Abstract
Ornaments are created by repeating a base motif via combination of four primitive geometric repetition operations: translation, rotation, reflection, and glide reflection. The way the operations are combined defines symmetry groups. Thus, the classical study of ornaments is based on group theory. However, the discrete and inflexible nature of symmetry groups fail to capture relations among ornaments when artistic freedom is used to break symmetry via intriguing choices of base motifs and color permutations. In this work, we present a data driven modeling approach, where we go beyond group-theoretical framework and suggest continuous characterization of planar ornaments.
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
G. Polya, Über die analogie der kristallsymmetrie in der ebene. Z. Kristallogr. 60(1), 278–282 (1924)
P. Niggli, Die flächensymmetrien homogener diskontinuen. Z. Kristallogr. 60, 283–298 (1924)
P. Niggli, Die regelmässige punktverteilung längs einer geraden in einer ebene. Z. Kristallogr. 63, 255–274 (1926)
Y. Liu, R.T. Collins, Y. Tsin, A computational model for periodic pattern perception based on frieze and wallpaper groups. IEEE Trans. Pattern Anal. Mach. Intell. 26(3), 354–371 (2004)
H. Zabrodsky, S. Peleg, D. Avnir, Symmetry as a continuous feature. IEEE Trans. Pattern Anal. Mach. Intell. 17(12), 1154–1166 (1995)
V. Adanova, S. Tari, Beyond symmetry groups: a grouping study on Escher’s Euclidean ornaments. Graph. Model. 83(C), 15–27 (2016)
D.G. Lowe, Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)
Y. Aflalo, R. Kimmel, Spectral multidimensional scaling. Proc. Natl. Acad. Sci. U.S.A. 110(45), 246–247 (2013)
L.J.P. van der Maaten, G.E. Hinton, Visualizing high-dimensional data using t-SNE. Mach. Learn. Res. 9, 2579–2605 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 The Author(s) and the Association for Women in Mathematics
About this chapter
Cite this chapter
Adanova, V., Tari, S. (2019). A Data Driven Modeling of Ornaments. In: Gasparovic, E., Domeniconi, C. (eds) Research in Data Science. Association for Women in Mathematics Series, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-030-11566-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-11566-1_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11565-4
Online ISBN: 978-3-030-11566-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)