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.
Earlier work on rotation symmetry detection includes the use of autocorrelation @cite_46 @cite_65 and image moments @cite_45 @cite_49 @cite_0 . Loy and Eklundh @cite_51 use a variation on their SIFT feature-based reflection symmetry approach to find rotation symmetry as well. The orientations of matched SIFT feature pairs are used to find a rotation symmetry center. The detected rotation symmetry centers emerge as maxima in the voting space. This algorithm stands out from all others since the authors have made their code publicly available, and the symmetry competition workshops in CVPR 2011 2013 have used it as the baseline algorithm for both reflection and rotation symmetry detection. Thus far, this algorithm is considered to be the best baseline algorithm for reflection and rotation symmetry detection.
@cite_65 @cite_0 @cite_45 @cite_49 @cite_46 @cite_51
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Symmetry is a pervasive phenomenon presenting itself in all forms and scales in natural and manmade environments. Its detection plays an essential role at all levels of human as well as machine perception. The recent resurging interest in computational symmetry for computer vision and computer graphics applications has motivated us to conduct a US NSF funded symmetry detection algorithm competition as a workshop affiliated with the Computer Vision and Pattern Recognition (CVPR) Conference, 2013. This competition sets a more complete benchmark for computer vision symmetry detection algorithms. In this report we explain the evaluation metric and the automatic execution of the evaluation workflow. We also present and analyze the algorithms submitted, and show their results on three test sets of real world images depicting reflection, rotation and translation symmetries respectively. This competition establishes a performance baseline for future work on symmetry detection. We present a novel and effective algorithm for affinely skewed rotation symmetry group detection from real-world images. We define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group: 1) the center of rotation, 2) the affine deformation, 3) the type of the symmetry group, 4) the cardinality of the symmetry group, and 5) the supporting region of the symmetry group in the image. We propose a frieze-expansion (FE) method that transforms rotation symmetry group detection into a simple, 1D translation symmetry detection problem. We define and construct a pair of rotational symmetry saliency maps, complemented by a local feature method. Frequency analysis, using Discrete Fourier Transform (DFT), is applied to the frieze-expansion patterns (FEPs) to uncover the types (cyclic, dihedral, and O(2)), the cardinalities, and the corresponding supporting regions, concentric or otherwise, of multiple rotation symmetry groups in an image. The phase information of the FEP is used to rectify affinely skewed rotation symmetry groups. Our result advances the state of the art in symmetry detection by offering a unique combination of region-based, feature-based, and frequency-based approaches. Experimental results on 170 synthetic and natural images demonstrate superior performance of our rotation symmetry detection algorithm over existing methods. We present a novel and effective algorithm for rotation symmetry group detection from real-world images. We propose a frieze-expansion method that transforms rotation symmetry group detection into a simple translation symmetry detection problem. We define and construct a dense symmetry strength map from a given image, and search for potential rotational symmetry centers automatically. Frequency analysis, using discrete Fourier transform (DFT), is applied to the frieze-expansion patterns to uncover the types and the cardinality of multiple rotation symmetry groups in an image, concentric or otherwise. Furthermore, our detection algorithm can discriminate discrete versus continuous and cyclic versus dihedral symmetry groups, and identify the corresponding supporting regions in the image. Experimental results on over 80 synthetic and natural images demonstrate superior performance of our rotation detection algorithm in accuracy and in speed over the state of the art rotation detection algorithms. We present an algorithm that detects rotational and reflectional symmetries of two-dimensional objects. Both symmetry types are effectively detected and analyzed using the angular correlation (AC), which measures the correlation between images in the angular direction. The AC is accurately computed using the pseudopolar Fourier transform, which rapidly computes the Fourier transform of an image on a near-polar grid. We prove that the AC of symmetric images is a periodic signal whose frequency is related to the order of the symmetry. This frequency is recovered via spectrum estimation, which is a proven technique in signal processing with a variety of efficient solutions. We also provide a novel approach for finding the center of symmetry and demonstrate the applicability of our scheme to the analysis of real images 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. We present an algorithm for detecting multiple rotational symmetries in natural images. Given an image, its gradient magnitude field is computed, and information from the gradients is spread using a diffusion process in the form of a gradient vector flow (GVF) field. We construct a graph whose nodes correspond to pixels in tire image, connecting points that are likely to be rotated versions of one another The n-cycles present in tire graph are made to vote for C sub n symmetries, their votes being weighted by the errors in transformation between GVF in the neighborhood of the voting points, and the irregularity of the n-sided polygons formed by the voters. The votes are accumulated at tire centroids of possible rotational symmetries, generating a confidence map for each order of symmetry. We tested the method with several natural images. 