An Escher aware pattern analysis: Symmetry beyond symmetry groups

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü, Türkiye

Tezin Onay Tarihi: 2015

Öğrenci: VENERA ADANOVA

Danışman: ZEHRA SİBEL TARI

Özet:

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, we study all aspects of ornamental patterns not only considering the usual mathematical properties but also other idiosyncratic features that are often more important in perception, aesthetics, art and design and as well as in appreciating cultural heritage. Our novelty is to replace the structure extraction problem with a content attenuation or suppression problem. When content is suppressed, clues to the repetition structure emerge. We show that based on content-suppressed images, unit cells and fundamental regions of planar ornaments can be robustly extracted even for ornaments with peculiar color permutations. Moreover, using tools of deep learning, we perform key validation tests showing that our coding via content-suppression makes it possible to construct content-dependent, subjective and more importantly continuous characterizations of the underlying symmetry behavior.