Péter Kardos

Thinning combined with iteration-by-iteration smoothing for 3D binary images

In this work we present a new thinning scheme for reducing the noise sensitivity of 3D thinning algorithms. It uses iteration-by-iteration smoothing that removes some border points that are considered as extremities. The proposed smoothing algorithm is composed of two parallel topology preserving reduction operators. An efficient implementation of our algorithm is sketched and its topological correctness for (26,6) pictures is proved.

Topology preserving 3d thinning algorithms using four and eight subfields

Thinning is a frequently applied technique for extracting skeleton-like shape features (i.e., centerline, medial surface, and topological kernel) from volumetric binary images. Subfield-based thinning algorithms partition the image into some subsets which are alternatively activated, and some points in the active subfield are deleted. This paper presents a set of new 3D parallel subfield-based thinning algorithms that use four and eight subfields. The three major contributions of this paper are: 1) The deletion rules of the presented algorithms are derived from some sufficient conditions for topology preservation. 2) A novel thinning scheme is proposed that uses iteration-level endpoint checking. 3) Various characterizations of endpoints yield different algorithms.

On topology preservation in triangular, square, and hexagonal grids

There are three possible partitionings of the continuous plane into regular polygons that leads to triangular, square, and hexagonal grids. The topology of the square grid is fairly well-understood, but it cannot be said of the remaining two regular sampling schemes. This paper presents a general characterization of simple pixels and some simplified sufficient conditions for topology-preserving operators in all the three types of regular grids.

On Topology Preservation for Triangular Thinning Algorithms

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.

Topology preserving 2-subfield 3D thinning algorithms

This paper presents a new family of 3D thinning algorithms for extracting skeleton–like shape features (i.e, centerline, medial surface, and topological kernel) from volumetric images. A 2-subfield strategy is applied: all points in a 3D picture are partitioned into two subsets which are alternatively activated. At each iteration, a parallel operator is applied for deleting some border points in the active subfield. The proposed algorithms are derived from Ma’s sufficient conditions for topology preservation, and they use various endpoint characterizations.

An Order---Independent Sequential Thinning Algorithm

Thinning 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.

2D parallel thinning and shrinking based on sufficient conditions for topology preservation

Thinning and shrinking algorithms, respectively, are capable of extracting medial lines and topological kernels from digital binary objects in a topology preserving way. These topological algorithms are composed of reduction operations: object points that satisfy some topological and geometrical constraints are removed until stability is reached. In this work we present some new sufficient conditions for topology preserving parallel reductions and fiftyfour new 2D parallel thinning and shrinking algorithms that are based on our conditions. The proposed thinning algorithms use five characterizations of endpoints.

Order-Independent Sequential Thinning in Arbitrary Dimensions

Skeletons are region based shape descriptors that play important role in shape representation. This paper introduces a novel sequential thinning approach for n-dimensional binary objects ( n = 1, 2, 3, . . .). Its main strength lies in its order–independency, i.e., it can produce the same skeletons for any visiting orders of border points. Furthermore, this is the first scheme in this field that is also applicable for higher dimensions.

Sufficient conditions for topology preserving additions and general operators

Topology preservation is a crucial issue of digital topology. Various applications of binary image processing rest on topology preserving operators. Earlier studies in this topic mainly concerned with reductions (i.e., operators th at only delete some object points from binary images), as they form the basis for thinning algorithms. However, additions (i.e., operators that never change object points) als o play important role for the purpose of generating discrete Voronoi diagrams or skeletons by influence zones (SKIZ). Furthermore, the use of general operators that may both add and delete some points to and from objects in pictures are suitable for contour smoothing. Therefore, in this paper we present some new sufficient conditions for topology preserving reductions, additions, and general operators. Two additions for 2D and 3D contour smoothing are also reported.

A family of topology-preserving 3D parallel 6-subiteration thinning algorithms

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.