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. Reflection symmetry detection receives increasing attentions in recent years. The state-of-the-art algorithms mainly use the matching of intensity-based features (such as the SIFT) within a single image to find symmetry axes. This paper proposes a novel approach by establishing the correspondence of locally affine invariant edge-based features, which are superior to the intensity based in the aspects that it is insensitive to illumination variations, and applicable to textureless objects. The locally affine invariance is achieved by simple linear algebra for efficient and robust computations, making the algorithm suitable for detections under object distortions like perspective projection. Commonly used edge detectors and a voting process are, respectively, used before and after the edge description and matching steps to form a complete reflection detection pipeline. Experiments are performed using synthetic and real-world images with both multiple and single reflection symmetry axis. The test results are compared with existing algorithms to validate the proposed method. We present a spectral approach for detecting and analyzing rotational and reflectional symmetries in n-dimensions. Our main contribution is the derivation of a symmetry detection and analysis scheme for sets of points IRn and its extension to image analysis by way of local features. Each object is represented by a set of points S ∈ IRn, where the symmetry is manifested by the multiple self-alignments of S . The alignment problem is formulated as a quadratic binary optimization problem, with an efficient solution via spectral relaxation. For symmetric objects, this results in a multiplicity of eigenvalues whose corresponding eigenvectors allow the detection and analysis of both types of symmetry. We improve the scheme's robustness by incorporating geometrical constraints into the spectral analysis. Our approach is experimentally verified by applying it to 2D and 3D synthetic objects as well as real images. We generalize the concept of bilateral reflection symmetry to curved glide-reflection symmetry in 2D euclidean space, such that classic reflection symmetry becomes one of its six special cases. We propose a local feature-based approach for curved glide-reflection symmetry detection from real, unsegmented 2D images. Furthermore, we apply curved glide-reflection axis detection for curved reflection surface detection in 3D images. Our method discovers, groups, and connects statistically dominant local glide-reflection axes in an Axis-Parameter-Space (APS) without preassumptions on the types of reflection symmetries. Quantitative evaluations and comparisons against state-of-the-art algorithms on a diverse 64-test-image set and 1,125 Swedish leaf-data images show a promising average detection rate of the proposed algorithm at 80 and 40 percent, respectively, and superior performance over existing reflection symmetry detection algorithms. Potential applications in computer vision, particularly biomedical imaging, include saliency detection from unsegmented images and quantification of deviations from normality. We make our 64-test-image set publicly available. Abstract The purpose of this paper is to detect and characterize geometric rosettes which are among many different star-like motifs used in the most common Islamic Geometric Patterns. Based on symmetry group theory, a geometric rosette can be characterized by its center; order and group of symmetry. It is easy to observe that a rosette is formed by a central star surrounded by two types of shapes (mid-cells and outer-cells) called “ furmah” by Moroccan artisans. The center of symmetry is the center of the concentric circles circum-circling respectively the central star, mid-cells and outer-cells. The order of the rosette is connected with the number of mid-cells. To detect the center of symmetry in a rosette image, we propose an original method based on genetic algorithm that extracts the circle passing by the maximum pixels belonging to the binary rosette image. The center and the radius of the detected circle correspond respectively to the symmetry center of the rosette and the radius of its supporting concentric region. To determine the type and the order of symmetry, Frequency analysis using Discrete Fourier Transform is applied to the Frieze-expansion pattern. This later is obtained by applying the Frieze-Expansion technique to the extracted supporting concentric region. Experimental results prove that the proposed algorithm for rotational symmetry detection is rather successful because it manages to localize the real center of symmetry of any rosette pattern. The key point of this algorithm lies at the same time in its simplicity and its efficiency. Symmetry is an important cue for many applications, including object alignment, recognition, and segmentation. In this paper, we describe a planar reflective symmetry transform (PRST) that