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.
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.
@cite_28 @cite_26 @cite_10
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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. 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. In this paper, a simple and yet robust Hough transform algorithm is proposed to detect and analyze reflectional symmetry and skew-symmetry (reflectional symmetry under parallel projection). It is applicable to shapes that contain global, local and slightly deformed reflectional skew-symmetries under the presence of noise and occlusion. 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. We investigate the constraints placed on the image projection of a planar object having local reflectional symmetry. Under the affine approximation to projection, we demonstrate an efficient (low-complexity) algorithm for detecting and verifying symmetries despite the distorting effects of image skewing. The symmetries are utilized for three distinct tasks: first, determining image back-projection up to a similarity transformation ambiguity; second, determining the object plane orientation (slant and tilt); and third, as a test for non-coplanarity amongst a collection of objects. These results are illustrated throughout with examples from images of real scenes. Local reflection symmetry detection in nature images is a quite important but challenging task in computer vision. The main obstacle is both the scales and the orientations of symmetric structure are unknown. The multiple instance learning (MIL) framework sheds lights onto this task owing to its capability to well accommodate the unknown scales and orientations of the symmetric structures. However, to differentiate symmetry vs non-symmetry remains to face extreme confusions caused by clutters scenes and ambiguous object structures. In this paper, we propose a novel multiple instance learning framework for local reflection symmetry detection, named multiple instance subspace learning (MISL), which instead learns a group of models respectively on well partitioned subspaces. To obtain such subspaces, we propose an efficient dividing strategy under MIL setting, named partial random projection tree (PRPT), by taking advantage of the fact that each sample (bag) is represented by the proposed symmetry features computed at specific scale and orientation combinations (instances). Encouraging experimental results on two datasets demonstrate that the proposed local reflection symmetry detection method outperforms current state-of-the-arts. HighlightsWe perform clustering on samples represented by multiple instances.We learn a group of MIL classifiers on subspaces.We report state-of-the-arts results on the symmetry detection benchmark. 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. 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. 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. 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. We present two methods for detecting symmetry in images, one based directly on the intensity values and another one based on a discrete representation of local orientation. A symmetry finder has been developed which uses the intensity-based method to search an image for compact regions which display some degree of mirror symmetry due to intensity similarities across a straight axis. In a different approach, we look at symmetry as a bilateral relationship between local orientations. A symmetryenhancing edge detector is presented which indicates edges dependent on the orientations at two different image positions. SEED, as we call it, is a detector element implemented by a feedforward network that holds the symmetry conditions. We use SEED to find the contours of symmetric objects of which we know the axis of symmetry from the intensity-based symmetry finder. The methods presented have been applied to the problem of visually guided car-following. Real-time experiments with a system for automatic headway control on motorways have been successful. 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 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 We present an algorithm for multi-scale partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region. To identify prominent symmetric regions which overlap and vary in form and scale, we decouple scale extraction and symmetry extraction by performing two levels of clustering. First, significant symmetry scales are identified by clustering sample point pairs from an input shape. Since different point pairs can share a common point, shape regions covered by points in different scale clusters can overlap. We introduce the symmetry scale matrix (SSM), where each entry estimates the likelihood two point pairs belong to symmetries at the same scale. The pair-to-pair symmetry affinity is computed based on a pair signature which encodes scales. We perform spectral clustering using the SSM to obtain the scale clusters. Then for all points belonging to the same scale cluster, we perform the second-level spectral clustering, based on a novel point-to-point symmetry affinity measure, to extract partial symmetries at that scale. We demonstrate our algorithm on complex shapes possessing rich symmetries at multiple scales. 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 propose a novel approach for detecting partial reflectional symmetry in images. Our method consists of two principal stages: candidate selection and validation. In the first step, candidates for mirror-symmetric patches are identified using an existing heuristic procedure based on Hough voting. The candidates are then validated using a principled statistical procedure inspired from the a contrario theory, which minimizes the number of false positives. Our algorithm uses integral image properties to enhance the execution time. 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 investigate the role of symmetry detection and symmetry breaking in answer set programming to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We reduce symmetry detection to a graph automorphism problem which allows us to extract symmetries of a logic program from the symmetries of the constructed coloured graph. The correctness of our reduction is proven. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process to implicitly represent symmetries with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. In this paper, we establish a baseline for object symmetry detection in complex backgrounds by presenting a new benchmark and an end-to-end deep learning approach, opening up a promising direction for symmetry detection in the wild. The new benchmark, named Sym-PASCAL, spans challenges including object diversity, multi-objects, part-invisibility, and various complex backgrounds that are far beyond those in existing datasets. The proposed symmetry detection approach, named Side-output Residual Network (SRN), leverages output Residual Units (RUs) to fit the errors between the object symmetry groundtruth and the outputs of RUs. By stacking RUs in a deep-to-shallow manner, SRN exploits the 'flow' of errors among multiple scales to ease the problems of fitting complex outputs with limited layers, suppressing the complex backgrounds, and effectively matching object symmetry of different scales. Experimental results validate both the benchmark and its challenging aspects related to realworld images, and the state-of-the-art performance of our symmetry detection approach. The benchmark and the code for SRN are publicly available at this https URL.