Rotation Transformation Research Articles

The application of big data technology in the art of visual communication design with information technology

Abstract Based on big data technology, this paper firstly proposes that visual image generation design based on the improved adversarial generative network becomes one of the ideas to solve the current dilemma of visual communication design, which is not only a convenient, creative means but also changes the traditional way of visual communication design. Secondly, in the extension of visual image samples, in addition to using some operations such as rotation, translation and scale transformation of visual images, an improved DCGAN adversarial generative network algorithm is also used. The improved DCGAN network is then used to augment the number of visual images while maintaining the quality of visual image generation. Finally, intelligent generation models based on visual communication design processes and thinking are investigated, focusing on intelligent data sets and retrieval, image generation techniques, and intelligent solution recommendations. The results show that DCGAN has a lower value of IS = 1.5, FID = 249.39, IS and a higher value of FID, indicating that it generates better quality visual images and greatly improves the efficiency and accuracy of visual communication design. This study can extract effective information and generate visual images more accurately and efficiently, and provide technical support for visual communication designers.

Blood Flow Energy Identifies Coronary Lesions Culprit of Future Myocardial Infarction

The present study establishes a link between blood flow energy transformations in coronary atherosclerotic lesions and clinical outcomes. The predictive capacity for future myocardial infarction (MI) was compared with that of established quantitative coronary angiography (QCA)-derived predictors. Angiography-based computational fluid dynamics (CFD) simulations were performed on 80 human coronary lesions culprit of MI within 5 years and 108 non-culprit lesions for future MI. Blood flow energy transformations were assessed in the converging flow segment of the lesion as ratios of kinetic and rotational energy values (KER and RER, respectively) at the QCA-identified minimum lumen area and proximal lesion sections. The anatomical and functional lesion severity were evaluated with QCA to derive percentage area stenosis (%AS), vessel fractional flow reserve (vFFR), and translesional vFFR (ΔvFFR). Wall shear stress profiles were investigated in terms of topological shear variation index (TSVI). KER and RER predicted MI at 5 years (AUC = 0.73, 95% CI 0.65–0.80, and AUC = 0.76, 95% CI 0.70–0.83, respectively; p < 0.0001 for both). The predictive capacity for future MI of KER and RER was significantly stronger than vFFR (p = 0.0391 and p = 0.0045, respectively). RER predictive capacity was significantly stronger than %AS and ΔvFFR (p = 0.0041 and p = 0.0059, respectively). The predictive capacity for future MI of KER and RER did not differ significantly from TSVI. Blood flow kinetic and rotational energy transformations were significant predictors for MI at 5 years (p < 0.0001). The findings of this study support the hypothesis of a biomechanical contribution to the process of plaque destabilization/rupture leading to MI.

Splicing Measurement and Compensation of Straightness Errors for Ultra-Precision Guideways.

The straightness error of guideways is one of the key indicators of an ultra-precision machine, which plays an important role in the machining accuracy of a workpiece. In order to measure the straightness error of a long-distance ultra-precision guideway accurately, a splicing measurement for the straightness error of a guideway using a high-precision flat mirror and displacement sensor was proposed in this paper, and the data splicing processing algorithm based on coordinate transformation was studied. Then, comparative experiments on a splicing measurement and direct measurement of the straightness error were carried out on a hydrostatic guideway grinder. The maximum difference between the two measurements was 0.3 μm, which was far less than the straightness error of 5.8 μm. The experiment demonstrated the correctness of the proposed splicing measurement method and data processing algorithm. To suppress the influence of the straightness error on machining accuracy, a straightness error compensation algorithm based on error rotation transformation and vertical axis position correction was proposed, and the grinding experiment of a plane optics with a size of 1400 mm × 500 mm was carried out. Without error compensation grinding, the flatness error of the element was 7.54 μm. After error compensation grinding, the flatness error was significantly reduced to 2.98 μm, which was less than the straightness errors of the guideways. These results demonstrated that the straightness error of the grinding machine had been well suppressed.

