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_73: Abstract This paper proposes an artificial neural network that extracts axes of symmetry from visual patterns. The input patterns can be plane figures, complicated line drawings or gray-scaled natural images taken by CCD cameras. The network has a hierarchical multi-layered architecture, which resembles that of the lower stages of the neocognitron. It consists of a contrast-extracting layer, edge-extracting layers (simple and complex types), and layers extracting symmetry axes. The network extracts oriented edges from the input image first, and then tries to extract axes of symmetry. Our network checks conditions of symmetry, not directly from the oriented edges, but from a blurred version of them. The use of blurred signals not only reduces the computational cost greatly, but also endows the network with a large tolerance to deformation of input patterns. It is important to get blurred signals, not directly from an input image, but from the oriented edges. Although information of edge locations becomes ambiguous after the blurring operation, most of important features of the original image can still remain stable. If the input image is directly blurred, however, most of the important features in the image will be lost.
  @cite_60: A significant problem in image understanding (IU) is to represent objects as models stored in a machine environment for IU systems to use in model driven pattern matching for object recognition. This paper presents a technique for autonomous machine description of objects presented as spatial data, i.e., data presented as point sets in Euclidean n-space. This general definition of objects as spatial data encompasses the cases of explicit listings of points, lines or other spatial features, objects defined by light pen in a CAD system, generalized cone representations, polygonal boundary representations, quad-trees, etc. The description technique decomposes an object into component sub-parts which are meaningful to a human being. It is based upon a measure of symmetry of point sets. Most spatial data has no global symmetry. In order to arrive at a reasonable description of a point set, we attempt to decompose the data into the fewest subsets each of which is as symmetric as possible. The technique is based upon statistics which capture the opposing goals of fewest pieces and most symmetry. An algorithm is proposed which operates sequentially in polynomial time to reach an optimal (but not necessarily unique) decomposition. The semantic content of the descriptions which the technique produces agrees with results of experiments on qualitative human perception of spatial data. In particular, the technique provides a step toward a quantitative measure of the old perceptual Gestalt school of psychology's concept of "goodness of figure".
  @cite_36: We present a new technique for extracting local features from images of architectural scenes, based on detecting and representing local symmetries. These new features are motivated by the fact that local symmetries, at different scales, are a fundamental characteristic of many urban images, and are potentially more invariant to large appearance changes than lower-level features such as SIFT. Hence, we apply these features to the problem of matching challenging pairs of photos of urban scenes. Our features are based on simple measures of local bilateral and rotational symmetries computed using local image operations. These measures are used both for feature detection and for computing descriptors. We demonstrate our method on a challenging new dataset containing image pairs exhibiting a range of dramatic variations in lighting, age, and rendering style, and show that our features can improve matching performance for this difficult task.
  @cite_41: This paper shows that the introduction of non-uniform blur is very useful for comparing images, and proposes a neural network model that extracts axes of symmetry from visual patterns. The blurring operation greatly increases robustness against deformations and various kinds of noise, and largely reduces computational cost. Asymmetry between two groups of signals can be detected in a single action by the use of non-uniform blur having a cone-shaped distribution.The proposed model is a hierarchical multi-layered network, which consists of a contrast-extracting layer, edge-extracting layers (simple and complex types), and layers extracting symmetry axes. The model extracts oriented edges from an input image first, and then tries to extract axes of symmetry. The model checks conditions of symmetry, not directly from the oriented edges, but from a blurred version of the response of edge-extracting layer. The input patterns can be complicated line drawings, plane figures or gray-scaled natural images taken by CCD cameras.
  @cite_9: In this work we propose a learning-based approach to symmetry detection in natural images. We focus on ribbon-like structures, i.e. contours marking local and approximate reflection symmetry and make three contributions to improve their detection. First, we create and make publicly available a ground-truth dataset for this task by building on the Berkeley Segmentation Dataset. Second, we extract features representing multiple complementary cues, such as grayscale structure, color, texture, and spectral clustering information. Third, we use supervised learning to learn how to combine these cues, and employ MIL to accommodate the unknown scale and orientation of the symmetric structures. We systematically evaluate the performance contribution of each individual component in our pipeline, and demonstrate that overall we consistently improve upon results obtained using existing alternatives.
