Symmetry Detection Research Articles

Identification of acute intracranial bleed on computed tomography using computer aided detection

Intracranial haemorrhage can be life threatening. Timely detection of acute intracranial haemorrhage in an emergency room is essential so that the patient can be given medical attention without delay. This has led to the use of Computer Aided Detection (CAD) systems which can help to pick up and prioritize patients with high risk of bleeding. A CAD for identification of acute intracranial haemorrhage in Computed Tomography (CT) on a per patient basis was developed in this project. The CAD is aimed to be a triage tool which determines the priority of image being read by radiologists. It was developed and validated using 119 and 108 volumes of brain CT images respectively. The volumes were first registered to standard Montreal Neurological Institute (MNI) space. Slices close to the base and top of the skull that tend to contribute to false positives were omitted. Then, the volumes were analysed by a fully automated CAD program developed in MATLAB. The algorithm involved multiple thresholding and symmetry detection in 3D to detect acute intracranial haemorrhage. The evaluation took around 5s per volume. On a per patient basis, the CAD achieved sensitivity of 75.0%, specificity of 83.8%, and accuracy of 80.6% in the validation set.

Symmetry detection algorithm to detect forwarded spoofing interference signals of BOC modulation receivers

In this paper, the symmetry detection algorithm based on the symmetry of binary offset carrier (BOC) modulation signals is proposed to solve the problem of the global navigation satellite system (GNSS) spoofing interference in BOC modulation and acquisition phase which set on the base of the characters of correlation peaks, and achieve the detection of the forwarded spoofing interference signals. The theoretical value and the simulation value of the receiver operating characteristic (ROC) curve of the symmetry detection algorithm can be obtained by the numerical calculation and the experimental simulation. It can be seen from the simulation that with the increase of the accumulation times after the correlation, the signal to noise ratio (SNR) of the spoofing signal compared to the real signal, and the SNR of the real signal, the detection probability of the spoofing signal increases as well. When the power of the spoofing signal is 3 dB greater than that of the real signal, the detection probability can be more than 99% under the condition that the false alarm probability is 0.1%. Given that it only needs to add the module to the software receiver to detect spoofing signals, the algorithm proposed in this paper is of practical significance.

Different neural representations for detection of symmetry in dot-patterns and in faces: A state-dependent TMS study

The occipital face area (OFA) has been shown to code the presence of symmetry in faces and in vertically symmetric dot patterns. However, it is not clear whether symmetry processing of face and non-face stimuli involve overlapping neural mechanisms in OFA. This was assessed using state-dependent TMS by employing a priming paradigm. Specifically, we examined whether prior presentation of low-level symmetry affects the impact of TMS on discrimination of symmetry in subsequently presented faces – indicating that the same neural mechanisms encode symmetry in both face and non-face stimuli. Participants performed a symmetry discrimination task on a series of faces, each of which was preceded by either a vertically symmetric, a horizontally symmetric or a non-symmetric dot configuration (prime) while receiving stimulation over either the right OFA, the right Lateral Occipital Cortex (rLO) or over a control site (Vertex). Vertically symmetric dot patterns primed symmetry discrimination in faces. The key finding was that the priming effect was not affected by TMS applied over OFA; stimulation of this site (but not of rLO) impaired the discrimination of facial symmetry regardless of prime type. Overall, these results suggest that distinct neural representations in OFA are involved in symmetry detection in face and non-face stimuli.

Orientation-Preserving Spectral Correspondence for 3D Shape Analysis

Abstract In this article, the authors present an orientation-preserving spectral correspondence for three-dimensional (3D) shape analysis, which is robust and efficient for topological and deformable changes, even for non-isometric shapes. Our technique introduces an optimal spectral representation by combining the eigendecomposition with principal components analysis (PCA) to the heat kernel Laplacian matrix, and we further propose an efficient symmetry detection method based on so-called dominant eigenfunctions. Finally, a 3D descriptor encoding intrinsic symmetry structure and local geometric feature is constructed which effectively reveals the consistent structure between the deformable shapes. Consequently, sufficient orientation-preserving correspondence can be established in our embedding space. Experimental results showed that our method produces stable matching results in comparison with state-of-the-art methods.