Convolutional Neural Network-Based Approximation of Coverage Path Planning Results for Parking Lots

Parking lots have wide variety of shapes because of surrounding environment and the objects inside the parking lot, such as trees, manholes, etc. In the case of paving the parking lot, as much area as possible should be covered by the construction vehicle to reduce the need for manual workforce. Thus, the coverage path planning (CPP) problem is formulated. The CPP of the parking lots is a complex problem with constraints regarding various issues, such as dimensions of the construction vehicle and data processing time and resources. A strategy based on convolutional neural networks (CNNs) for the fast estimation of the CPP’s average track length, standard deviation of track lengths, and number of tracks was suggested in this article. Two datasets of different complexity were generated to analyze the suggested approach. The first case represented a simple case with a working polygon constructed out of several rectangles with applied shear and rotation transformations. The second case represented a complex geometry generated out of rectangles and ellipses, narrow construction area, and obstacles. The results were compared with the linear regression models, with the area of the working polygon as an input. For both generated datasets, the strategy to use an approximator to estimate outcomes led to more accurate results compared to the respective linear regression models. The suggested approach enables us to have rough estimates of a large number of geometries in a short period of time and organize the working process, for example, planning construction time and price, choosing the best decomposition of the working polygon, etc.

Some Transformation Properties with Omitted Value

The purpose of this paper is to show that for a holomorphic and univalent function in class S, an omitted –value transformation yields a class of starlike functions as a rotation transformation of the Koebe function, allowing both the image and rotation of the function to be connected. Furthermore, these functions have several properties that are not far from a convexity properties. We also show that Pre- Schwarzian derivative is not invariant since the convexity property of the function is so weak.

A rotation-invariant corner detector based on the median of subpixelized triangle

Corners are stable local image features that have played a crucial role in various computer vision and image processing tasks. Existing corner detectors generally assume that the distance between every two adjacent pixels is a constant during curvature estimation. However, this assumption is actually invalid, and thus those pixel-based measures of discrete curvature developed and exploited in the existing corner detectors may suffer instability under rotation transformations. To address this fundamental problem, a novel curvature measure is proposed in this paper, which exploits the median of a subpixelized triangle located at the current point to estimate its discrete curvature. It is shown that our proposed curvature measure is invariant under rotation transformations. Based on this novel curvature measure, a new corner detector is further developed. Extensive experimental results show that our proposed corner detector can deliver superior performance over the existing state-of-the-art methods.

SF-FWA: A Self-Adaptive Fast Fireworks Algorithm for effective large-scale optimization

Computationally efficient algorithms for large-scale black-box optimization have become increasingly important in recent years due to the growing complexity of engineering and scientific problems. In this paper, a novel algorithm called the Self-adaptive Fast Fireworks Algorithm (SF-FWA) is proposed to effectively conduct large-scale black-box optimization. The main idea is to utilize a set of expressive and computationally efficient search distributions to cope with different function landscapes while tuning the hyperparameters of the search distributions in an online fashion. To achieve this, the Expressive Fast Explosion (EFE) mechanism is designed to achieve effective and efficient sampling, and the Inter-Fireworks Competitive Cooperation (IFCC) mechanism is designed to adapt hyperparameter distributions. This new optimization paradigm equips the population with the ability to automatically adjust to a rich set of function landscapes with linear computational complexity in terms of problem dimensionality. Experimental studies show that SF-FWA can not only exploit the separability of the problem efficiently but can also deal with rotational transformations to the coordinate system. The numerical results on the standard large-scale optimization benchmark suite indicate that SF-FWA outperforms current state-of-the-art large-scale optimization algorithms. The outstanding performance of SF-FWA on optimizing neural network controllers for solving reinforcement learning tasks demonstrates its great potential to be applied to a wider range of real-world problems.

Transformation-Equivariant 3D Object Detection for Autonomous Driving

3D object detection received increasing attention in autonomous driving recently. Objects in 3D scenes are distributed with diverse orientations. Ordinary detectors do not explicitly model the variations of rotation and reflection transformations. Consequently, large networks and extensive data augmentation are required for robust detection. Recent equivariant networks explicitly model the transformation variations by applying shared networks on multiple transformed point clouds, showing great potential in object geometry modeling. However, it is difficult to apply such networks to 3D object detection in autonomous driving due to its large computation cost and slow reasoning speed. In this work, we present TED, an efficient Transformation-Equivariant 3D Detector to overcome the computation cost and speed issues. TED first applies a sparse convolution backbone to extract multi-channel transformation-equivariant voxel features; and then aligns and aggregates these equivariant features into lightweight and compact representations for high-performance 3D object detection. On the highly competitive KITTI 3D car detection leaderboard, TED ranked 1st among all submissions with competitive efficiency. Code is available at https://github.com/hailanyi/TED.

