## Abstract

The majority of Cellular Automata (CA) described in the literature are binary or three-state. While several abstractions are possible to generalise to more than three states, only a negligible number of multi-state CA rules exist with concrete practical applications.

This paper proposes a generic rule for multi-state CA. The rule allows for any number of states, and allows for the states are semantically related. The rule is illustrated on the concrete example of image segmentation, where the CA agents are pixels in an image, and their states are the pixels’ greyscale values.

We investigate in detail the proposed rule and some of its variations, and we also compare its effectiveness against its closest relative, the existing Greenberg–Hastings automaton. We apply the proposed methods to both synthetic and real-world images, evaluating the results with a variety of measures. The experimental results demonstrate that our proposed method can segment images accurately and effectively.

## Authors

**Irina Voiculescu
**Department of Computer Science, University of Oxford, Oxford, UK

## Keywords

unconstrained optimization problems; splitting; neural network training;

## Paper coordinates

Dioşan L., Andreica A., Boros I., Voiculescu I. (2017) *Avenues for the Use of Cellular Automata in Image Segmentation*. In: Squillero G., Sim K. (eds) Applications of Evolutionary Computation. EvoApplications 2017. Lecture Notes in Computer Science, vol 10199. Springer, Cham, https://doi.org/10.1007/978-3-319-55849-3_19

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## About this paper

##### Journal

European Conference on the Applications of Evolutionary Computation

##### Publisher Name

Springer, Cham

##### Print ISSN

978-3-319-55848-6

##### Online ISSN

978-3-319-55849-3

[1] von Neumann, J., *Theory of Self-reproducing Automata. University of Illinois Press*, Urbana (1966). Edited and Completed by Arthur W. Burks

[2] Wolfram, S.: *A New Kind of Science*. Wolfram Media Inc., Champaign (2002)

[3] Potts, R.B.: *Some generalized order-disorder transformations.* Math. Proc. Camb. Philos. Soc. 48(1), 106–109 (1952)

[4] Wu, F.Y.: *The potts model*. Rev. Mod. Phys. 54, 235–268 (1982)

[5] Greenberg, J.M., Hastings, S.P.: *Spatial patterns for discrete models of diffusion in excitable media*. SIAM J. Appl. Math. 34, 515–523 (1978)

[6] Fisch, R., Gravner, J., Griffeath, D.: *Metastability in the Greenberg-Hastings model*. Ann. Appl. Probab. 3(4), 935–967 (1993)

[7] Fisch, R., Gravner, J.: *One-dimensional deterministic Greenberg-Hastings models.* Complex Syst. 9, 329–348 (1995)

[8] Baetens, J.M., Baets, B.: *Towards a comprehensive understanding of multistate cellular automata*. In: W as, J., Sirakoulis, G.C., Bandini, S. (eds.) ACRI

2014. LNCS, vol. 8751, pp. 16–24. Springer, Heidelberg (2014). doi:10.1007/978-3-319-11520-7 3

[9] dos Santos, R.M.Z., Coutinho, S.: *Dynamics of HIV infection: a cellular automata approach*. Phys. Rev. Lett. 87, 168102 (2001)

[10] Chaudhuri, P.P., Chowdhury, D.R., Nandi, S., Chattopadhyay, S.: *Additive Cellular Automata: Theory and Applications*. Wiley-IEEE Computer Society Press, Hoboken (1997)

[11] Vezhnevets, V., Konouchine, V.: *Growcut – interactive multi-label N-D image segmentation by cellular automata* (2005)

[12] Ghosh, P., Antani, S.K., Long, L.R., Thoma, G.R.: *Unsupervised grow-cut: cellular automata-based medical image segmentation*. In: 2011 First IEEE International Conference on Healthcare Informatics, Imaging and Systems Biology (HISB), pp. 40–47. IEEE (2011)

[13] RajKumar, R., Niranjana, G.: *Image segmentation and classification of MRI brain tumor based on cellular automata and neural networks*. IJREAT Int. J. Res. Eng. Adv. Technol. 1(1), 323–327 (2013)

[14] Kauffmann, C., Piche, N.: *Seeded ND medical image segmentation by cellular **automaton on GPU*. Int. J. Comput. Assist. Radiol. Surg. 5(3), 251–262 (2010)

[15] Anitha, J., Peter, J.D.: *Mammogram segmentation using maximal cell strength updation in cellular automata*. Med. Biol. Eng. Comput. 53(8), 737–749 (2015) 296 L. Dio¸san et al.

[16] Hamamci, A., Kucuk, N., Karaman, K., Engin, K., Unal, G.B.: *Tumor-Cut: segmentation of brain tumors on contrast enhanced MR images for radiosurgery applications*. IEEE Trans. Med. Imaging 31(3), 790–804 (2012)

[17] Diosan, L., Andreica, A., Voiculescu, I.: *Parameterized cellular automata in image segmentation*. In: 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) (2016)

[18] Martin, D.R., Fowlkes, C.C., Tal, D., Malik, J.: *A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics.* In: ICCV, vol. II, pp. 416–423 (2001)

[19] Dice, L.R.: *Measures of the amount of ecologic association between species*. Ecology 26(3), 297–302 (1945)

[21] Unnikrishnan, R., Pantofaru, C., Hebert, M.: *Toward objective evaluation of image segmentation algorithms*. IEEE Trans. Pattern Anal. Mach. Intell. 29(6), 929–944 (2007)