  @cite_53: Local feature-based symmetry detection algorithms can simultaneously consider symmetries over all locations, scales and orientations and achieve state-of-the-art performance. This paper demonstrates the limitations of these algorithms in case of dealing with background clutters, low contrast and smooth surfaces, and presents an adaptive feature point detection algorithm to overcome those limitations. Quantitative evaluations and subjective comparisons against the state-of-the-art reflection symmetry detection algorithm on the image dataset released by "Symmetry Detection from Real World Images Competition 2013" show a significant improvement in detection accuracy and computation efficiency. Furthermore, the proposed algorithm is also tested on the non-human primates' (NHPs') video surveillance data as a preprocessing step before NHPs' behaviors analysis, and a good performance is obtained as well.
  @cite_42: 
  @cite_56: An unsupervised procedure to local symmetry detection in natural images is proposed.Achieved via a Hough-style voting approach made at different scales and coordinate spaces.A final denoising scheme aims at removing noise and spurious local symmetries.Experiments have been conducted on the recent extension of the Berkeley Segmentation Dataset.The proposed method performs well compared to the state-of-the-art algorithms. Display Omitted In this paper, we propose a new unsupervised and simple approach to local symmetry detection of ribbon-like structure in natural images. The proposed model consists in quantifying the presence of a partial medial axis segment, existing between each pair of (preliminary detected) line segments delineating the boundary of two textured regions, by a set of heuristics related both to the geometrical structure of each pair of line segments and its ability to locally delimit a homogeneous texture region in the image. This semi-local approach is finally embedded in a two-step algorithm with an amplification step, via a Hough-style voting approach achieved at different scales and coordinate spaces which aims at determining the dominant local symmetries present in the image and a final denoising step, via an averaging procedure, which aims at removing noise and spurious local symmetries. The experiments, reported in this paper and conducted on the recent extension of the Berkeley Segmentation Dataset for the local symmetry detection task, demonstrate that the proposed symmetry detector performs well compared to the best existing state-of-the-art algorithms recently proposed in the literature.
  @cite_57: 
  @cite_19: Abstract A simple method of analyzing symmetries of a line drawing is presented. The procedure consists of three stages: (1) computing the axes of ‘microsymmetry’ for pairs of microsegments based on the mean square error criterion, (2) mapping the axes into two-dimensional parameter space, and (3) detecting the peaks in the parameter space to obtain the global axes of symmetry.
  @cite_72: We propose a novel, self-validating approach for detecting curved reflection symmetry patterns from real, unsegmented images. Our method benefits from the observation that any curved symmetry pattern can be approximated by a sequence of piecewise rigid reflection patterns. Pairs of symmetric feature points are first detected (including both inliers and outliers) and treated as 'particles'. Multiple-hypothesis sampling and pruning are used to sample a smooth path going through inlier particles to recover the curved reflection axis. Our approach generates an explicit supporting region of the curved reflection symmetry, which is further used for intermediate self-validation, making the detection process more robust than prior state-of-the-art algorithms. Experimental results on 200+ images demonstrate the effectiveness and superiority of the proposed approach.
  @cite_2: 
  @cite_76: 
  @cite_51: A novel and efficient method is presented for grouping feature points on the basis of their underlying symmetry and characterising the symmetries present in an image. We show how symmetric pairs of features can be efficiently detected, how the symmetry bonding each pair is extracted and evaluated, and how these can be grouped into symmetric constellations that specify the dominant symmetries present in the image. Symmetries over all orientations and radii are considered simultaneously, and the method is able to detect local or global symmetries, locate symmetric figures in complex backgrounds, detect bilateral or rotational symmetry, and detect multiple incidences of symmetry.
  @cite_17: 
summary: Reflection symmetry algorithms fall into two different categories depending on whether they detect sparse symmetries (straight lines or curves) @cite_36 @cite_76 @cite_2 @cite_72 @cite_51 @cite_17 or a dense heatmap @cite_41 @cite_73 @cite_9 . The most common sparse approach to detect reflection symmetry is to match up symmetric points or contours in the image to determine midpoint and direction of the symmetry axis @cite_53 @cite_60 @cite_51 @cite_56 @cite_19 @cite_42 . These approaches often use a Hough transform to accumulate the axes of reflection, derived from the matched feature's midpoints and angles, and vote on the dominant symmetries. Atadjanov and Lee @cite_57 extend the Loy and Eklundh @cite_51 algorithm by taking the matched keypoints and then comparing the histogram of curvature around the keypoints. Wang al @cite_42 uses local affine invariant edge correspondences to make the algorithms more resilient to perspective distortion contours. The method does not use a Hough space to vote, opting instead to use an affine invariant pairwise (dis)similarity metric to vote for symmetries.