Symmetry analysis from human perspective

Çengel, Furkan
Ornaments are repetitive patterns. They are created by repeating a base unit using four primitive geometric operations: translation, reflection, glide reflection and rotation. Using combinations of these primitive operations one can fill the plane in 17 different ways, which are known as 17 Wallpaper groups. In recent studies, an automated method is presented which can detect the symmetry group of given ornament. While automated methods aim to capture theoretical representation of the symmetry, they lack the ability to understand how the symmetries are perceived by human. In this study we focused on understanding human perception of symmetry and symmetry groups. We used an ornament that is challenging to classify for stimulating human perception and conducted an experiment to understand which symmetries people see in it and which wallpaper groups they tend to match the ornament. The results show that current groupings are not adequate to fully cover symmetry.


Analysis of Planar Ornament Patterns via Motif Asymmetry Assumption and Local Connections
Adanova, Venera; Tarı, Zehra Sibel (2019-03-01)
Planar ornaments, a.k.a. wallpapers, are regular repetitive patterns which exhibit translational symmetry in two independent directions. There are exactly 17 distinct planar symmetry groups. We present a fully automatic method for complete analysis of planar ornaments in 13 of these groups, specifically, the groups called p6, p6m, p4g, p4m, p4, p31m, p3m, p3, cmm, pgg, pg, p2 and p1. Given the image of an ornament fragment, we present a method to simultaneously classify the input into one of the 13 groups a...
An Escher aware pattern analysis: symmetry beyond symmetry groups
Adanova, Venera; Tarı, Zehra Sibel; Department of Computer Engineering (2015)
Ornaments constructed by repeating a base motif, timeless and ubiquitous, link culture, art, science and mathematics. To this date, the mathematical study of the ornaments has been the study of discrete symmetry groups and permutations. As such, the study merely focuses on the mechanical side of repetition, ignoring the artistic aspects (symmetry breaking strategies via intriguing choices of form and color permutations) that make ornaments such bewildering objects. Taking our inspiration from Escher's art, ...
Beyond symmetry groups: A grouping study on Escher's Euclidean ornaments
Adanova, V.; Tarı, Zehra Sibel (2016-01-01)
© 2015 Elsevier Inc.From art to science, ornaments constructed by repeating a base motif (tiling) have been a part of human culture. These ornaments exhibit various kinds of symmetries depending on the construction process as well as the symmetries of the base motif. The scientific study of the ornaments is the study of symmetry, i.e., the repetition structure. There is, however, an artistic side of the problem too: intriguing color permutations, clever choices of asymmetric interlocking forms, several symm...
A Data Driven Modeling of Ornaments
Adanova, Venera; Tarı, Zehra Sibel (Springer, 2019)
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....
Normalizers in homogeneous symmetric groups
Güven, Ülviye Büşra; Kuzucuoğlu, Mahmut; Department of Mathematics (2017)
We study some properties of locally finite simple groups, which are the direct limit of finite (finitary) symmetric groups of (strictly) diagonal type. The direct limit of the finite (finitary) symmetric groups of strictly diagonal type is called textbf{homogeneous (finitary) symmetric groups}. In cite{gkk}, Kegel, Kuzucuou{g}lu and myself studied the structure of centralizer of finite groups in the homogeneous finitary symmetric groups. Instead of strictly diagonal embeddings, if we have diagonal embedding...
Citation Formats
F. Çengel, “Symmetry analysis from human perspective,” Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Computer Engineering., Middle East Technical University, 2019.