Research on the Detection Method of Implicit Self Symmetry in a High-Level Semantic Model

In order to improve the accuracy of semantic model intrinsic detection, a skeleton-based high-level semantic model intrinsic self-symmetry detection method is proposed. The semantic analysis of the model set is realized by the uniform segmentation of the model within the same style, the component correspondence of the model between different styles, and the shape content clustering. Based on the results of clustering analysis, for a given three-dimensional (3D) point cloud model, according to the curve skeleton, the skeleton point pairs reflecting the symmetry between the model surface points are obtained by the election method, and the symmetry is extended to the model surface vertices according to these skeleton point pairs. With the help of skeleton, the symmetry of the point cloud model is obtained, and then the symmetry region of point cloud model is obtained by the symmetric correspondence matrix and spectrum method, so as to realize the intrinsic symmetry detection of the model. The experimental results show that the proposed method has the advantages of less time, high accuracy, and high reliability.

Point-group symmetry detection in three-dimensional charge density of biomolecules.

No rigorous statistical tests for detecting point-group symmetry in three-dimensional (3D) charge density maps obtained by electron microscopy (EM) and related techniques have been developed. We propose a method for determining the point-group symmetry of 3D charge density maps obtained by EM and related techniques. Our ab initio algorithm does not depend on atomic coordinates but utilizes the density map directly. We validate the approach for a range of publicly available single-particle cryo-EM datasets. In straightforward cases, our method enables fully automated single-particle 3D reconstruction without having to input an arbitrarily selected point-group symmetry. When pseudo-symmetry is present, our method provides statistics quantifying the degree to which the 3D density agrees with the different point-groups tested. The software is freely available at https://github.com/hael/SIMPLE3.0.

Automatic Symmetry Detection From Brain MRI Based on a 2-Channel Convolutional Neural Network.

Symmetry detection is a method to extract the ideal mid-sagittal plane (MSP) from brain magnetic resonance (MR) images, which can significantly improve the diagnostic accuracy of brain diseases. In this article, we propose an automatic symmetry detection method for brain MR images in 2-D slices based on a 2-channel convolutional neural network (CNN). Different from the existing detection methods that mainly rely on the local image features (gradient, edge, etc.) to determine the MSP, we use a CNN-based model to implement the brain symmetry detection, which does not require any local feature detections and feature matchings. By training to learn a wide variety of benchmarks in the brain images, we can further use a 2-channel CNN to evaluate the similarity between the pairs of brain patches, which are randomly extracted from the whole brain slice based on a Poisson sampling. Finally, a scoring and ranking scheme is used to identify the optimal symmetry axis for each input brain MR slice. Our method was evaluated in 2166 artificial synthesized brain images and 3064 collected in vivo MR images, which included both healthy and pathological cases. The experimental results display that our method achieves excellent performance for symmetry detection. Comparisons with the state-of-the-art methods also demonstrate the effectiveness and advantages for our approach in achieving higher accuracy than the previous competitors.

Symmetry Detection for Quadratic Optimization Using Binary Layered Graphs

Symmetry in mathematical optimization may create multiple, equivalent solutions. In nonconvex optimization, symmetry can negatively affect algorithm performance, e.g., of branch-and-bound when symmetry induces many equivalent branches. This paper develops detection methods for symmetry groups in quadratically-constrained quadratic optimization problems. Representing the optimization problem with adjacency matrices, we use graph theory to transform the adjacency matrices into binary layered graphs. We enter the binary layered graphs into the software package nauty that generates important symmetric properties of the original problem. Symmetry pattern knowledge motivates a discretization pattern that we use to reduce computation time for an approximation of the point packing problem. This paper highlights the importance of detecting and classifying symmetry and shows that knowledge of this symmetry enables quick approximation of a highly symmetric optimization problem.

ZoomOut

We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.

MemSTATS: A Benchmark Set of Membrane Protein Symmetries and Pseudosymmetries

In membrane proteins, symmetry and pseudosymmetry often have functional or evolutionary implications. However, available symmetry detection methods have not been tested systematically on this class of proteins because of the lack of an appropriate benchmark set. Here we present MemSTATS, a publicly available benchmark set of both quaternary- and internal-symmetries in membrane protein structures. The symmetries are described in terms of order, repeated elements, and orientation of the axis with respect to the membrane plane. Moreover, using MemSTATS, we compare the performance of four widely used symmetry detection algorithms and highlight specific challenges and areas for improvement in the future.

