text: Humans take advantage of real world symmetries for various tasks, yet capturing their superb symmetry perception mechanism into a computational model remains elusive. Encouraged by a new discovery (CVPR 2016) demonstrating extremely high inter-person accuracy of human perceived symmetries in the wild, we have created the first deep-learning neural network for reflection and rotation symmetry detection (Sym-NET), trained on photos from MS-COCO (Common Object in COntext) dataset with nearly 11K symmetry-labels from more than 400 human observers. We employ novel methods to convert discrete human labels into symmetry heatmaps, capture symmetry densely in an image and quantitatively evaluate Sym-NET against multiple existing computer vision algorithms. Using the symmetry competition testsets from CVPR 2013 and unseen MS-COCO photos, Sym-NET comes out as the winner with significantly superior performance over all other competitors. Beyond mathematically well-defined symmetries on a plane, Sym-NET demonstrates abilities to identify viewpoint-varied 3D symmetries, partially occluded symmetrical objects and symmetries at a semantic level.
  @cite_28: A method for efficient detection of the dominant local reflectional symmetry in grey level images is described. The general approach is to define a local measure of reflectional symmetry that transforms the symmetry detection problem to an optimization problem, and obtain the symmetric regions by an efficient global optimization algorithm. The symmetry of a 1D function can be measured in the frequency domain as the fraction of its energy that resides in symmetric Fourier basis functions. This approach is extended to two dimensions. Locality can be formally treated in terms of the Gabor decomposition and implemented via soft windowing. The resulting measure is a complicated multimodal function of the location of the center of the supporting region, its size, and the orientation of the symmetry axis. A new probabilistic generic algorithm is applied to the determination of the global maximum of the reflectional symmetry function. Less than one thousand evaluations of the local symmetry measure are typically needed in order to locate the dominant symmetry in natural, wildlife test images.
  @cite_26: 
  @cite_10: We present a geometric framework for the efficient detection of regular repetitions of planar (but not necessarily coplanar) patterns. At the heart of our system, lie the fixed structures of the transformations that describe these regular configurations. The approach detects a number of symmetric configurations that have traditionally been dealt with separately, in that all configurations corresponding to planar homologies are detected. These include important cases such as periodicities, mirror symmetries, and reflections about a point. The approach can handle perspective distortions. It avoids to get trapped in combinatorics; through invariant-based hashing for pattern matching and through Hough transforms for the detection of fixed structures. Additional efficiency and robustness are obtained from the system's ability to "reason" about the consistency of multiple homologies. The performance of the system is demonstrated with several examples.
summary: Pritts al @cite_26 detect reflection, rotation and translation symmetry using SIFT and MSER features. The symmetries are found through non-linear optimization and RANSAC. Tuytelaars al @cite_10 detect reflection through a Cascade Hough Transform. Kiryati and Gofman @cite_28 define a Symmetry ID function implemented through Gaussian windows to find local reflection symmetry.