Robot vision
Optimal algorithms for finding the symmetries of a planar point set
Information Processing Letters
Finding axes of skewed symmetry
Computer Vision, Graphics, and Image Processing
Automatic rotational symmetry determination for shape analysis
Pattern Recognition
Using symmetry for detecting and locating objects in a picture
Computer Vision, Graphics, and Image Processing
On the Detection of the Axes of Symmetry of Symmetric and Almost Symmetric Planar Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detection of generalized principal axes is rotationally symmetric shapes
Pattern Recognition
Fold principal axis—a new tool for defining the orientations of rotationally symmetric shapes
Pattern Recognition Letters
A simple and efficient algorithm for determining the symmetries of polyhedra
CVGIP: Graphical Models and Image Processing
Intensity and edge-based symmetry detection with an application to car-following
CVGIP: Image Understanding
Two methods for detecting symmetries
Pattern Recognition Letters
Detecting number of folds by a simple mathematical property
Pattern Recognition Letters
Symmetry detection using gradient information
Pattern Recognition Letters
3D Symmetry Detection Using The Extended Gaussian Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetry Detection by Generalized Complex (GC) Moments: A Close-Form Solution
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Image Processing
IEEE Transactions on Computers
A noise-robust frequency domain technique for estimating planarroto-translations
IEEE Transactions on Signal Processing
Islamic geometrical patterns indexing and classification using discrete symmetry groups
Journal on Computing and Cultural Heritage (JOCCH)
A unifying approach to moment-based shape orientation and symmetry classification
IEEE Transactions on Image Processing
Testing for image symmetries: with application to confocal microscopy
IEEE Transactions on Information Theory
3-D Symmetry Detection and Analysis Using the Pseudo-polar Fourier Transform
International Journal of Computer Vision
Water reflection recognition via minimizing reflection cost based on motion blur invariant moments
Proceedings of the 1st ACM International Conference on Multimedia Retrieval
Symmetry recognition in group-theoretic computational schemes for complex structural systems
Computers and Structures
Tensor based sparse decomposition of 3D shape for visual detection of mirror symmetry
Computer Methods and Programs in Biomedicine
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This paper presents a very simple and effective algorithm for classifying cyclic and dihedral symmetries from images of finite two-dimensional patterns. It consists in an extension of a frequency domain algorithm proposed by the author for estimating two-dimensional rotation of rigid objects. Within this framework, the estimation of rotation is conveniently turned into the problem of detecting two orthogonal lines within the locus of the zero crossings of a certain function represented in orthogonal Cartesian coordinates. The main contribution of this paper is the use and interpretation of the ambiguities that arise in such a locus in the form of additional pairs of orthogonal lines when applied to symmetric patterns and the development of other algorithmic steps which allow a simple and fast discrimination between cyclic and dihedral symmetries. Unlike any other available method, this algorithm does not require any conversion from Cartesian to polar image representations. Besides classification reliability and consistency, observed through several dozen testing experiments, the nice features of this new method also include robustness to noise and ease of implementation with fast Fourier transform algorithms, which makes it amenable to almost real-time pattern classifications applications. Several examples, representative of the performance of the algorithm through extensive testing, are reported and discussed in the paper.