An important requirement for various applications of binary image processing is to preserve topology. This issue has been earlier studied for two special types of image operators, namely, reductions and additions, and there have been some sufficient conditions proposed for them. In this paper, as an extension of those earlier results, we give novel sufficient criteria for general operators working on 2D pictures.

1 aKardos, Péter1 aPalágyi, Kálmán1 aBarneva, Reneta, P1 aBrimkov, Valentin E1 aŠlapal, Josef uhttp://dx.doi.org/10.1007/978-3-319-07148-0_1001224nas a2200181 4500008004100000245007800041210006900119260008200188300001400270520050400284100002000788700002000808700002300828700002300851700002500874700002200899856012100921 2012 eng d00aBinary image reconstruction from two projections and skeletal information0 aBinary image reconstruction from two projections and skeletal in aBerlin; Heidelberg; New York; London; Paris; TokyobSpringer VerlagcNov 2012 a263 - 2733 a

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.

1 aHantos, Norbert1 aBalázs, Péter1 aPalágyi, Kálmán1 aBarneva, Reneta, P1 aBrimkov, Valentin, E1 aAggarwal, Jake, K uhttps://www.inf.u-szeged.hu/en/publication/binary-image-reconstruction-from-two-projections-and-skeletal-information01137nas a2200181 4500008004100000020002200041245006400063210006100127260004700188300001400235520048800249100001900737700002300756700002300779700002400802700002200826856010700848 2012 eng d a978-3-642-34731-300aOn topology preservation for triangular thinning algorithms0 atopology preservation for triangular thinning algorithms aAustin, TX, USAbSpringer VerlagcNov 2012 a128 - 1423 aThinning is a frequently used strategy to produce skeleton-like shape features of binary objects. One of the main problems of parallel thinning is to ensure topology preservation. Solutions to this problem have been already given for the case of orthogonal and hexagonal grids. This work introduces some characterizations of simple pixels and some sufficient conditions for parallel thinning algorithms working on triangular grids (or hexagonal lattices) to preserve topology.

1 aKardos, Péter1 aPalágyi, Kálmán1 aBarneva, Reneta, P1 aBrimkov, Valentin E1 aAggarwal, Jake, K uhttps://www.inf.u-szeged.hu/en/publication/on-topology-preservation-for-triangular-thinning-algorithms01194nas a2200181 4500008004100000020002200041245005600063210005600119260002600175300001400201520058900215100002300804700002000827700001900847700002400866700002300890856009900913 2012 eng d a978-94-007-4173-700aTopology Preserving Parallel 3D Thinning Algorithms0 aTopology Preserving Parallel 3D Thinning Algorithms bSpringer-Verlagc2012 a165 - 1883 aA widely used technique to obtain skeletons of binary objects is thinning, which is an iterative layer-by-layer erosion in a topology preserving way. Thinning in 3D is capable of extracting various skeleton-like shape descriptors (i.e., centerlines, medial surfaces, and topological kernels). This chapter describes a family of new parallel 3D thinning algorithms for (26, 6) binary pictures. The reported algorithms are derived from some sufficient conditions for topology preserving parallel reduction operations, hence their topological correctness is guaranteed. ` `

Thinning is an iterative layer-by-layer erosion until only the skeleton-like shape features of the objects are left. This paper presents a family of new 3D parallel thinning algorithms that are based on our new sufficient conditions for 3D parallel reduction operators to preserve topology. The strategy which is used is called subiteration-based: each iteration step is composed of six parallel reduction operators according to the six main directions in 3D. The major contributions of this paper are: 1) Some new sufficient conditions for topology preserving parallel reductions are introduced. 2) A new 6-subiteration thinning scheme is proposed. Its topological correctness is guaranteed, since its deletion rules are derived from our sufficient conditions for topology preservation. 3) The proposed thinning scheme with different characterizations of endpoints yields various new algorithms for extracting centerlines and medial surfaces from 3D binary pictures. © 2011 Springer-Verlag Berlin Heidelberg.

1 aNémeth, Gábor1 aKardos, Péter1 aPalágyi, Kálmán1 aAggarwal, Jake, K1 aBarneva, Reneta, P1 aBrimkov, Valentin E1 aKoroutchev, Kostadin, N1 aKorutcheva, Elka, R uhttps://www.inf.u-szeged.hu/en/publication/a-family-of-topology-preserving-3d-parallel-6-subiteration-thinning-algorithms01289nas a2200205 4500008004100000020002200041245007200063210006900135260004500204300001200249520054400261100001900805700002300824700002200847700002300869700002400892700002800916700002400944856011500968 2011 eng d a978-3-642-21072-300aOn topology preservation for hexagonal parallel thinning algorithms0 atopology preservation for hexagonal parallel thinning algorithms aMadrid, SpainbSpringer VerlagcMay 2011 a31 - 423 aTopology preservation is the key concept in parallel thinning algorithms on any sampling schemes. This paper establishes some sufficient conditions for parallel thinning algorithms working on hexagonal grids (or triangular lattices) to preserve topology. By these results, various thinning (and shrinking to a residue) algorithms can be verified. To illustrate the usefulness of our sufficient conditions, we propose a new parallel thinning algorithm and prove its topological correctness. © 2011 Springer-Verlag Berlin Heidelberg.