An advantage for smooth compared with angular contours in the speed of processing shape.

Curvature along a contour is important for shape perception, and a special role may be played by points of maxima (extrema) along the contour. Angles are discontinuities in curvature, a special case at one extreme of the curvature continuum. We report 4 studies using abstract shapes and comparing polygons (curvature discontinuities at the vertices) and a smoothed version of polygons (no vertices). Polygons are simpler and are defined by a small set of vertices, whereas smoothed shapes have a continuous curvature change along the contour. Angles have also been discussed as an early signal of threat and danger, and on that basis, one may predict faster responses to polygons. However, curved shapes are more typical of the natural environment in which the visual system has evolved. For a detection task, we found faster responses to smooth shapes, not mediated by complexity (Experiment 1). We then tested 3 orthogonal shape tasks: comparison between shapes (detection of repetition; Experiment 2a), comparison after a rotation (Experiment 2b), and detection of bilateral symmetry (Experiment 3). In all tasks, responses for smoothed stimuli were faster; there was also an interaction with type of response: Trials with smooth shapes were faster when a positive response was produced. Overall, there was evidence that smooth shapes with continuous change in curvature along the contour are processed more efficiently, and they tend to be classified as targets. We discuss this in relation to shape analysis and to the preference for smoothed over angular shapes. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Intrinsic Symmetry Detection on 3D Models with Skeleton‐guided Combination of Extrinsic Symmetries

AbstractThe existing methods for intrinsic symmetry detection on 3D models always need complex measures such as geodesic distances for describing intrinsic geometry and statistical computation for finding non‐rigid transformations to associate symmetrical shapes. They are expensive, may miss symmetries, and cannot guarantee their obtained symmetrical parts in high quality. We observe that only extrinsic symmetries exist between convex shapes, and two intrinsically symmetric shapes can be determined if their belonged convex sub‐shapes are symmetrical to each other correspondingly and connected in a similar topological structure. Thus, we propose to decompose the model into convex parts, and use the similar structures of the skeleton of the model to guide combination of extrinsic symmetries between convex parts for intrinsic symmetry detection. In this way, we give up statistical computation for intrinsic symmetry detection, and avoid complex measures for describing intrinsic geometry. With the similar structures being from small to large gradually, we can quickly detect multi‐scale partial intrinsic symmetries in a bottom up manner. Benefited from the well segmented convex parts, our obtained symmetrical parts are in high quality. Experimental results show that our method can find many more symmetries and runs much faster than the existing methods, even by several orders of magnitude.

Orientation of pattern elements does not influence mirror-symmetry perception

Stimuli used to study symmetry perception often lack orientation information. However, orientation noise decreases the salience of symmetrical shapes suggesting that the two signals may interact (Machilsen et al., 2009, JoV). Here we investigate whether (i) orientation and position-symmetry signals interact in the perception of symmetry (Experiment 1), and (ii) symmetry detection mechanisms are sensitive to the orientation of pattern elements (Experiment 2). Stimuli were patterns made of oriented Gabors arranged either symmetrically about the vertical axis or randomly. We varied the amount of position-symmetry by changing the proportion of symmetrical Gabors and measured symmetry detection thresholds using a 2IFC procedure. Experiment 1 had two conditions: (a) ‘segregated’- position-symmetric Gabors had one orientation and the noise Gabors had a different orientation, and (b) ‘non-segregated’- position-symmetric Gabors were of two orientations in equal proportions, as were the random-positioned Gabors. We varied the separation between the two orientations (0°, 30°, 60°, 90°) in different trials. In Experiment 2, the orientation and position symmetry were manipulated independently. We used (a) position-symmetric patterns in which all Gabors had either the same (asymmetric), mirror-symmetric or random orientations. (b) position-symmetric Gabors had symmetric orientations and noise Gabors had random orientations and positions, (c) patterns with no position-symmetry, and varying amounts of orientation-symmetry. We found that symmetry detection thresholds were not significantly different for the segregated and non-segregated conditions, for all stimulus orientation differences (Experiment 1). The thresholds were also comparable across all conditions containing position-symmetry, but were significantly higher for the orientation-symmetry only (no position-symmetry) condition (Experiment 2). We conclude that symmetry detection mechanisms are not sensitive to orientation information. Although orientation is a dominant visual feature in many visual tasks, it does not affect symmetry detection even when the orientation signals are asymmetric, suggesting that symmetry detection mechanisms are solely reliant on position information.

