Abstract
A new method to compute the Euler number of a 2-D binary image is described in this paper. The method employs three comparisons unlike other proposals that utilize more comparisons. We present two variations, one useful for the case of images containing only 4-connected objects and one useful in the case of 8-connected objects. To numerically validate our method, we firstly apply it to a set of very simple examples; to demonstrate its applicability, we test it next with a set of images of different sizes and object complexities. To show competitiveness of our method against other proposals, we compare it in terms of processing times with some of the state-of-the-art-formulations reported in literature.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Yang, H.S., Sengupta, S.: Intelligent shape recognition for complex industrial tasks. IEEE Control Syst. Mag. 8(3), 23–30 (1988)
Snidaro, L., Foresti, G.L.: Real-time thresholding with Euler numbers. Pattern Recogn. Lett. 24, 1533–1544 (2003)
Lin, X., Ji, J., Gu, G.: The Euler number study of image and its application. In: Proceedings of 2nd IEEE Conference on Industrial Electronics and Applications (ICIEA 2007), pp. 910–912 (2007)
Al Faqheri, W., Mashohor, S.: A real-time Malaysian automatic license plate recognition (M-ALPR) using hybrid fuzzy. Int. J. Comput. Sci. Netw. Secur. 9(2), 333–340 (2009)
Gray, S.B.: Local properties of binary images in two dimensions. IEEE Trans. Comput. 20(5), 551–561 (1971)
Dyer, C.: Computing the Euler number of an image from its quadtree. Comput. Vis. Graph. Image Process. 13, 270–276 (1980)
Bieri, H., Nef, W.: Algorithms for the Euler characteristic and related additive functionals of digital objects. Comput. Vis. Graph. Image Process. 28, 166–175 (1984)
Bieri, H.: Computing the Euler characteristic and related additive functionals of digital objects from their bintree representation. Comput. Vis. Graph. Image Process. 40, 115–126 (1987)
Chen, M.H., Yan, P.F.: A fast algorithm to calculate the Euler number for binary images. Pattern Recogn. Lett. 8(12), 295–297 (1988)
Chiavetta, F.: Parallel computation of the Euler number via connectivity graph. Pattern Recogn. Lett. 14(11), 849–859 (1993)
Díaz de León, J.L., Sossa-Azuela, J.H.: On the computation of the Euler number of a binary object. Pattern Recogn. 29(3), 471–476 (1996)
Bribiesca, E.: Computation of the Euler number using the contact perimeter. Comput. Math Appl. 60, 136–137 (2010)
Sossa, H., Cuevas, E., Zaldivar, D.: Computation of the Euler Number of a binary image composed of hexagonal cells. J. Appl. Res. Technol. 8(3), 340–351 (2010)
Sossa, H., Cuevas, E., Zaldivar, D.: Alternative way to compute the Euler Number of a binary image. J. Appl. Res. Technol. 9(3), 335–341 (2011)
Imiya, A., Eckhardt, U.: The Euler characteristics of discrete objects and discrete quasi-objects. Comput. Vis. Image Underst. 75(3), 307–318 (1999)
Kiderlen, M.: Estimating the Euler characteristic of a planar set from a digital image. J. Vis. Commun. Image Represent. 17(6), 1237–1255 (2006)
Di Zenzo, S., Cinque, L., Levialdi, S.: Run-based algorithms for binary image analysis and processing. IEEE Trans. Pattern Anal. Mach. Intell. 18(1), 83–89 (1996)
Sossa, H., Cuevas, E., Zaldivar, D.: Computation of the Euler number of a binary image composed of hexagonal cells. JART 8(3), 340–351 (2010)
Sossa, H., Rubio, E., Peña, A., Cuevas, E., Santiago, R.: Alternative formulations to compute the binary shape euler number. IET-Comput. Vis. 8(3), 171–181 (2014)
Yao, B., Wu, H., Yang, Y., Chao, Y., He, L.: An improvement on the euler number computing algorithm used in MATLAB. In: TECNON 2013, 2013 IEEE Region 10 Conference, 22–25 October 2013, Xi’an, China (2013)
He, L., Chao, Y., Suzuki, K.: A linear-time two-scan labelling algorithm. In: Proceedings of IEEE International Conference on Image Processing (ICIP 2007), San Antonio, TX, USA, September 2007, pp. V-241–V-244 (2007)
Feng He, L., Yan Chao, Y., Susuki, K.: An Algorithm for connected-component labeling, hole labeling and Euler number computing. J. Comput. Sci. Technol. 28(3), 468–478 (2013)
He, L., Chao, Y.: A very fast algorithm for simultaneously performing connected-component labeling and Euler number computing. IEEE Trans. Image Process. 24(9), 2725–2735 (2015)
Yao, B., He, L., Kang, S., Chao, Y., Zhao, X.: A novel bit–quad–based Euler number computing algorithm. SpringerPlus 4(735), 1–16 (2015)
Yao, B., Kang, S., Zhao, X., Chao, Y., He, L.: A graph-theory-based Euler number computing algorithm. In: Proceedings of the 2015 IEEE International Conference on Information and Automation, Lijiang, China, pp. 1206–1209, August 2015
Acknowledgements
Humberto Sossa would like to thank IPN-CIC and CONACYT (projects SIP 20161126, and CONACYT under projects 155014 and 65 within the framework of call: Frontiers of Science 2015) for the economic support to carry out this research. Ángel Carreón thanks CONACYT for the economic support to carry out his Master studies.
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
Sossa-Azuela, J.H., Carreón-Torres, Á.A., Santiago-Montero, R., Bribiesca-Correa, E., Petrilli-Barceló, A. (2017). Efficient Computation of the Euler Number of a 2-D Binary Image. In: Sidorov, G., Herrera-Alcántara, O. (eds) Advances in Computational Intelligence. MICAI 2016. Lecture Notes in Computer Science(), vol 10061. Springer, Cham. https://doi.org/10.1007/978-3-319-62434-1_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-62434-1_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62433-4
Online ISBN: 978-3-319-62434-1
eBook Packages: Computer ScienceComputer Science (R0)