Curvature Information Research Articles

Multi-Beam Surveying Ocean Exploration Model and Applications

With the development of artificial intelligence, fiber Bragg grating (FBG) sensing technology has garnered increasing attention. This paper first proposes a surface reconstruction algorithm based on curvature information, which is applicable to two different sensor structures: implanted FBG sensors and whisker array sensors. The design and analysis of these sensors are based on a pure bending model, where the corresponding bending curvature is obtained by measuring the wavelength shift of the fiber Bragg grating at the measurement points. Next, the paper elaborates on the surface reconstruction algorithm for the implanted FBG sensor. This sensor contains FBG sensing points that are evenly distributed. Curvature information corresponding to the position can be obtained based on the direction and magnitude of the wavelength shift. The fiber bending is considered as a connection of multiple arc segments, and the coordinates of the sensing points are calculated in the Cartesian coordinate system using the properties of the tangents. The fiber bending curve is then reconstructed by connecting the arc segments in MATLAB. Finally, the paper provides a detailed introduction to the surface reconstruction algorithm for the whisker array sensor. When the whiskers bend, the FBGs fixed on them act as curvature sensors. The curvature is determined by the FBG wavelength shift, and the three-dimensional coordinates of the whisker tip relative to the base are calculated based on a geometric model. MATLAB is then used to connect the whisker tip coordinates, completing the construction of the surface.

SORM‐Enhanced Inverse Reliability Analysis for Geotechnical Multiobjective Reliability‐Based Design Optimization

ABSTRACTThe first‐order reliability method (FORM) is mostly employed in the existing geotechnical reliability‐based design (RBD) methods due to its computational simplicity and efficiency. However, the first‐order Taylor approximation of the limit state surface (LSS) may result in significant errors, especially in cases of highly nonlinear LSS characterized by substantial curvatures. Therefore, FORM‐based RBD methods require a modification of the curvatures to enhance the accuracy of the probabilistic constraints, specifically by converting the target reliability index into a more precise target failure probability. Correspondingly, reliability index‐based design is converted into failure probability‐based design. In this study, the parabolic second‐order reliability method (SORM), which avoids the Hessian calculations, is adopted to improve the accuracy of probabilistic constraints beyond what is achievable with FORM. The proposed SORM‐enhanced RBD method accounts for the curvature information of the nonlinear LSS, modifying the target reliability index to align with the exact target failure probability through the application of SORM. Moreover, by incorporating an implicit coupling function, multiobjective RBD can be effectively implemented without any additional surrogate model. Furthermore, the proposed RBD method is readily extended to reliability‐based design optimization (RBDO) through integration with an optimization strategy. The proposed RBDO method demonstrates a more precise convergence of the probabilistic constraints, surpassing the accuracy of FORM‐based RBDO methods. Notably, the proposed SORM‐enhanced RBDO method not only significantly improves accuracy but also bypasses the necessity for Hessian computation, which remains both the second‐order accuracy and first‐order efficiency. The feasibility of the proposed method is demonstrated through a mathematical example and three practical geotechnical design examples.

How the zebra got its stripes: Curvature-dependent diffusion orients Turing patterns on three-dimensional surfaces.

Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate animal-like patterns for many species. When diffusion of the inhibitor is high enough relative to the activator, a diffusion-driven instability can spontaneously form patterns. However, it is not just the type of pattern but also the orientation that matters, and it remains unclear how patterns are oriented in practice. Here, we propose a mechanism by which the curvature of the surface influences the rate of diffusion, and can recapture the correct orientation of stripes on models of a zebra and of a cat in numerical simulations. Previous work has shown how anisotropic diffusion can give stripe forming reaction-diffusion systems a bias in orientation. From the observation that zebra stripes run around the direction of highest curvature, that is around the torso and legs, we apply this result by modifying the anisotropic diffusion rates based on the local curvature. These results show how local geometry can influence the reaction dynamics to give robust, global-scale patterns. Overall, this model proposes a coupling between the system geometry and reaction-diffusion dynamics that can give global control over the patterning by using only local curvature information. Such a model can give shape and positioning information in animal development without the need for spatially dependent morphogen gradients.