Improving Formal Verification and Testing Techniques for Internet of Things and Smart Cities

We are interested in formal verification and model-based testing for Internet of Things and Smart Cities. In general these two techniques suffer from state explosion problem. To remedy this situation we propose a set of techniques which aim to reduce the cost, duration and complexity of the considered problems. On the first hand the techniques realted to formal verification are as follows. First, Abstraction consists in modelling a part of the system accurately and the other parts at high level. Second, Modularization and Compositionality consist in splitting the whole system into smaller subsystems. Third, Symmetry Detection exploits symmetries that take place during the system execution. Fourth, Data Independence consists in detecting that the behaviour of the considered system does not depend on some data inputs. Fifth, Eliminating Functional Dependencies consists in removing dependency among state variables. Sixth, Exploiting Reversible Rules consists in collapsing subgraphs of the graph of states into abstract states. On the second hand the techniques related to model-based testing are as follows. First, Refinement Techniques extract test scenarios directly from the untimed specification. Second, the Reduction of the Size of Digital-Clock Tests Technique provides a heuristic to reduce the size of the generated tests. Third, the Timed Automata Testers Generation Technique allows to produce testers in the form of deterministic timed automata. Fourth, the Test Cases Updating Technique after System Evolution makes it possible to reduce the number of tests to be generated after each adaptation. Fifth, the Resource Aware Test Component Placement Technique allows to produce a placement plan of the different testers. Sixth, Coverage Technique generates a reasonable-size set of tests. A case study is proposed in order to illustrate the use of these techniques.

Diffusion-based isometric depth correspondence

We propose an iterative isometric point correspondence method that relies on diffusion distance to handle challenges posed by commodity depth sensors which usually provide incomplete and noisy surface data exhibiting holes and gaps. We formulate the correspondence problem as finding an optimal partial mapping between two given point sets, that minimizes deviation from isometry. Our algorithm starts with an initial rough correspondence between keypoints, obtained via any point matching technique. This initial correspondence is then pruned and updated by iterating a perfect matching algorithm until convergence in order to find as many reliable correspondences as possible. The resulting set of sparse but reliable correspondences then serves as a base matching from which a dense correspondence set is estimated. We additionally provide a global intrinsic symmetry detection technique which clusters a point cloud into its symmetric sides. We incorporate this technique into our point-based correspondence method so as to address the symmetrical flip problem and to further improve the reliability of our matching results. Our symmetry-aware correspondence method is especially effective on human shapes with global reflectional symmetry. We hence conduct experiments on datasets comprising human shapes and show that our method provides state of the art performance over depth frames exhibiting occlusions, large deformations, and topological noise.

A fast and efficient 3D reflection symmetry detector based on neural networks

Determining the 3D reflection symmetry planes from 3D models is very difficult and time-consuming. In this paper, we formulate the symmetry detection as a per-point classification problem and present a deep neural network based method to solve it. During the training procedure, we firstly collect a lot of CAD mesh models with reflection symmetry as the training data, and then convert each mesh model into a dense point cloud with points located on the symmetry planes labeled as positive. Based on the PointNet++ architecture, we train a multi-scale deep neural network to capture the reflection symmetry property from the point cloud automatically. In addition, a novel weighted cross-entropy loss function is adopted to balance the positive and the negative samples. During the inference procedure, we firstly feed the down-sampled point cloud into the trained neural network. Then, the output per-point classification result is used to calculate an initial symmetry plane equation with RANSAC strategy and the least square method. Finally, iterative closest point algorithm is performed to optimize the fitted symmetry plane. Experimental results on both the synthetic and the real data demonstrate the efficiency, robustness and flexibility of our approach. Our method is pretty fast and generates comparable or better results than the existing methods.

