notes in Computer Science %I Springer Verlag %C Buffalo, NY, USA %P 242 - 253 %8 May 2010 %@ 978-3-642-12711-3 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-12712-0_22 %0 Book Section %B Combinatorial Image Analysis %D 2008 %T On the number of hv-convex discrete sets %A Péter Balázs %E Valentin E Brimkov %E Reneta P Barneva %E Herbert A Hauptman %X

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. © 2008 Springer-Verlag Berlin Heidelberg.

%B Combinatorial Image Analysis %S Lecture Notes in Computer Science %I Springer Verlag %C Buffalo, NY, USA %P 112 - 123 %8 Apr 2008 %@ 978-3-540-78274-2 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-540-78275-9_10