Local Frame Research Articles

The effects of gravitational waves on a hydrogen atom

We investigate the influence of gravitational waves on a freely falling hydrogen atom by analyzing the dynamics of the bound electron described by the Dirac equation in the curved spacetime of a gravitational wave. From this, we derive the corresponding Dirac Hamiltonian in the local inertial frame of the atom, assuming gravitational waves are described by the linearized theory of general relativity. To maintain meaningful physical interpretations while obtaining a non-relativistic description, we employ the Foldy–Wouthuysen transformation. Through the analysis of resulting interaction terms and comparison with flat spacetime counterparts, valuable insights into the effects of gravitational waves (GWs) on the hydrogen atom are gained. Additionally, we explore selection rules governing the coupling between GWs and the atom and utilize first-order perturbation theory to quantify the induced energy shifts and spectral line splitting. This investigation contributes to our understanding of the interplay between quantum systems and gravitational waves, which could lead to alternative method of GWs indirect detection. However, measuring such tiny energy shifts would require a telescope with very high spectral resolution.

Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space

A principal curve on a surface plays a paramount role in reasonable implementations. A curve on a surface is a principal curve if its tangents are principal directions. Using the Serret–Frenet frame, the surface pencil couple can be expressed as linear combinations of the components of the local frames in Galilean 3-space G3. With these parametric representations, a family of surfaces using principal curves (curvature lines) are constructed, and the necessary and sufficient condition for the given Bertrand couple to be the principal curves on these surfaces are derived in our approach. Moreover, the necessary and sufficient condition for the given Bertrand couple to satisfy the principal curves and the geodesic requirements are also analyzed. As implementations of our main consequences, we expound upon some models to confirm the method.

A local POE-based self-calibration method using position and distance constraints for collaborative robots

Collaborative robots are designed to not only work alongside humans but also adapt to new tasks quickly. To improve their absolute accuracy, self-calibration methods utilizing portable measurement devices are cost-effective solutions. Based on the local frame representation of the Product-of-Exponential (POE) formula, a new modular kinematic error model is derived for collaborative robots, in which all geometric errors in a joint-link assembly, i.e., a dyad, are lumped into a local rigid body motion applied to its nominal joint axis. Its major advantage over the conventional local POE-based kinematic error model is that all columns in the error transformation Jacobian matrix are functions of joint displacements, which is critical to formulate singularity-free self-calibration models based on geometric constraints. A portable and cost-effective self-calibration device with both position and distance constraints is proposed for collaborative robots, which can readily collect a wide range of constraint errors by drag teaching within a collaborative robot’s workspace. Additionally, a two-step self-calibration method is established for both the robot arm and its base calibration. Its effectiveness and robustness are validated through simulations and experiments. The experimental results on Aubo i5 show that its average position error is significantly reduced from 4.11mm to 0.36mm after calibration.

Research on Three-Dimensional Shape Curve Reconstruction Technology for a Scraper Conveyor on an Intelligent Working Face.

"Three straight and two flat" is the inevitable demand when realizing the intelligent mining of a fully mechanized mining face. To address the crucial technical issue of lacking accurate perception of the shape of the scraper conveyor during intelligent coal mining, a three-dimensional curvature sensor involving fiber Bragg grating (FBG) is used as a perceptive tool to conduct curve reconstruction research based on different local motion frames and to reconstruct the shape of the scraper conveyor. Firstly, the formation process of the 'S'-shaped bending section of the scraper conveyor during the pushing process is determined. Based on the FBG sensing principle, a mathematical model between the variation in the central wavelength and the strain and curvature is established, and the cubic B-spline interpolation method is employed to continuously process the obtained discrete curvature. Secondly, based on differential geometry, a spatial curve reconstruction algorithm based on the Frenet moving frame is derived, and the shape curve prediction interpolation model is built based on a gated recurrent unit (GRU) model, which reduces the impact of the decrease in curve reconstruction accuracy caused by damage to some grating measuring points. Finally, an experimental platform was designed and built, and sensors with curvature radii of 6 m, 7 m, and 8 m were tested. The experimental results showed that the reconstructed curve was essentially consistent with the actual shape, and the absolute error at the end was about 2 mm. The feasibility of this reconstruction algorithm in engineering has been proven, and this is of great significance in achieving shape curve perception and straightness control for scraper conveyors.