ALGORITHMS FOR ADJUSTMENT OF SYMMETRY AXIS FOUND FOR 2D SHAPES BY THE SKELETON COMPARISON METHOD

Abstract. Reflection symmetry detection for 2D shapes is a well-known task in Computer Vision, but there is a limited number of efficient and effective methods for its solution. Our previously proposed approach based on pair-wise comparison of sub-sequences of skeleton primitives finds the axis of symmetry within few seconds. In order to evaluate the value of symmetry relative to the found axis we use the Jaccard similarity measure. It is applied to the pixels subsets of a shape which are split by the axis. Often an axis found by the skeleton comparison method diverges more or less from the ground-truth axis found by the method of exhaustive search among all the potential candidates. That is why the algorithms that allow adjusting the axis found by the fast skeleton method are proposed. They are based on the idea of searching the axis which is located near the seed skeleton axis and has greater Jaccard similarity measure. The experimental study on the ”Flavia” and ”Butterflies” datasets shows that proposed algorithms find the ground-truth axis (or the axis which has slightly less Jaccard similarity value than the ground-truth axis) in near real time. It is considerably faster than any of the optimized brute-force methods.

Analyzing the symmetrical arrangement of structural repeats in proteins with CE-Symm.

Many proteins fold into highly regular and repetitive three dimensional structures. The analysis of structural patterns and repeated elements is fundamental to understand protein function and evolution. We present recent improvements to the CE-Symm tool for systematically detecting and analyzing the internal symmetry and structural repeats in proteins. In addition to the accurate detection of internal symmetry, the tool is now capable of i) reporting the type of symmetry, ii) identifying the smallest repeating unit, iii) describing the arrangement of repeats with transformation operations and symmetry axes, and iv) comparing the similarity of all the internal repeats at the residue level. CE-Symm 2.0 helps the user investigate proteins with a robust and intuitive sequence-to-structure analysis, with many applications in protein classification, functional annotation and evolutionary studies. We describe the algorithmic extensions of the method and demonstrate its applications to the study of interesting cases of protein evolution.

Detecting Approximate Reflection Symmetry in a Point Set Using Optimization on Manifold

We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb {R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting approximate reflection symmetry as the problem of establishing correspondences between the points which are reflections of each other and we determine the reflection symmetry transformation. We formulate an optimization framework in which the problem of establishing the correspondences amounts to solving a linear assignment problem and the problem of determining the reflection symmetry transformation amounts to solving an optimization problem on a smooth Riemannian product manifold. The proposed approach estimates the symmetry from the geometry of the points and is descriptor independent. We evaluate the performance of the proposed approach on the standard benchmark dataset and achieve the state-of-the-art performance. We further show the robustness of our approach by varying the amount of distortion in a perfect reflection symmetry pattern where we perturb each point by a different amount of perturbation. We demonstrate the effectiveness of the method by applying it to the problem of 2-D (two-dimensional) and 3-D reflection symmetry detection along with comparisons.

Speed tuning properties of mirror symmetry detection mechanisms

The human visual system is often tasked with extracting image properties such as symmetry from rapidly moving objects and scenes. The extent to which motion speed and symmetry processing mechanisms interact is not known. Here we examine speed-tuning properties of symmetry detection mechanisms using dynamic dot-patterns containing varying amounts of position and local motion-direction symmetry. We measured symmetry detection thresholds for stimuli in which symmetric and noise elements either drifted with different relative speeds, were relocated at different relative temporal frequencies or were static. We also measured percentage correct responses under two stimulus conditions: a segregated condition in which symmetric and noise elements drifted at different speeds, and a non-segregated condition in which the symmetric elements drifted at two different speeds in equal proportions, as did the noise elements. We found that performance (i) improved gradually with increasing the difference in relative speed between symmetric and noise elements, but was invariant across relative temporal frequencies/lifetime duration differences between symmetric and noise elements, (ii) was higher in the segregated compared to non-segregated conditions, and in the moving compared to the static conditions. We conclude that symmetry detection mechanisms are broadly tuned to speed, with speed-selective symmetry channels combining their outputs by probability summation.