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_1001137nas 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 a

Thinning 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-algorithms01336nas 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 aThis 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-images