A novel physics-informed neural network for modeling electromagnetism of a permanent magnet synchronous motor

This study presents a novel physics-informed neural network (PINN) architecture designed to address the challenges of replicating an electric motor. The proposed architecture has three key features. First, it uses three partial differential equations with rotational coordinate transformation to supervise the neural network during training with limited data, which improves the accuracy of the solution. One of the differential equations is expressed in variational form to effectively compute the numerical integration. Second, separate networks are proposed for the rotor and stator domains due to their distinct characteristics during operation, namely, that the rotor rotates while the stator remains fixed. An interface loss is included in the entire loss function to compensate for the significant discontinuity and incompatibility between the separate networks when estimating the results of both domains. Third, a learning rate annealing method is introduced to update the adaptive weights of each loss term, thus improving the accuracy and robustness during the training of the neural network. The performance of the proposed PINN was validated using electromagnetic response datasets obtained from both measurements and finite element analyses. Systematic analysis demonstrated that the three features significantly improved the accuracy and robustness of the neural network when estimating the electromagnetic responses of an electric motor. Furthermore, the inference time of the PINN is ten times faster than that of a finite element analysis with a similar level of accuracy, making it suitable for control and design purposes in various real-world applications. Consequently, the versatility of the proposed PINN can accelerate the development of digital twins for intelligent systems by deploying an electric motor, and it could also be used for prognostics and health management because it can estimate electromagnetic responses under both normal and failure conditions.

Normal forms of double Hopf oscillators with radial nonlinearities

We are concerned with the simplest normal forms of non-resonant double Hopf oscillators with radial nonlinearities. Due to the required Lie algebraic structure for preserving the radial structure in the normal form process, we appeal to the Lie algebra of radial and rotational transformation generators. The structure constants of the Lie algebra are presented, where we notice a Lie ideal structure for the rotational vector fields. This gives rise to an effective reduction technique through the use of its corresponding quotient Lie algebra. Yet, computations of kernel spaces of the generalized homological maps seem a formidable project and thus, we employ the multiple Lie brackets method to skip explicit kernel space derivations. The simplest normal forms and orbital normal forms of the nonlinear family are presented. We also address their parametric normal forms as multiple parametric perturbations of the corresponding vector fields. Transformation symmetry groups associated with truncated normal forms are also derived. An efficient algorithm is provided for the normal form computations using computer algebra systems. Finally, we derive state-feedback controllers for a two-arm vibrator using normal forms of radial double Hopf singularity. This is to illustrate how our normal forms can be applied on classical control engineering problems as a new alternative nonlinear controller technique to the existing methods in nonlinear control theory.

Contactless Palm Vein Recognition Based on Attention-Gated Residual U-Net and ECA-ResNet

Palm vein recognition has received some considerable attention regarding its use in biometric identification. Palm vein characteristics offer a superior level of security and reliability in personal identification compared to extrinsic methods such as fingerprint, face, and palm print recognition, as vein patterns are difficult to duplicate and do not change throughout one’s lifetime. This study proposes both segmentation and recognition methods to enhance the authentication performance and achieve correct identification using palm vein features. First, we propose a segmentation model based on the U-Net model, enhanced with an attention gate, to effectively segment palm vein patterns. The incorporation of both the attention gate and residual block allows the segmentation model for the learning of the essential features required for specific segmentation tasks. The Hessian-based Jerman filtering method is used for ground-truth labeling. The segmentation model extracts the palm vein patterns and filters out the irrelevant and noisy pixels for the purpose of recognition. The efficient channel attention residual network is trained to learn discriminative features for personal identification using combined margin-based loss functions for palm vein recognition. The channel attention module enhances the useful information and suppresses irrelevant features in the feature maps, which overcomes the problem of rotation, position translation, and scale transformation, as well as improves the recognition rate. The combined loss function used in this study increases the similarity between the intra-class samples and the diversity between inter-class samples. The proposed recognition model achieved 100% accuracy for palm vein recognition and an equal error rate of 0.018 for palm vein verification.

Algorithms for constructing suboptimal coverings of plane figures with disks in the class of regular lattices

The problem of covering a compact planar set $M$ with a set of congruent disks is considered. It is assumed that the centers of the circles belong to some lattice. The criterion of optimality in one case is the minimum of the number of elements of the covering, and in the other case — the minimum of the Hausdorff deviation of the union of elements of the covering from the set $M$. To solve the problems, transformations of parallel transfer and rotation with the center at the origin can be applied to the lattice. Statements concerning sufficient conditions for sets of circles that provide solutions to the problems are proved. Numerical algorithms based on minimizing the Hausdorff deviation between two flat compacts are proposed. Solutions of a number of examples are given for various figures of $M$.

