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

A 3D parallel shrinking algorithm

Shrinking is a frequently used preprocessing step in image processing. This paper presents an efficient 3D parallel shrinking algorithm for transforming a binary object into its topological kernel. The applied strategy is called directional: each iteration step is composed of six subiterations each of which can be executed in parallel. The algorithm makes easy implementation possible, since deletable points are given by 3 x 3 x 3 matching templates. The topological correctness of the algorithm is proved for (26,6) binary pictures

Real places and torus bundles

If M is a hyperbolic once-punctured torus bundle over the circle, then the trace field of M has no real places.Comment: 15 pages; v4 incorporates referee's comment

Automatic correction of Ma and Sonka's thinning algorithm using P-simple points

International audienceMa and Sonka proposed a fully parallel 3D thinning algorithm which does not always preserve topology. We propose an algorithm based on P-simple points which automatically corrects Ma and Sonka's Algorithm. As far as we know, our algorithm is the only fully parallel curve thinning algorithm which preserves topology