Shape-position perceptive fusion electronic skin with autonomous learning for gesture interaction

Wearable devices, such as data gloves and electronic skins, can perceive human instructions, behaviors and even emotions by tracking a hand's motion, with the help of knowledge learning. The shape or position single-mode sensor in such devices often lacks comprehensive information to perceive interactive gestures. Meanwhile, the limited computing power of wearable applications restricts the multimode fusion of different sensing data and the deployment of deep learning networks. We propose a perceptive fusion electronic skin (PFES) with a bioinspired hierarchical structure that utilizes the magnetization state of a magnetostrictive alloy film to be sensitive to external strain or magnetic field. Installed at the joints of a hand, the PFES realizes perception of curvature (joint shape) and magnetism (joint position) information by mapping corresponding signals to the two-directional continuous distribution such that the two edges represent the contributions of curvature radius and magnetic field, respectively. By autonomously selecting knowledge closer to the user's hand movement characteristics, the reinforced knowledge distillation method is developed to learn and compress a teacher model for rapid deployment on wearable devices. The PFES integrating the autonomous learning algorithm can fuse curvature-magnetism dual information, ultimately achieving human machine interaction with gesture recognition and haptic feedback for cross-space perception and manipulation.

Automatic 3D reconstruction of vertebrae from orthogonal bi-planar radiographs

When conducting spine-related diagnosis and surgery, the three-dimensional (3D) upright posture of the spine under natural weight bearing is of significant clinical value for physicians to analyze the force on the spine. However, existing medical imaging technologies cannot meet current requirements of medical service. On the one hand, the mainstream 3D volumetric imaging modalities (e.g. CT and MRI) require patients to lie down during the imaging process. On the other hand, the imaging modalities conducted in an upright posture (e.g. radiograph) can only realize 2D projections, which lose the valid information of spinal anatomy and curvature. Developments of deep learning-based 3D reconstruction methods bring potential to overcome the limitations of the existing medical imaging technologies. To deal with the limitations of current medical imaging technologies as is described above, in this paper, we propose a novel deep learning framework, ReVerteR, which can realize automatic 3D Reconstruction of Vertebrae from orthogonal bi-planar Radiographs. With the utilization of self-attention mechanism and specially designed loss function combining Dice, Hausdorff, Focal, and MSE, ReVerteR can alleviate the sample-imbalance problem during the reconstruction process and realize the fusion of the centroid annotation and the focused vertebra. Furthermore, aiming at automatic and customized 3D spinal reconstruction in real-world scenarios, we extend ReVerteR to a clinical deployment-oriented framework, and develop an interactive interface with all functions in the framework integrated so as to enhance human–computer interaction during clinical decision-making. Extensive experiments and visualization conducted on our constructed datasets based on two benchmark datasets of spinal CT, VerSe 2019 and VerSe 2020, demonstrate the effectiveness of our proposed ReVerteR. In this paper, we propose an automatic 3D reconstruction method of vertebrae based on orthogonal bi-planar radiographs. With the 3D upright posture of the spine under natural weight bearing effectively constructed, our proposed method is expected to better support doctors make clinical decision during spine-related diagnosis and surgery.

An improved approximate integral method for nonlinear reliability analysis

In order to evaluate the failure probability corresponding to the Limit State Function (LSF) in structural reliability, the First Order Reliability Method (FORM) linearizes the LSF and directly calculates the failure probability based on the Most Probable Point (MPP). But this method is unable to effectively handle nonlinear problems. The Second Order Reliability Method (SORM), on the other hand, utilizes the Hessian matrix to obtain curvature information at the MPP and computes the failure probability with Breitung's second-order approximation formula. However, SORM is unable to maintain satisfactory computational accuracy in highly nonlinear problems due to its lack of detailed analysis on the shape of the limit state surface. To address this issue, this paper proposes an Improved Approximation Integration Method (IAIM). The initial approximation of the limit state surface is based on the intersection region between the hypersphere and the n-dimensional paraboloid. Subsequently, a statistical analysis of the deviation between the aforementioned region and its projected area is conducted to construct a corresponding fitting function, which is then utilized for dimensionality reduction in the multidimensional integration of the approximation area. Finally, several examples are presented to demonstrate the accuracy and feasibility of the proposed IAIM.

Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization

Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise. We propose a Bayesian approach to obtain a Hessian matrix approximation for stochastic optimization that minimizes the secant equations residue while retaining the extreme eigenvalues between a specified range. Thus, the proposed approach assists stochastic gradient descent to converge to local minima without augmenting gradient noise. We propose maximizing the log posterior using the Newton-CG method. Numerical results on a stochastic quadratic function and an ℓ 2 -regularized logistic regression problem are presented. In all the cases tested, our approach improves the convergence of stochastic gradient descent, compensating for the overhead of solving the log posterior maximization. In particular, pre-conditioning the stochastic gradient with the inverse of our Hessian approximation becomes more advantageous the larger the condition number of the problem is.