A contact formulation using local frame of SE(3) group for corotational beam against rigid solid via moving signed distance field

In this paper, we present a contact formulation for corotational beam and rigid body based on body-attached signed distance field (SDF). All formulations are based on the unified SE(3) framework, whose prominent advantage lies in its frame invariance property. For solid body, the geometry surface can be implicitly described by a moving SDF. Consequently, the interaction between beams and rigid solids can be viewed as immersion in a field-described force. The contact force is formulated using SDF interpolation, and exact tangent matrices are provided to facilitate implicit iteration. Notably, this approach eliminates the need for contact detection during simulation, because the SDF database is constructed before the simulation. To enhance the spatial adaptivity of the SDF algorithm, we introduce an octree refinement strategy. Besides, we incorporate the concept of contact potential volume into the subdivided stopping criterion. Compared to the uniform SDF, this approach demonstrates higher generation speed and smaller errors. Several examples are used to verify the accuracy, convergence and efficiency of the proposed formulation. It is observed that the invariance property of SE(3) description leads to enhanced computational performance. Both frame invariance and SDF-based approach are expected to improve efficiency for large-scale problems. The presented method is easily applicable to other types of flexible bodies.

Orbit-attitude-structure coupled modelling method in local translational coordinate frame for multibody systems

The absolute coordinate-based (ACB) method, including absolute nodal coordinate formulation and natural coordinate formulation, is a widely-used dynamic modelling method for multibody systems. However, the problem of accuracy loss would arise when multi-scale motions are described in the same global coordinate system, such as large-scale orbital motions, small-scale attitude motions and structural vibrations, and micro-scale contact/collision. To address this problem, an ACB method in local translational coordinate system is proposed such that the large-scale orbital motions can be separated from other smaller-scale motions. The dynamic equations are derived by the Hamilton's equations and the Kronecker product. The validity of the proposed method is studied using an orbit-attitude coupled model of an orbiting rigid plate. It is found that the attitude errors of the original ACB method increase as time step size decreases. The reason for this counterintuitive phenomenon is that more serious accuracy loss is encountered for smaller time step size. In addition, more iterations are required for the original ACB method to obtain the prescribed tolerable error in each time step due to accuracy loss. In comparison, the proposed method is more accurate and efficient in numerical simulations. Finally, the proposed method is applied to the orbit-attitude-structure coupled simulation of a space robotic system.

Balancing Rotation Minimizing Frames with Additional Objectives

AbstractWhen moving along 3D curves, one may require local coordinate frames for visited points, such as for animating virtual cameras, controlling robotic motion, or constructing sweep surfaces. Often, consecutive coordinate frames should be similar, avoiding sharp twists. Previous work achieved this goal by using various methods to approximate rotation minimizing frames (RMFs) with respect to a curve's tangent. In this work, we use Householder transformations to construct preliminary tangent‐aligned coordinate frames and then optimize these initial frames under the constraint that they remain tangent‐aligned. This optimization minimizes the weighted sum of squared distances between selected vectors within the new frames and fixed vectors outside them (such as the axes of previous frames). By selecting different vectors for this objective function, we reproduce existing RMF approximation methods and modify them to consider additional objectives beyond rotation minimization. We also provide some example computer graphics use cases for this new frame tracking.

