Symmetry Detection Algorithm Research Articles

Reflection Symmetry Detection in Earth Observation Data.

The paper presents a new algorithm for reflection symmetry detection, which is specialized to detect maximal symmetric patterns in an Earth observation (EO) dataset. First, we stress the particularities that make symmetry detection in EO data different from detection in other geometric sets. The EO data acquisition cannot provide exact pairs of symmetric elements and, therefore, the approximate symmetry must be addressed, which is accomplished by voxelization. Besides this, the EO data symmetric patterns in the top view usually contain the most useful information for further processing and, thus, it suffices to detect symmetries with vertical symmetry planes. The algorithm first extracts the so-called interesting voxels and then finds symmetric pairs of line segments, separately for each horizontal voxel slice. The results with the same symmetry plane are then merged, first in individual slices and then through all the slices. The detected maximal symmetric patterns represent the so-called partial symmetries, which can be further processed to identify global and local symmetries. LiDAR datasets of six urban and natural attractions in Slovenia of different scales and in different voxel resolutions were analyzed in this paper, demonstrating high detection speed and quality of solutions.

Ferroaxial Transitions in Glaserite-type Compounds: Database Screening, Phonon Calculations, and Experimental Verification

The so-called ferroaxial transition characterized by a rotational structural distortion that breaks a mirror symmetry has gained growing interest in terms of a new class of ferroic state in crystalline materials. RbFe(MoO4)2, which belongs to glaserite-type compounds, X(□;1)Y(□;2)[M(TO4)2], is one of the most representative materials showing a ferroaxial transition, i.e., ferroaxial materials. Considering a variety of glaserite-type compounds, we expect that they provide a good arena for ferroaxial materials. In this work, we explored new ferroaxial materials by formula-based screening using a regular expression search and the symmetry detection algorithm. As a result, we found that a glaserite-type compound, K2Zr(PO4)2, is one of the promising candidates for ferroaxial materials. Experimentally, we demonstrate that K2Zr(PO4)2 shows a ferroaxial transition at about 700 K, which is well explained by ab initio phonon calculations. The ferroaxial nature of K2Zr(PO4)2 is further confirmed by the observation of its domain structures using a linear electrogyration effect, i.e., optical rotation in proportion to an applied electric field. Our work provides an effective approach to exploring ferroaxial materials.

Symmetry detection algorithm to classify the tea grades using artificial intelligence

In classifying tea grades the current available used methods are not consistent to extract the tea texture features accurately. which is resulting low efficiency and poor classification results. To overcome this challenge the novel symmetry detection algorithm based on artificial intelligence is proposed. The symmetry detection algorithm is used to detect the edge of tea image, which is the region of interest to process further based on the captured data. The vertigo model is constructed from captured inputs. The tea feature vector is extracted with the help of BP algorithm and the tea grade is analyzed using the artificial intelligence support. Using the proposed algorithm method, the experimental results shows high classification efficiency and higher accuracy results.

Dominant Symmetry Plane Detection for Point-Based 3D Models

In this paper, a symmetry detection algorithm for three-dimensional point cloud model based on weighted principal component analysis (PCA) is proposed. The proposed algorithm works as follows: first, using the point element’s area as the initial weight, a weighted PCA is performed and a plane is selected as the initial symmetry plane; and then an iterative method is used to adjust the approximate symmetry plane step by step to make it tend to perfect symmetry plane (dominant symmetry plane). In each iteration, we first update the weight of each point based on a distance metric and then use the new weights to perform a weighted PCA to determine a new symmetry plane. If the current plane of symmetry is close enough to the plane of symmetry in the previous iteration or if the number of iterations exceeds a given threshold, the iteration terminates. After the iteration is terminated, the plane of symmetry in the last iteration is taken as the dominant symmetry plane of the model. As shown in experimental results, the proposed algorithm can find the dominant symmetry plane for symmetric models and it also works well for nonperfectly symmetric models.

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.

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.

Smart data driven traffic sign detection method based on adaptive color threshold and shape symmetry

Detection and recognition of road traffic signs constitute an important element in Advanced Driver Assistance Systems (ADAS), which can provide real-time road sign perception information to vehicles. In this paper, we proposed a new traffic sign detection method based on adaptive color threshold segmentation and the hypothesis testing of shape symmetry by leveraging traffic signs and image data. First, we calculated an adaptive segmentation threshold using the cumulative distribution function of the image histogram. Based on this, we designed an approximate maximum and minimum normalization method, which is used to suppress the interference of high brightness area and background in image thresholding processes. Secondly, we transformed the highlight shape feature of thresholding image into a connected domain feature vector. And we formulated a shape symmetry detection algorithm based on statistical hypothesis testing to efficiently extract the ROI of traffic signs based on traffic data analysis. We performed some comprehensive experiments on the GTSDB (German Traffic Sign Detection Benchmark) dataset. The accuracy of traffic sign detection exceeded 94%. This method has higher detection accuracy and time efficiency than other methods, and better robustness under complex traffic environment.