captures a continuous measure of the reflectional symmetry of a shape with respect to all possible planes. This transform combines and extends previous work that has focused on global symmetries with respect to the center of mass in 3D meshes and local symmetries with respect to points in 2D images. We provide an efficient Monte Carlo sampling algorithm for computing the transform for surfaces and show that it is stable under common transformations. We also provide an iterative refinement algorithm to find local maxima of the transform precisely. We use the transform to define two new geometric properties, center of symmetry and principal symmetry axes, and show that they are useful for aligning objects in a canonical coordinate system. Finally, we demonstrate that the symmetry transform is useful for several applications in computer graphics, including shape matching, segmentation of meshes into parts, and automatic viewpoint selection. 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. 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. Natural images often exhibit symmetries that should be taken into account when editing them. In this paper we present Nautilus --- a method for automatically identifying symmetric regions in an image along with their corresponding symmetry transformations. We compute dense local similarity symmetry transformations using a novel variant of the Generalised PatchMatch algorithm that uses Metropolis-Hastings sampling. We combine and refine these local symmetries using an extended Lucas-Kanade algorithm to compute regional transformations and their spatial extents. Our approach produces dense estimates of complex symmetries that are combinations of translation, rotation, scale, and reflection under perspective distortion. This enables a number of automatic symmetry-aware image editing applications including inpainting, rectification, beautification, and segmentation, and we demonstrate state-of-the-art applications for each of them. Symmetry in visual data represents repeated patterns or shapes that is easily found in natural and human-made objects. Symmetry pattern on an object works as a salient visual feature attracting human attention and letting the object to be easily recognized. Most existing symmetry detection methods are based on sparsely detected local features describing the appearance of their neighborhood, which have difficulty in capturing object structure mostly supported by edges and contours. In this work, we propose a new reflection symmetry detection method extracting robust 4-dimensional Appearance of Structure descriptors based on a set of outstanding neighbourhood edge segments in multiple scales. Our experimental evaluations on multiple public symmetry detection datasets show promising reflection symmetry detection results on challenging real world and synthetic images. We propose a new model for digital pathology segmentation, based on the observation that histopathology images are inherently symmetric under rotation and reflection. Utilizing recent findings on rotation equivariant CNNs, the proposed model leverages these symmetries in a principled manner. We present a visual analysis showing improved stability on predictions, and demonstrate that exploiting rotation equivariance significantly improves tumor detection performance on a challenging lymph node metastases dataset. We further present a novel derived dataset to enable principled comparison of machine learning models, in combination with an initial benchmark. Through this dataset, the task of histopathology diagnosis becomes accessible as a challenging benchmark for fundamental machine learning research. A simple and fast reflectional symmetry detection algorithm has been developed in this paper. The algorithm employs only the original gray scale image and the gradient information of the image, and it is able to detect multiple reflectional symmetry axes of an object in the image. The directions of the symmetry axes are obtained from the gradient orientation histogram of the input gray scale image by using the Fourier method. Both synthetic and real images have been tested using the proposed algorithm. 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. Symmetry, as one of the key components of Gestalt theory, provides an important mid-level cue that serves as input to higher visual processes such as segmentation. In this work, we propose a complete approach that links the detection of curved reflection symmetries to produce symmetry-constrained segments of structures regions in real images with clutter. For curved reflection symmetry detection, we leverage on patch-based symmetric features to train a Structured Random Forest classifier that detects multiscaled curved symmetries in 2D images. Next, using these curved symmetries, we modulate a novel symmetry-constrained foreground-background segmentation by their symmetry scores so that we enforce global symmetrical consistency in the final segmentation. This is achieved by imposing a pairwise symmetry prior that encourages symmetric pixels to have the same labels over a MRF-based representation of the input image edges, and the final segmentation is obtained via graph-cuts. Experimental results over four publicly available datasets containing annotated symmetric structures: 1) SYMMAX-300 [38], 2) BSD-Parts, 3) Weizmann Horse (both from [18]) and 4) NY-roads [35] demonstrate the approach's applicability to different environments with state-of-the-art performance.