Structural deformation and clamping force monitoring of reconfigurable tooling motivated by strain data in aircraft assembly

The quality of aircraft assembly is mainly guaranteed by toolings which are vital to the geometrical accuracy and service performance of aviation products. In this research, a real-time monitoring system that determines the structural deformation and clamping force of reconfigurable toolings using strain data is developed to perceive the service state of the toolings. By laying fiber Bragg gratings on positioning beam and baseplate of the reconfigurable tooling, strain data of the tooling structures are gauged and transferred to curvatures. The beam and baseplate are modeled as one and two-dimensional objects respectively and shape reconstruction algorithms are established to obtain their deflection curve and surface using curvature information. Distribution of fibers is optimized to minimize the conversion error from strain to curvature. An estimation that reveals the mathematical relationship between the shape reconstruction error and measurement interval is implemented, and a mapping model from strains to clamping force of the beam is established. These algorithms are integrated into the self-developed monitoring software and undergo simulating and experimental tests. The maximum relative errors of deformation and force are 4.53% and 4.12% respectively in simulation, and 9.21% and 7.29% individually in experiment, which validates the efficiencies of the method. Tests of the monitoring system suggest that it can provide a timely and accurate sensing of the deformation and force of the tooling.

Fast and Highly Accurate Zonal Wavefront Reconstruction from Multi-Directional Slope and Curvature Information Using Subregion Cancelation

The wavefront reconstruction is a crucial step in determining the performance of wavefront detection instruments. The wavefront reconstruction algorithm is primarily evaluated in three dimensions: accuracy, speed, and noise immunity. In this paper, we propose a hybrid zonal reconstruction algorithm that introduces slope and curvature information in the diagonal, anti-diagonal, horizontal, and vertical directions by dividing the neighbor sampling points into subregions in groups of four. By canceling the same parameters in integration equations, an algorithm using multi-directional slope–curvature information is achieved with only two sets of integration equations in each subregion, reducing the processing time. Simulation experiments show that the relative root-mean-square reconstruction error of this algorithm is improved by about 4 orders of magnitude compared with existing algorithms that use multi-directional slope information or slope–curvature information alone. Compared with the hybrid multi-directional slope–curvature algorithm, the proposed algorithm can reduce computation time by about 50% as well as provide better noise immunity and reconstruction accuracy. Finally, the validity of the proposed algorithm is verified by the null test experiment.

Interior point algorithm for second-order cone optimization based on a new kernel function

Second-order cone optimization (SOCO) problems are crucial in various fields such as engineering, finance, and machine learning due to their ability to model complex convex optimization tasks efficiently. In this article, we propose an interior point algorithm tailored for SOCO, leveraging a novel kernel function to enhance optimization performance. Traditional interior point methods for SOCO often encounter challenges in scalability and efficiency, particularly with large-scale problems. These methods typically rely on barrier functions that may suffer from slow convergence rates, especially when dealing with highly ill-conditioned or degenerate cones. To address these limitations, our approach introduces a new kernel function that exploits the geometric properties of second-order cones, thereby improving convergence behavior and computational efficiency. The key innovation of our algorithm lies in the construction of the kernel function, which incorporates insights from the structure of second-order cones to efficiently capture the curvature information of the optimization problem. By exploiting this curvature information, our algorithm can effectively navigate the optimization landscape, leading to faster convergence and enhanced robustness compared to traditional methods. Furthermore, our algorithm is equipped with advanced techniques for handling various challenges encountered in SOCO, such as dealing with degenerate cones and exploiting problem structure to accelerate convergence. Additionally, we incorporate strategies for warm-starting and adaptive step-size selection to further improve efficiency, particularly in iterative optimization processes. Finally, our proposed interior point algorithm for second-order cone optimization, based on a new kernel function, derives the iteration bounds O (Nlog (N/∊)) for large update methods. Here denotes N the number of second-order cones in the problem formulation and ∊ the desired accuracy. These iteration bounds are currently the best known bounds for such methods.

An Adaptive Learning Rate Deep Learning Optimizer Using Long and Short-Term Gradients Based on G–L Fractional-Order Derivative

AbstractDeep learning model is a multi-layered network structure, and the network parameters that evaluate the final performance of the model must be trained by a deep learning optimizer. In comparison to the mainstream optimizers that utilize integer-order derivatives reflecting only local information, fractional-order derivatives optimizers, which can capture global information, are gradually gaining attention. However, relying solely on the long-term estimated gradients computed from fractional-order derivatives while disregarding the influence of recent gradients on the optimization process can sometimes lead to issues such as local optima and slower optimization speeds. In this paper, we design an adaptive learning rate optimizer called AdaGL based on the Grünwald–Letnikov (G–L) fractional-order derivative. It changes the direction and step size of parameter updating dynamically according to the long-term and short-term gradients information, addressing the problem of falling into local minima or saddle points. To be specific, by utilizing the global memory of fractional-order calculus, we replace the gradient of parameter update with G–L fractional-order approximated gradient, making better use of the long-term curvature information in the past. Furthermore, considering that the recent gradient information often impacts the optimization phase significantly, we propose a step size control coefficient to adjust the learning rate in real-time. To compare the performance of the proposed AdaGL with the current advanced optimizers, we conduct several different deep learning tasks, including image classification on CNNs, node classification and graph classification on GNNs, image generation on GANs, and language modeling on LSTM. Extensive experimental results demonstrate that AdaGL achieves stable and fast convergence, excellent accuracy, and good generalization performance.