An algorithm for identifying symmetric variables based on the order eigenvalue matrix

To simplify the process for identifying 12 types of symmetric variables in Boolean functions, we propose a new symmetry detection algorithm based on minterm expansion or the truth table. First, the order eigenvalue matrix based on a truth table is defined according to the symmetry definition of a logic variable. By analyzing the constraint conditions of the order eigenvalue matrix for 12 types of symmetric variables, an algorithm is proposed for identifying symmetric variables of the Boolean function. This algorithm can be applied to identify the symmetric variables of Boolean functions with or without don’t-care terms. The proposed method avoids the restriction by the number of logic variables of the graphical method, spectral coefficient methods, and AND-XOR expansion coefficient methods, and solves the problem of completeness in the fast compu-tation method. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. The application results show that, compared with the traditional methods, the new algorithm is an optimal detection method in terms of the applicability of the number of logic variables, the Boolean function including don’t-care terms, detection type, and complexity of the identification process.

Roof model recommendation for complex buildings based on combination rules and symmetry features in footprints

ABSTRACTCurrently, very few roof shape information for complex buildings is available on OSM. Moreover, additional data requirements (e.g. 3D point clouds) limit the applicability of many roof reconstruction approaches. To mitigate this issue, we propose an approach to roof shape recommendations for complex buildings by exploring the inherited characteristics of building footprints: the disclosure of rectangles combinations in a partition of footprints and the symmetrical features of footprints. First, it decomposes a complex footprint into rectangles by using an advanced minimal non-overlapping cover algorithm. Second, a graph-based symmetry detection algorithm is proposed to identify all the symmetrical sub-clusters in partitions. Then, a set of selection rules are defined to rank partitions, and the best ones are chosen for roof shape recommendation. Finally, a set of combination rules and a symmetry rule are defined. It enables to evaluate the probability of a footprint being a certain combination of roof shapes. Experimental results show the growth of the probability of correctly recommending roof shapes for single rectangles and buildings from a prior probability of 17–45% and from a prior probability of 0.29–14.3%, removing 60% and 93% of the incorrect roof shape options, respectively.

Automatic procedure for generating symmetry adapted wavefunctions

Automatic detection of point groups as well as symmetrisation of molecular geometry and wavefunctions are useful tools in computational quantum chemistry. Algorithms for developing these tools as well as an implementation are presented. The symmetry detection algorithm is a clustering algorithm for symmetry invariant properties, combined with logical deduction of possible symmetry elements using the geometry of sets of symmetrically equivalent atoms. An algorithm for determining the symmetry adapted linear combinations (SALCs) of atomic orbitals is also presented. The SALCs are constructed with the use of projection operators for the irreducible representations, as well as subgroups for determining splitting fields for a canonical basis. The character tables for the point groups are auto generated, and the algorithm is described. Symmetrisation of molecules use a projection into the totally symmetric space, whereas for wavefunctions projection as well and partner function determination and averaging is used. The software has been released as a stand-alone, open source library under the MIT license and integrated into both computational and molecular modelling software.Graphical abstract.

On local domain symmetry for model expansion

AbstractSymmetry in combinatorial problems is an extensively studied topic. We continue this research in the context of model expansion problems, with the aim of automating the workflow of detecting and breaking symmetry. We focus onlocal domain symmetry, which is induced by permutations of domain elements, and which can be detected on a first-order level. As such, our work is a continuation of the symmetry exploitation techniques of model generation systems, while it differs from more recent symmetry breaking techniques in answer set programming which detect symmetry on ground programs. Our main contributions are sufficient conditions for symmetry of model expansion problems, the identification oflocal domain interchangeability, which can often be broken completely, and efficient symmetry detection algorithms for both local domain interchangeability as well as local domain symmetry in general. Our approach is implemented in the model expansion system IDP, and we present experimental results showcasing the strong and weak points of our approach compared tosbass, a symmetry breaking technique for answer set programming.

An Algorithm for Identifying Symmetric Variables in the Canonical Reed–Muller Algebra System

To simplify the process for identifying 12 types of symmetric variables in the canonical Reed–Muller (CRM) algebra system, we propose a new symmetry detection algorithm based on AND-XOR expansion. By analyzing the relationships between the coefficient matrices of sub-functions and the order coefficient subset matrices based on AND-XOR expansion around two arbitrary logical variables, the constraint conditions of the order coefficient subset matrices are revealed for 12 types of symmetric variables. Based on the proposed constraints, the algorithm is realized by judging the order characteristic square value matrices. The proposed method avoids the complicated process for separating the AND–XOR expansion coefficients into different groups in the Reed–Muller transform methods and solves the problem of completeness in the RM type decomposition map method. The application results show that, compared with traditional methods the new algorithm is an optimal detection method in terms of applicability of the number of logical variables, detection types, and complexity of the identification process. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. Experimental results show that the proposed algorithm is convenient and efficient.

