Abstract
The concept of a simple point is well known in digital topology: a black point in a binary picture is called a simple point if its deletion preserves topology. This paper introduces the notion of a simplifier point: a black point in a binary picture is simplifier if it is simple, and its deletion turns a non-simple border point into simple. We show that simplifier points are line end points for both (8, 4) and (4, 8) pictures on the square grid. Our result makes efficient implementation of endpoint-based topology-preserving 2D thinning algorithms possible.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bertrand, G., Couprie, M.: Transformations topologiques discrètes. In: Coeurjolly, D., Montanvert, A., Chassery, J. (eds.): Géométrie discrète et images numériques, pp. 187–209. Hermès Science Publications (2007)
Hall, R.W.: Parallel connectivity-preserving thinning algorithms. In: Kong, T.Y., Rosenfeld, A. (eds.) Topological Algorithms for Digital Image Processing, pp. 145–179. Elsevier Science B.V, Amsterdam (1996)
Kardos, P., Palágyi, K.: On topology preservation in triangular, square, and hexagonal grids. In: Proceedings of the 8th International Symposium on Image and Signal Processing and Analysis, ISPA 2013, pp. 782–787 (2013)
Kong, T.Y.: On topology preservation in 2-D and 3-D thinning. Int. J. Pattern Recognit. Artif. Intell. 9, 813–844 (1995)
Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Comput. Vis. Graph. Image Process. 48, 357–393 (1989)
Kovalevsky, V.A.: Geometry of Locally Finite Spaces. Publishing House, Berlin (2008)
Lam, L., Lee, S.-W., Suen, S.-W.: Thinning methodologies – a comprehensive survey. IEEE Trans. Pattern Anal. Mach. Intell. 14, 869–885 (1992)
Marchand-Maillet, S., Sharaiha, Y.M.: Binary Digital Image Processing - A Discrete Approach. Academic Press, New York (2000)
Palágyi, K.: Equivalent sequential and parallel reductions in arbitrary binary pictures. Int. J. Pattern Recognit. Artif. Intell. 28, 1460009-1–1460009-16 (2014)
Palágyi, K., Németh, G., Kardos, P.: Topology preserving parallel 3D thinning algorithms. In: Brimkov, V.E., Barneva, R.P. (eds.) Digital Geometry Algorithms, vol. 2, pp. 165–188. Springer, Dordrecht (2012)
Palágyi, K., Németh, G., Kardos, P.: Topology-preserving equivalent parallel and sequential 4-subiteration 2D thinning algorithms. In: Proceedings of the 9th International Symposium on Image and Signal Processing and Analysis, ISPA 2015, pp. 306–311 (2015)
Suen, C.Y., Wang, P.S.P. (eds.): Thinning Methodologies for Pattern Recognition. Series in Machine Perception and Artificial Intelligence. World Scientific, Singapore (1994)
Acknowledgements
This work was supported by the grant OTKA K112998 of the National Scientific Research Fund.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Palágyi, K. (2017). Simplifier Points in 2D Binary Images. In: Brimkov, V., Barneva, R. (eds) Combinatorial Image Analysis. IWCIA 2017. Lecture Notes in Computer Science(), vol 10256. Springer, Cham. https://doi.org/10.1007/978-3-319-59108-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-59108-7_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59107-0
Online ISBN: 978-3-319-59108-7
eBook Packages: Computer ScienceComputer Science (R0)