Novel 3D local feature descriptor of point clouds based on spatial voxel homogenization for feature matching

Obtaining a 3D feature description with high descriptiveness and robustness under complicated nuisances is a significant and challenging task in 3D feature matching. This paper proposes a novel feature description consisting of a stable local reference frame (LRF) and a feature descriptor based on local spatial voxels. First, an improved LRF was designed by incorporating distance weights into Z- and X-axis calculations. Subsequently, based on the LRF and voxel segmentation, a feature descriptor based on voxel homogenization was proposed. Moreover, uniform segmentation of cube voxels was performed, considering the eigenvalues of each voxel and its neighboring voxels, thereby enhancing the stability of the description. The performance of the descriptor was strictly tested and evaluated on three public datasets, which exhibited high descriptiveness, robustness, and superior performance compared with other current methods. Furthermore, the descriptor was applied to a 3D registration trial, and the results demonstrated the reliability of our approach.

Analysis of the effect of the translational-rotational coupling on the pseudo-diffusion along the molecular axes of meta-cresol: A molecular dynamics analysis

We investigate the dynamical properties (translation and rotation) of the glass-forming liquid meta-cresol by molecular dynamics simulations. This system is investigated at 9 temperatures between 230 K and 400 K, encompassing the liquid and glassy states of meta-cresol. In order to get insight into the coupling between the translational and rotational motions, the centre of mass velocity autocorrelation function is calculated along the principal axes of meta-cresol. We show that the time behaviour of the velocity and angular velocity is connected to the change in the local structure occurring upon the glass transition. Indeed, the long-time negative region in the velocity autocorrelations is associated with a caging effect while the occurrence of a short time negative region in these functions is considered as a signature of hydrogen bonding interactions. By studying, the centre of mass velocity of meta-cresol in the molecular frame, the translation and rotation coupling was directly evidenced. The time evolution of the translational-rotational coupling is evaluated from the difference ΔαRTC(t) between the velocity autocorrelation function calculated with respect to the molecular frame (where α stands for the three axes of the local cartesian frame fixed to the individual molecule, x, y, and z) of the meta-cresol molecule and that of the same function calculated in the frame of the hypothesis that there is no statistical correlation between the translational and rotational motions. The positive regions of ΔαRTC(t) indicate an occurrence of a cooperative effect, which means that the each of the two motions is realized in the favour of the other. Conversely, negative regions indicate that the rotation and translation motions are anti-cooperative. Our results show that a strong coupling between translation and rotation occurs along the × axis that is perpendicular to the ring of meta-cresol molecule, and also along which the hydrogen bond is established.

The Method of Moving Frames for Surface Global Parametrization

This article introduces a new representation of surface global parametrization based on Cartan’s method of moving frames . We show that a system of structure equations , characterizing the local coordinates changes with respect to a local frame system, completely characterizes the set of possible cone parametrizations. The discretization of this system provably provides necessary and sufficient conditions for the existence of a valid mapping. We are able to derive a versatile algorithm for surface parametrization, allowing feature constraints and singularities. As the first structure equation is independent of the global coordinate system, we do not require prior knowledge of cuts or cone positions. So, a single non-linear least-square problem is enough to place quantized cones while minimizing a given distortion energy. We are therefore able to take full advantage of the link between the parametrization geometry and the topology of its cone metric to solve challenging constrained parametrization problems.

A Spatio-Temporal Spotting Network with Sliding Windows for Micro-Expression Detection

Micro-expressions reveal underlying emotions and are widely applied in political psychology, lie detection, law enforcement and medical care. Micro-expression spotting aims to detect the temporal locations of facial expressions from video sequences and is a crucial task in micro-expression recognition. In this study, the problem of micro-expression spotting is formulated as micro-expression classification per frame. We propose an effective spotting model with sliding windows called the spatio-temporal spotting network. The method involves a sliding window detection mechanism, combines the spatial features from the local key frames and the global temporal features and performs micro-expression spotting. The experiments are conducted on the CAS(ME)2 database and the SAMM Long Videos database, and the results demonstrate that the proposed method outperforms the state-of-the-art method by 30.58% for the CAS(ME)2 and 23.98% for the SAMM Long Videos according to overall F-scores.