Multiresolution Rotational Symmetry Detection via Radius-Based Frieze-Expansion

Rotational symmetry is important for many applications in computer graphics, vision, and image processing. However, it remains difficult to design an effective algorithm for automatic symmetry recognition. In this paper, we present a rotational symmetry detection algorithm, which is easy to use and can determine both the center and the radius of the rotational symmetry supporting region without human interaction. Our algorithm is derived from frieze-expansions approach and improved through a radius-based expansion idea. Multiresolution pyramid is used to accelerate this detection process. We also discuss a solution to deal with rotational symmetry detection under slight affine transformation. Experimental results show that the method is effective for most nature images with rotational symmetry.

A rotation symmetry group detection technique for the characterization of Islamic Rosette Patterns

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.

A universal symmetry detection algorithm.

Research on symmetry detection focuses on identifying and detecting new types of symmetry. The paper presents an algorithm that is capable of detecting any type of permutation-based symmetry, including many types for which there are no existing algorithms. General symmetry detection is library-based, but symmetries that can be parameterized, (i.e. total, partial, rotational, and dihedral symmetry), can be detected without using libraries. In many cases it is faster than existing techniques. Furthermore, it is simpler than most existing techniques, and can easily be incorporated into existing software. The algorithm can also be used with virtually any type of matrix-based symmetry, including conjugate symmetry.

An algorithm for identifying symmetric variables in the canonical OR-coincidence algebra system

To simplify the process for identifying 12 types of symmetric variables in the canonical OR-coincidence (COC) algebra system, we propose a new symmetry detection algorithm based on OR-NXOR expansion. By analyzing the relationships between the coefficient matrices of sub-functions and the order coefficient subset matrices based on OR-NXOR expansion around two arbitrary logical variables, the constraint conditions of the order coefficient subset matrices are revealed for 12 types of symmetric variables. Based on the proposed constraints, the algorithm is realized by judging the order characteristic square value matrices. The proposed method avoids the transformation process from OR-NXOR expansion to AND-OR-NOT expansion, or to AND-XOR expansion, and solves the problem of completeness in the dj-map method. The application results show that, compared with traditional methods, the new algorithm is an optimal detection method in terms of applicability of the number of logical variables, detection type, and complexity of the identification process. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. Experimental results show that the proposed algorithm is convenient and efficient.

Probably Approximately Symmetric: Fast Rigid Symmetry Detection With Global Guarantees

AbstractWe present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user‐specified threshold, with very high probability. Our method uses a carefully designed sampling of the transformation space, where each transformation is efficiently evaluated using a sublinear algorithm. We prove that the density of the sampling depends on the total variation of the shape, allowing us to derive formal bounds on the algorithm's complexity and approximation quality. We further investigate different volumetric shape representations (in the form of truncated distance transforms), and in such a way control the total variation of the shape and hence the sampling density and the runtime of the algorithm. A comprehensive set of experiments assesses the proposed method, including an evaluation on the eight categories of the COSEG data set. This is the first large‐scale evaluation of any symmetry detection technique that we are aware of.

Skeleton-based intrinsic symmetry detection on point clouds

We present a skeleton-based algorithm for intrinsic symmetry detection on imperfect 3D point cloud data. The data imperfections such as noise and incompleteness make it difficult to reliably compute geodesic distances, which play essential roles in existing intrinsic symmetry detection algorithms. In this paper, we leverage recent advances in curve skeleton extraction from point clouds for symmetry detection. Our method exploits the properties of curve skeletons, such as homotopy to the input shape, approximate isometry-invariance, and skeleton-to-surface mapping, for the detection task. Starting from a curve skeleton extracted from an input point cloud, we first compute symmetry electors, each of which is composed of a set of skeleton node pairs pruned with a cascade of symmetry filters. The electors are used to vote for symmetric node pairs indicating the symmetry map on the skeleton. A symmetry correspondence matrix (SCM) is constructed for the input point cloud through transferring the symmetry map from skeleton to point cloud. The final symmetry regions on the point cloud are detected via spectral analysis over the SCM. Experiments on raw point clouds, captured by a 3D scanner or the Microsoft Kinect, demonstrate the robustness of our algorithm. We also apply our method to repair incomplete scans based on the detected intrinsic symmetries.

Curved Glide-Reflection Symmetry Detection

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 glidereflection 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 glidereflection 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.

Symmetry detection based on phase information and its application in DR fundus image

Symmetry exists widely in the real world and plays a remarkable role in perception problems. The existing symmetry detection algorithms are mainly based on luminance or gradient information. Upon analyzing the relationship between symmetry and phase, based on phase congruency, we propose a phase-based symmetry detection (PSD) algorithm. PSD is calculated based on log Gabor wavelet. We test it with fundus image and the experiments show that this algorithm can be applied directly to original images without segmentation.