1 aKardos, Péter1 aPalágyi, Kálmán1 aAggarwal, Jake, K1 aBarneva, Reneta, P1 aBrimkov, Valentin E1 aKoroutchev, Kostadin, N1 aKorutcheva, Elka, R uhttps://www.inf.u-szeged.hu/en/publication/on-topology-preservation-for-hexagonal-parallel-thinning-algorithms01538nas a2200217 4500008004100000020002200041245007400063210006900137260004800206300001400254520074200268100002701010700002001037700001601057700002301073700002501096700002501121700002601146700003101172856011701203 2010 eng d a978-3-642-12711-300aDirection-dependency of a binary tomographic reconstruction algorithm0 aDirectiondependency of a binary tomographic reconstruction algor aBuffalo, NY, USAbSpringer VerlagcMay 2010 a242 - 2533 aWe 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.

1 aVarga, László Gábor1 aBalázs, Péter1 aNagy, Antal1 aBarneva, Reneta, P1 aBrimkov, Valentin, E1 aHauptman, Herbert, A1 aJorge, Renato M Natal1 aTavares, João, Manuel R S uhttps://www.inf.u-szeged.hu/en/publication/direction-dependency-of-a-binary-tomographic-reconstruction-algorithm00565nas a2200145 4500008004100000245009800041210006900139260006100208300001400269100002000283700002300303700002200326700002300348856004800371 2010 eng d00aParallel Thinning Algorithms Based on Ronse's Sufficient Conditions for Topology Preservation0 aParallel Thinning Algorithms Based on Ronses Sufficient Conditio aSingaporebScientific Research Publishing Inc.cMay 2010 a183 - 1941 aNémeth, Gábor1 aPalágyi, Kálmán1 aWiederhold, Petra1 aBarneva, Reneta, P uhttp://rpsonline.com.sg/rpsweb/iwcia09.html01336nas a2200217 4500008004100000245006400041210006400105260004400169300001400213490000900227520058400236100002000820700001900840700002300859700002300882700002400905700002500929700002600954700003100980856010701011 2010 eng d00aTopology Preserving Parallel Smoothing for 3D Binary Images0 aTopology Preserving Parallel Smoothing for 3D Binary Images aBuffalo, USAbSpringer VerlagcMay 2010 a287 - 2980 v60263 a

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. © 2010 Springer-Verlag.

1 aNémeth, Gábor1 aKardos, Péter1 aPalágyi, Kálmán1 aBarneva, Reneta, P1 aBrimkov, Valentin E1 aHauptman, Herbert, A1 aJorge, Renato M Natal1 aTavares, João, Manuel R S uhttps://www.inf.u-szeged.hu/en/publication/topology-preserving-parallel-smoothing-for-3d-binary-images01114nas a2200181 4500008004100000020002200041245005500063210005100118260005600169300001400225520052000239100001900759700002000778700002300798700002200821700002300843856006600866 2009 eng d a978-3-642-10208-000aAn order-independent sequential thinning algorithm0 aorderindependent sequential thinning algorithm aPlaya del Carmen, MexicobSpringer VerlagcNov 2009 a162 - 1753 aThinning is a widely used approach for skeletonization. Sequential thinning algorithms use contour tracking: they scan border points and remove the actual one if it is not designated a skeletal point. They may produce various skeletons for different visiting orders. In this paper, we present a new 2-dimensional sequential thinning algorithm, which produces the same result for arbitrary visiting orders and it is capable of extracting maximally thinned skeletons. © Springer-Verlag Berlin Heidelberg 2009.

1 aKardos, Péter1 aNémeth, Gábor1 aPalágyi, Kálmán1 aWiederhold, Petra1 aBarneva, Reneta, P uhttp://link.springer.com/chapter/10.1007/978-3-642-10210-3_1301310nas a2200157 4500008004100000020002200041245009700063210006900160260008200229300001400311520062200325100002000947700002200967700002300989856014001012 2009 eng d a978-3-642-10208-000aReconstruction of canonical hv-convex discrete sets from horizontal and vertical projections0 aReconstruction of canonical hvconvex discrete sets from horizont aBerlin; Heidelberg; New York; London; Paris; TokyobSpringer VerlagcNov 2009 a280 - 2883 aThe problem of reconstructing some special hv-convex discretesets from their two orthogonal projections is considered. In general, the problem is known to be NP-hard, but it is solvable in polynomial time if the discrete set to be reconstructed is also 8-connected. In this paper, we define an intermediate class - the class of hv-convex canonical discrete sets - and give a constructive proof that the above problem remains computationally tractable for this class, too. We also discuss some further theoretical consequences and present experimental results as well. © Springer-Verlag Berlin Heidelberg 2009.

1 aBalázs, Péter1 aWiederhold, Petra1 aBarneva, Reneta, P uhttps://www.inf.u-szeged.hu/en/publication/reconstruction-of-canonical-hv-convex-discrete-sets-from-horizontal-and-vertical-projections01433nas a2200169 4500008004100000020002200041245004500063210003700108260004800145300001400193520087500207100002001082700002501102700002301127700002501150856008801175 2008 eng d a978-3-540-78274-200aOn the number of hv-convex discrete sets0 anumber of hvconvex discrete sets aBuffalo, NY, USAbSpringer VerlagcApr 2008 a112 - 1233 aOne 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.

1 aBalázs, Péter1 aBrimkov, Valentin, E1 aBarneva, Reneta, P1 aHauptman, Herbert, A uhttps://www.inf.u-szeged.hu/en/publication/on-the-number-of-hv-convex-discrete-sets