Integrating end-to-end learning with deep geometrical potentials for ab initio RNA structure prediction

RNAs are fundamental in living cells and perform critical functions determined by their tertiary architectures. However, accurate modeling of 3D RNA structure remains a challenging problem. We present a novel method, DRfold, to predict RNA tertiary structures by simultaneous learning of local frame rotations and geometric restraints from experimentally solved RNA structures, where the learned knowledge is converted into a hybrid energy potential to guide RNA structure assembly. The method significantly outperforms previous approaches by >73.3% in TM-score on a sequence-nonredundant dataset containing recently released structures. Detailed analyses showed that the major contribution to the improvements arise from the deep end-to-end learning supervised with the atom coordinates and the composite energy function integrating complementary information from geometry restraints and end-to-end learning models. The open-source DRfold program with fast training protocol allows large-scale application of high-resolution RNA structure modeling and can be further improved with future expansion of RNA structure databases.

Corotational Finite Element Dynamic Analysis of Space Frames with Geometrically Nonlinear Behavior Based on Tait–Bryan Angles

The aim of this study is to compose a corotational finite element formulation for space frames with geometrically nonlinear behavior under dynamic loads. Using a moving frame through three successive rotations similar to Euler angles is one of the oldest techniques; however, there are still some gaps that require attention, mainly due to singularity. Hence, alternative techniques had been developed, sometimes elusive and computationally expensive. In this paper, we went back to the old technique and filled the gaps. Three-coordinate systems are used, i.e., the fixed global coordinate system, the fixed local coordinate system that is attached individually to every element, and the corotational local frame for each element that moves and rotates with the element. The deformation is always small relative to the corotational frame. The successive rotations between different coordinate systems are expressed using Tait–Bryan angles. Lagrange’s equation is used to derive the equation of motion, and the stiffness and mass matrices are obtained using the Euler–Bernoulli beam model. A MATLAB code is developed based on the Newton–Raphson method and the Newmark direct integration implicit method. In traditional techniques, singularity is attained when any rotation angle in the fixed local frame approaches π / 2 , and if any is greater than π / 2 , the techniques could fail to specify the location of the element. In this paper, each case is treated with a proper procedure, and special handling of trigonometric formulations prevents singularity and correctly specifies the location of elements in all situations. Different examples of beams and frames are analysed. While the method is not intricate, it is timesaving, is highly effective, provides more stable and robust analysis, and gives sufficiently accurate results. Compared to the parametrization of the finite rotations technique, the method has a significant reduction in the convergence rate because it avoids the storage of joint orientation matrices.

A weighted local‐spherical grid based lightweight descriptor for 3D point cloud registration

AbstractEstablishing effective feature descriptors is a crucial step in 3D point cloud registration task. Existing manual‐based methods are noise‐susceptible and time‐consuming when running on low‐cost edge computing devices. To this end, the authors proposed a Local Reference Frame (LRF) based approach that can quickly and robustly register point clouds by using a novel lightweight local‐spherical grid weighted descriptor (LSGWD). Firstly, the LRF of the proposed algorithm is established by the covariance matrix eigenvector of KeyPoint's spherical support set and the centroid vector's projection on its orthogonal plane. Then the spherical support is grided to 32 bins, and the 4D geometric features of each subset are constructed by the centroid moment and the cosine value of the angles between the centroid vector and axes of LRF. Secondly, to restrain the insufficient discriminative information presented in the purely geometric features, the Gaussian projection and gradient mapping are proposed to calculate the smooth density and the correlation of structural characteristics, which are obtained as the distribution information of each bin to weigh the feature representation. Finally, the 32 × 4‐dimensional KeyPoint descriptor is obtained and used in the 3D point cloud registration framework. Experiments are carried out on three test datasets and real scene data. Compared to previous baselines, our descriptor achieves the state‐of‐the‐art performance in terms of efficiency and accuracy owing to its compact structure and noise robustness. The proposed method enhances the recognition and registration performance of 3D point cloud matching in low‐cost edge computing applications.

