A 3D 6-subiteration curve thinning algorithm based on P-simple points

Abstract

In a recent study C. Lohou, G. Bertrand [A new 3D 12-subiteration thinning algorithm based on P-simple points, in: International Workshop on Combinatorial Image Analysis, IWCIA 2001, Philadelphia, PA, USA, ENTCS, vol. 46, 2001, pp. 39–58; A new 3D 6-subiteration thinning algorithm based on P-simple points, in: International Conference on Discrete Geometry for Computer Imagery, DGCI’2002, Bordeaux, France, ENTCS, vol. 2301, Springer, Berlin, 2002, pp. 102–113; A 3D 12-subiteration thinning algorithm based on P-simple points, Discrete Appl. Math. 139(1–3) (2004) 171–195.], we proposed a new methodology to build thinning algorithms based on the deletion of P-simple points. This methodology may permit to conceive a thinning algorithm A ′ from an existent thinning algorithm A, such that A ′ deletes at least all the points removed by A, while preserving the same end points (in particular, we have already proposed a 12-subiteration thinning algorithm C. Lohou, G. Bertrand [International Workshop on Combinatorial Image Analysis, IWCIA 2001, Philadelphia, PA, USA, ENTCS, vol. 46, 2001, pp. 39–58; A 3D 12-subiteration thinning algorithm based on P-simple points, Discrete Appl. Math. 139(1–3) (2004) 171–195.]). In this paper, by applying this methodology, we propose a 6-subiteration curve thinning algorithm which deletes at least all the points removed by two 6-subiteration curve thinning algorithms: either the one proposed by Palágyi and Kuba [A 3D 6-subiteration thinning algorithm for extracting medial lines, Pattern Recogn. Lett. 19(7) (1998) 613–627.], or the one proposed by Gong and Bertrand [A simple parallel 3D thinning algorithm, in: International Conference on Pattern Recognition, Atlantic City, NJ, USA, 1990, pp. 188–190.].