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.

%B Combinatorial Image Analysis %S Lecture Notes in Computer Science %I Springer %C May 2014, Brno, Czech Republic %V 8466 %P 101 - 112 %8 2014 %@ 978-3-319-07147-3 %G eng %U http://dx.doi.org/10.1007/978-3-319-07148-0_10 %9 Conference paper %! Conference Paper %R 10.1007/978-3-319-07148-0_10 %0 Book Section %B Combinatorial Image Analysis (IWCIA) %D 2012 %T On topology preservation for triangular thinning algorithms %A Péter Kardos %A Kálmán Palágyi %E Reneta P Barneva %E Valentin E Brimkov %E Jake K Aggarwal %X

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.

%B Combinatorial Image Analysis (IWCIA) %S Lecture Notes in Computer Science %I Springer Verlag %C Austin, TX, USA %P 128 - 142 %8 Nov 2012 %@ 978-3-642-34731-3 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-34732-0_10 %0 Book Section %B Digital Geometry Algorithms %D 2012 %T Topology Preserving Parallel 3D Thinning Algorithms %A Kálmán Palágyi %A Gábor Németh %A Péter Kardos %E Valentin E Brimkov %E Reneta P Barneva %XA 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.

%B Combinatorial Image Analysis (IWCIA) %S Lecture Notes in Computer Science %I Springer Verlag %C Madrid, Spain %P 17 - 30 %8 May 2011 %@ 978-3-642-21072-3 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-21073-0_5 %0 Book Section %B Combinatorial Image Analysis (IWCIA) %D 2011 %T On topology preservation for hexagonal parallel thinning algorithms %A Péter Kardos %A Kálmán Palágyi %E Jake K Aggarwal %E Reneta P Barneva %E Valentin E Brimkov %E Kostadin N Koroutchev %E Elka R Korutcheva %XTopology 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.

%B Combinatorial Image Analysis (IWCIA) %S Lecture Notes in Computer Science %I Springer Verlag %C Madrid, Spain %P 31 - 42 %8 May 2011 %@ 978-3-642-21072-3 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-21073-0_6 %0 Book Section %B Proceedings of the Computational Modeling of Objects Represented in Images (CMORI) %D 2010 %T Topology Preserving Parallel Smoothing for 3D Binary Images %A Gábor Németh %A Péter Kardos %A Kálmán Palágyi %E Reneta P Barneva %E Valentin E Brimkov %E Herbert A Hauptman %E Renato M Natal Jorge %E João Manuel R S Tavares %XThis 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.

%B Proceedings of the Computational Modeling of Objects Represented in Images (CMORI) %I Springer Verlag %C Buffalo, USA %V 6026 %P 287 - 298 %8 May 2010 %G eng %9 Conference paper %R 10.1007/978-3-642-12712-0_26