This chapter is about rotational symmetry. A corresponding n-ary operation is defined on the Gestalt domain. The resulting Gestalten will have periodicity n; i.e., when rotated by \(2\pi /n\), they remain the same. They have a phase feature, which is used as their orientation. The optimal a posteriori value is assigned to this attribute by an iterative least squares optimization. Although there is no linear one-step solution, rotational Gestalten are of great algebraic elegance and beauty, which also evidently show in their appearance. Their value in applications is less dominant. Most examples are either flowers, mechanical parts, or religious symbols. The chapter investigates how rotational symmetry must be fused with similarity and proximity. A greedy search rationale is presented avoiding the otherwise combinatorically growing search efforts. Many if not most rotational patterns occurring in the visual world are also reflection symmetric. Algebraically, a different group applies the dihedral group.
- 1.Liu J, Slota G, Zheng G, Wu Z, Park M, Lee S, Rauschert I, Liu Y (2013) Symmetry detection from realworld images competition 2013: summary and results. In: CVPR 2013, workshopsGoogle Scholar
- 2.Michaelsen E (2014) Searching for rotational symmetries based on the gestalt algebra operation. In: OGRW 2014, 9-th open German-Russian workshop on pattern recognition and image understandingGoogle Scholar
- 4.Kondra S, Petrosino A, Iodice S (2013) Multi-scale kernel operators for reflection and rotation symmetry: further achievements. In: CVPR 2013 competition on symmetry detectionGoogle Scholar
- 7.Funk C, Lee S, Oswald MR, Tsokas S, Shen W, Cohen A, Dickinson S, Liu Y. (2017) ICCV challenge: detecting symmetry in the wild. In ICCV 2017, workshopsGoogle Scholar
- 8.Förstner W, Wrobel B (2016) Photogrammetric computer vision. SpringerGoogle Scholar
- 9.Matas J, Chum O, Urban M, Pajdla T (2002) Robust wide baseline stereo from maximally stable extremal regions. In: British machine vision conference BMVC 2002, pp 384–396Google Scholar