Heterogeneous scene matching based on the gradient direction distribution field

Heterogeneous scene matching is a key technology in the field of computer vision. The image rotation problem is popular and difficult in the field of heterogeneous scene matching. In this paper, a heterogeneous scene matching method based on the gradient direction distribution field is proposed, and distributed field theory is introduced into heterogeneous scene matching for the first time. First, the distribution field of the gradient direction is constructed and fuzzified, and then the effective regions are selected. Then, the distribution field of the main direction is defined to solve the matching errors due to the existence of rotational transformations between heterogeneous source images. Third, the chi-square distance is introduced as a similarity measure. Finally, the hill-climbing method search strategy, which greatly improves the efficiency of the algorithm, is adopted. Experimental results on 8 pairs of infrared and visible heterogeneous images demonstrate that the proposed method outperforms the other state-of-the-art region-based matching methods in terms of the robustness, accuracy, and real-time performance.

Fast Point Cloud Registration Method with Incorporation of RGB Image Information

Point cloud registration has a wide range of applications in 3D reconstruction, pose estimation, intelligent driving, heritage conservation, and digital cities. The traditional iterative closest point (ICP) algorithm has strong dependence on the initial position, poor robustness, and low timeliness. To address the above issues, a fast point cloud registration method that incorporates RGB image information is proposed. The SIFT algorithm is used to detect feature points of point clouds corresponding to the RGB image, followed by feature point matching. The RANSAC algorithm is applied to remove erroneous point pairs in order to calculate the initial transformation matrix. After applying a pass-through filter for noise reduction and transiting down with a voxel grid, the point cloud is subjected to rotation and translation transformation for initial registration. On the basis of initial alignment, the FR-ICP algorithm is utilized for achieving precise registration. This method not only avoids the problem of ICP easily getting stuck in local optima, but also has higher registration accuracy and efficiency. Experimental studies were conducted based on point clouds of automotive parts collected in real scenes, and the results showed that the proposed method has a registration error of only 0.487 mm. Among the same group of experimental point clouds with comparable registration error, the proposed method showed a speed improvement of 69%/48% compared to ICP/FR-ICP with regard to registration speed.

A COMPREHENSIVE STUDY OF LIMITATIONS ASSOCIATED WITH SIX DEGREES OF FREEDOM SPINE TESTING

Lower back pain (LBP) is a worldwide clinical problem and a prominent area for research. Numerous in vitro biomechanical studies on spine specimens have been undertaken, attempting to understand spinal response to loading and possible factors contributing to LBP. However, despite employing similar testing protocols, there are challenges in replicating in vivo conditions and significant variations in published results. The aim of this study was to use the University of Bath (UoB) spine simulator to perform tests to highlight the major limitations associated with six degree of freedom (DOF) dynamic spine testing.A steel helical spring was used as a validation model and was potted in Wood's metal. Six porcine lumbar spinal motion segments were harvested and dissected to produce isolated spinal disc specimens. These were potted in Wood's metal, ensuring the midplane of the disc remained horizontal and then sprayed with 0.9% saline and wrapped in saline-soaked tissue and plastic wrap to prevent dehydration. A 400N axial preload was used for spinal specimens. Specimens were tested under the stiffness and flexibility protocols.Tests were performed using the UoB custom 6-axis spine simulator with coordinate axes. Tests comprised five cycles with data acquired at 100Hz. Stiffness and flexibility matrices were evaluated from the last three motion cycles using the linear least squares method.According to theory, inverted flexibility matrices should equal stiffness matrices. In the case of the spring, the matrices matched analytical solutions and inverted flexibility matrices were equivalent to stiffness matrices. Matrices from the spinal tests demonstrated some symmetry, with similarities between inverted flexibility- and stiffness matrices, though these were unequal overall. Matrix element values were significantly affected by displacements assumed to occur at disc centre.Spring tests proved that for linear, elastic specimens, the spine simulator functioned as expected. However, multiple factors limit the confidence in spine test results. Centre of rotation, displacement assumptions and rigid body transformations are known to impact the results from spinal testing, and these should be addressed going forward to improve the replication of in vivo conditions.