A Framework for Optimal Navigation in Situations of Localization Uncertainty.

The basic functions of an autonomous vehicle typically involve navigating from one point to another in the world by following a reference path and analyzing the traversability along this path to avoid potential obstacles. What happens when the vehicle is subject to uncertainties in its localization? All its capabilities, whether path following or obstacle avoidance, are affected by this uncertainty, and stopping the vehicle becomes the safest solution. In this work, we propose a framework that optimally combines path following and obstacle avoidance while keeping these two objectives independent, ensuring that the limitations of one do not affect the other. Absolute localization uncertainty only has an impact on path following, and in no way affects obstacle avoidance, which is performed in the robot's local reference frame. Therefore, it is possible to navigate with or without prior information, without being affected by position uncertainty during obstacle avoidance maneuvers. We conducted tests on an EZ10 shuttle in the PAVIN experimental platform to validate our approach. These experimental results show that our approach achieves satisfactory performance, making it a promising solution for collision-free navigation applications for mobile robots even when localization is not accurate.

Transformer-Guided Video Inpainting Algorithm Based on Local Spatial-Temporal joint

INTRODUCTION: Video inpainting is a very important task in computer vision, and it’s a key component of various practical applications. It also plays an important role in video occlusion removal, traffic monitoring and old movie restoration technology. Video inpainting is to obtain reasonable content from the video sequence to fill the missing region, and maintain time continuity and spatial consistency.OBJECTIVES: In previous studies, due to the complexity of the scene of video inpainting, there are often cases of fast motion of objects in the video or motion of background objects, which will lead to optical flow failure. So the current video inpainting algorithm hasn’t met the requirements of practical applications. In order to avoid the problem of optical flow failure, this paper proposes a transformer-guided video inpainting model based on local Spatial-temporal joint.METHODS: First, considering the rich Spatial-temporal relationship between local flows, a Local Spatial-Temporal Joint Network (LSTN) including encoder, decoder and transformer module is designed to roughly inpaint the local corrupted frames, and the Deep Flow Network is used to calculate the local bidirectional corrupted flows. Then, the local corrupted optical flow map is input into the Local Flow Completion Network (LFCN) with pseudo 3D convolution and attention mechanism to obtain a complete set of bidirectional local optical flow maps. Finally, the roughly inpainted local frame and the complete bidirectional local optical flow map are sent to the Spatial-temporal transformer and the inpainted video frame is output.RESULTS: Experiments show that the algorithm achieves high quality results in the video target removal task, and has a certain improvement in indicators compared with advanced technologies.CONCLUSION: Transformer-Guided Video Inpainting Algorithm Based on Local Spatial-Temporal joint can obtain high-quality optical flow information and inpainted result video.

LGBQ+ in Ghana

This article offers an original analysis of the sociocultural and political situation of same-sex (LGB) and queer (Q) people in Ghana, especially in the context of political repression. There is a lack of literature on Ghana’s LGBQ politics in various edited collections on African sexualities, so this article fills the gap from anthropological and sociological perspectives, emphasising the cultural-sociolinguistic nuances of gender and sex as well as the politics of same-sex and the contradictions in them. Drawing on personal biographies and media reports of power dynamics in local and (post)colonial frames of reference to LGBQ rights, I argue that regardless of the cultural and moral antics in local politics that bedevil the LGBQ community, LGBQ rights cannot achieve any enduring success if discourse continues to be spearheaded by the West since the devil is in the details. Therefore, the need to reconsider the role of the West in local discourse about LGBQ rights and to promote narratives that highlight indigenous cultural and character strengths (e.g., neighbourliness, love, work ethic, hard work, philanthropy, and honesty) in celebrating diversity and individual expression has never been more imperative. This could be a critical mass to revolutionise Ghanaian queerness and related West African homophobic and xenophobic behaviour. At the same time, the queer and LGB communities should be sensitive to the cultural milieu in which they operate and rethink ways of organising because culture and the moral community can be agentic depending upon knowledge pathways and continued resistance may lead to backlash.

