# Maximal Nucleus Clusters in Pawlak Paintings. Nerves as approximating tools in Visual Arts

## James Peters, Sheela Ramanna

DOI: http://dx.doi.org/10.15439/2016F004

Citation: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 8, pages 199–202 (2016)

Abstract. This paper is an application of Edelsbrunner-Harer (EH) nerves as approximating tools in discovering interesting perceptual clusters in Pawlak's painting of landscapes, thus giving us an insight into the style of the artist. A variation of EH nerves (collections of Vorono\i{}̈ regions called nucleus clusters) are used in this paper. The Rényi entropy is used to measure the information level of Vorono\i{}̈ regions. It is shown that the information levels (i.e., Rényi entropy) of maximal nucleus clusters in tesselled paintings are the highest compared with surrounding regions, thereby highlighting regions in the paintings with the greatest detail by the artist

### References

- J. Peters, Computational Proximity. Excursions in the Topology of Digital Images. Berlin: Springer, 2016, Intelligent Systems Reference Library, 102.
- J. Gratus and T. Porter, “Spatial representation: Discrete vs. continuous computational models a spatial view of information,” Theoretical Computer Science, vol. 365, no. 3, p. 206.
- H. Edelsbrunner, “Modeling with simplical complexes,” ser. Proceedings of the Canadian Conference on Computational Geometry, Canada, 1994, pp. 36–44.
- J. Peters and E. İnan, “Strongly proximal edelsbrunner-harer nerves,” Proceedings of the Jangjeon Mathematical Society, vol. 19, no. 3, pp. 563–582, 2016.
- E. A-iyeh and J. Peters, “Rényi entropy in measuring information levels in Voronı̈ tessellation cells with application in digital image analysis,” Theory and Applications of Math. & Comp. Sci., vol. 6, no. 1, pp. 77–95, 2016.
- Q. Du and M. Gunzburger, “Advances in studies and applications of centroidal voronoı̈ tessellations,” Numer. Math. Theory Methods Appl., vol. 3, no. 2, pp. 119–142, 2010.
- R. Hettiarachchi and J. Peters, “Multi-manifold LLE learning in Pattern-Recognition,” Pattern Recognition, vol. 48, pp. 2947–2960, 2015.
- J. Wang, “Edge-weighted centroidal voronoı̈ tessellation based algorithms for image segmentation,” Ph.D. dissertation, Department of Scientific Computing, 2011.
- J. Peters, A. Tozzi, and S. Ramanna, “Brain tissue tessellation shows absence of canonical microcircuits,” Neuroscience Letters, vol. 626, pp. 99–105, 2016.
- H. Edelsbrunner and J. Harer, Computational Topology. An Introduction. Providence, RI: Amer. Math. Soc., 2010, xii+241 pp. ISBN: 978-0-8218- 4925-5, MR2572029.
- A. Rényi, “On measures of entropy and information,” in Proceedings of the 4th Berkeley Symposium on Math., Statist. and Probability. University of California Press, Berkeley, Calif., 2011, pp. 547–547, vol. 1, Math. Sci. Net. Review MR0132570.
- R. Hartley, “Transmission of information,” Bell Systems Technical Journal, p. 535, 1928.
- H. Nyquist, “Certain factors affecting telegraph speed,” Bell Systems Technical Journal, p. 324, 1924.