Modeling Noncommutative Composition of Relations for Knowledge Graph Embedding

Knowledge Graph Embedding (KGE) is a powerful way to express Knowledge Graphs (KGs), which can help machines learn patterns hidden in the KGs. Relation patterns are useful hidden patterns, and they usually assist machines to predict unseen facts. Many existing KGE approaches can model some common relation patterns like symmetry/antisymmetry, inversion, and commutative composition patterns. However, most of them are weak in modeling noncommutative composition patterns. It means these approaches can not distinguish a lot of composite relations like “father’s mother” and “mother’s father”. In this work, we propose a new KGE method called QuatRotatScalE (QRSE) to overcome this weakness, since it utilizes rotation and scaling transformations of quaternions to design the relation embedding. Specifically, we embed the relations and entities into a quaternion vector space under the difference norm KGE framework. Since the multiplication of quaternions does not satisfy the commutative law, QRSE can model noncommutative composition patterns naturally. The experimental results on the synthetic dataset also support that QRSE has this ability. In addition, the experimental results on real-world datasets show that QRSE reaches state-of-the-art in link prediction problem.

Algebra of the spinor invariants and the relativistic hydrogen atom

It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac Hamiltonian is invariant with respect to the rotation transformation, which indicates the dynamical (hidden) symmetry SU(2) of the Dirac equation. The total symmetry of the Dirac equation is the symmetry SO(3)⊗SU(2). The generator of the SO(3) symmetry group is given by the total momentum operator, and the generator of SU(2) group is given by the rotation of the vector-states in the spinor space, determined by the Dirac, Johnson–Lippmann, and the new spinor invariants. It is shown that using algebraic approach to the Dirac problem allows one to calculate the eigenstates and eigenenergies of the relativistic hydrogen atom and reveals the fundamental role of the principal quantum number as an independent number, even though it is represented as the combination of other quantum numbers.

Rotation in vacuum and scalar background: Are there alternatives to Newman–Janis algorithm?

The Newman–Janis (NJ) algorithm is the standard approach to rotation in general relativity which, in vacuum, builds the Kerr metric from the Schwarzschild spacetime. Recently, we have shown that the same algorithm applied to the Papapetrou antiscalar spacetime produces a rotational metric devoid of horizons and ergospheres. Though exact in the scalar sector, this metric, however, satisfies the Einstein equations only asymptotically. We argue that this discrepancy between geometric and matter parts (essential only inside gravitational radius scale) is caused by the violation of the Hawking–Ellis energy conditions for the scalar energy–momentum tensor. The axial potential functions entering the metrics appear to be of the same form both in vacuum and scalar background, and they also coincide with the linearized Yang–Mills field, which might hint at their common nongravitational origin. As an alternative to the Kerr-type spacetimes produced by NJ algorithm we suggest the exact solution obtained by local rotational coordinate transformation from the Schwarzschild spacetime. Then, comparison with the Kerr-type metrics shows that the Lense–Thirring phenomenon might be treated as a coordinate effect, similar to the Coriolis force.

Design and dynamic analysis of a scissors hoop-rib truss deployable antenna mechanism

As the support mechanism of space-borne antennas, space deployable antenna mechanism belongs to complex multi-closed-loop coupling mechanism, configuration design and dynamic analysis are more difficult than general parallel mechanism. In this paper, an unequal-length scissors mechanism (ULSM) is proposed by changing the position of the internal rotational joint through a basic scissors mechanism. A scissors hoop-rib truss deployable antenna mechanism (SHRTDAM) is constructed by replacing the parabolic rib with the ULSM. Kinematic analysis of SHRTDAM is conducted, and the degree of freedom (DOF) of the whole antenna mechanism is analyzed based on screw theory, the result showed that it has only one DOF. Velocity and acceleration characteristics of SHRTDAM are obtained by the screw derivative and rotation transformation. Based on Lagrange equation, dynamic model of this mechanism is established, the torque required to drive the mechanism is simulated and verified by Adams and MATLAB software. In addition, a ground experiment prototype of 1.5-m diameter was fabricated and a deployment test is conducted, which demonstrated the mobility and deployment performance of the whole mechanism. The mechanism proposed in this paper can provide a good reference for the design and analysis of large aperture space deployable antennas.

Reconstruction of 3D Random Media from 2D Images: Generative Adversarial Learning Approach

This paper presents an algorithm for stochastic reconstruction of three-dimensional material microstructure from its single two-dimensional cross-sectional image, based on the neural network operating on a principle of generative adversarial learning. The novelty of the proposed algorithm is in introduction of the reconstruction error, which is invariant to translational and rotational transformations and increases stability of the neural-network training and quality of generated structures. It is shown that a use of variational autoencoder helps to extract useful features from a cross-sectional image and provide additional information to a generator for accurate structure reconstruction. A set of 3D microstructures with corresponding 2D slice from each of them is required for model training. The model was trained and tested on sets of binary microstructures of porous materials with open-cell and closed-cell internal morphology. The obtained results for statistical evaluation of material microstructure demonstrate the effectiveness of the proposed algorithm.