Poisson Manifold Reconstruction — Beyond Co‐dimension One

AbstractScreened Poisson Surface Reconstruction creates 2D surfaces from sets of oriented points in 3D (and can be extended to co‐dimension one surfaces in arbitrary dimensions). In this work we generalize the technique to manifolds of co‐dimension larger than one. The reconstruction problem consists of finding a vector‐valued function whose zero set approximates the input points. We argue that the right extension of screened Poisson Surface Reconstruction is based on exterior products: the orientation of the point samples is encoded as the exterior product of the local normal frame. The goal is to find a set of scalar functions such that the exterior product of their gradients matches the exterior products prescribed by the input points. We show that this setup reduces to the standard formulation for co‐dimension 1, and leads to more challenging multi‐quadratic optimization problems in higher co‐dimension. We explicitly treat the case of co‐dimension 2, i.e., curves in 3D and 2D surfaces in 4D. We show that the resulting bi‐quadratic problem can be relaxed to a set of quadratic problems in two variables and that the solution can be made effective and efficient by leveraging a hierarchical approach.

Zero‐shot temporal event localisation: Label‐free, training‐free, domain‐free

AbstractTemporal event localisation (TEL) has recently attracted increasing attention due to the rapid development of video platforms. Existing methods are based on either fully/weakly supervised or unsupervised learning, and thus they rely on expensive data annotation and time‐consuming training. Moreover, these models, which are trained on specific domain data, limit the model generalisation to data distribution shifts. To cope with these difficulties, the authors propose a zero‐shot TEL method that can operate without training data or annotations. Leveraging large‐scale vision and language pre‐trained models, for example, CLIP, we solve the two key problems: (1) how to find the relevant region where the event is likely to occur; (2) how to determine event duration after we find the relevant region. Query guided optimisation for local frame relevance relying on the query‐to‐frame relationship is proposed to find the most relevant frame region where the event is most likely to occur. Proposal generation method relying on the frame‐to‐frame relationship is proposed to determine the event duration. The authors also propose a greedy event sampling strategy to predict multiple durations with high reliability for the given event. The authors’ methodology is unique, offering a label‐free, training‐free, and domain‐free approach. It enables the application of TEL purely at the testing stage. The practical results show it achieves competitive performance on the standard Charades‐STA and ActivityCaptions datasets.

Invariant Extended Kalman Filtering for Tightly Coupled LiDAR-Inertial Odometry and Mapping

In this article, we extend the invariant extended Kalman filter (EKF) to light detection and ranging (LiDAR)-inertial odometry and mapping systems using invariant observer design and the theory of Lie groups for directly fusing LiDAR and inertial measurement unit (IMU) measurements. We consider this from two different aspects and implement two independent systems. Specifically, we propose a robo-centric invariant EKF LiDAR-inertial odometry termed Inv-LIO1. Its mapping module is an ordinary used one and two modules run in separate threads. A world-centric invariant EKF LiDAR-inertial odometry termed Inv-LIO2 is designed and implemented, which has an integrated odometry and mapping architecture. In Inv-LIO1, the output of the filter is the pose estimated by the scan-to-scan match method, which serves as the initial estimate of the mapping module that refines the odometry and constructs a 3-D map. The robo-centric formulation represents that the state in a local frame shifted at every LiDAR time to prevent filter divergence. Inv-LIO2 directly fuses LiDAR feature points and IMU data to obtain the map-refined odometry by scan-to-map match method, followed by global map update. To validate the effectiveness and robustness of the proposed method, we conduct extensive experiments in various indoor and outdoor environments. Overall, Inv-LIO1 offers pure odometry with higher accuracy than other state-of-the-art systems, improving the overall performance. Inv-LIO2 achieves superior accuracy over other state-of-the-art systems in the map-refined odometry comparison.