A Finger Vein Recognition Algorithm Based on the Histogram of Variable Curvature Directional Binary Statistics

Structural features are capable of effectively capturing the overall texture variations in images. However, in locally prominent areas with visible veins, other characteristics such as directionality, convexity–concavity, and curvature also play a crucial role in recognition, and their impact cannot be overlooked. This paper introduces a novel approach, the histogram of variable curvature directional binary statistical (HVCDBS), which combines the structural and directional features of images. The proposed method is designed for extracting discriminative multifeature information in vein recognition. First, a multidirection and multicurvature Gabor filter is introduced for convolution with vein images, yielding directional and convexity–concavity information at each pixel, along with curvature information for the corresponding curve. Simultaneously incorporating the original image feature information, these four aspects of information are fused and encoded to construct a variable curvature binary pattern (VCBP) with multifeatures. Second, the feature map containing multifeature information is blockwise processed to build variable curvature binary statistical features. Finally, competitive Gabor directional binary statistical features are combined, and a matching score‐level fusion scheme is employed based on maximizing the interclass distance and minimizing the intraclass distance to determine the optimal weights. This process fuses the two feature maps into a one‐dimensional feature vector, achieving an effective representation of vein images. Extensive experiments were conducted on four widely utilized vein databases, and the results indicate that the proposed algorithm, compared with solely extraction of structural features, achieved higher recognition rates and lower equal error rates.

New CG-Based Algorithms With Second-Order Curvature Information for NLS Problems and a 4DOF Arm Robot Model

New CG-Based Algorithms With Second-Order Curvature Information for NLS Problems and a 4DOF Arm Robot Model

SOLID: a novel similarity metric for mono-modal and multi-modal deformable image registration

Medical image registration is an integral part of various clinical applications including image guidance, motion tracking, therapy assessment and diagnosis. We present a robust approach for mono-modal and multi-modal medical image registration. To this end, we propose the novel shape operator based local image distance (SOLID) which estimates the similarity of images by comparing their second-order curvature information. Our similarity metric is rigorously tailored to be suitable for comparing images from different medical imaging modalities or image contrasts. A critical element of our method is the extraction of local features using higher-order shape information, enabling the accurate identification and registration of smaller structures. In order to assess the efficacy of the proposed similarity metric, we have implemented a variational image registration algorithm that relies on the principle of matching the curvature information of the given images. The performance of the proposed algorithm has been evaluated against various alternative state-of-the-art variational registration algorithms. Our experiments involve mono-modal as well as multi-modal and cross-contrast co-registration tasks in a broad variety of anatomical regions. Compared to the evaluated alternative registration methods, the results indicate a very favorable accuracy, precision and robustness of the proposed SOLID method in various highly challenging registration tasks.

An Adaptive Low Computational Cost Alternating Direction Method of Multiplier for RELM Large-Scale Distributed Optimization

In a class of large-scale distributed optimization, the calculation of RELM based on the Moore–Penrose inverse matrix is prohibitively expensive, which hinders the formulation of a computationally efficient optimization model. Attempting to improve the model’s convergence performance, this paper proposes a low computing cost Alternating Direction Method of Multipliers (ADMM), where the original update in ADMM is solved inexactly with approximate curvature information. Based on quasi-Newton techniques, the ADMM approach allows us to solve convex optimization with reasonable accuracy and computational effort. By introducing this algorithm into the RELM model, the model fitting problem can be decomposed into a set of subproblems that can be executed in parallel to achieve efficient classification performance. To avoid the storage of expensive Hessian for large problems, BFGS with limited memory is proposed with computational efficiency. And the optimal parameter values of the step-size search method are obtained through Wolfe line search strategy. To demonstrate the superiority of our methods, numerical experiments are conducted on eight real-world datasets. Results on problems arising in machine learning suggest that the proposed method is competitive with other similar methods, both in terms of better computational efficiency as well as accuracy.

Curvature Consistent Network for Microscope Chip Image Super-Resolution.

Detecting hardware Trojan (HT) from a microscope chip image (MCI) is crucial for many applications, such as financial infrastructure and transport security. It takes an inordinate cost in scanning high-resolution (HR) microscope images for HT detection. It is useful when the chip image is in low-resolution (LR), which can be acquired faster and at a lower cost than its HR counterpart. However, the lost details and noises due to the electric charge effect in LR MCIs will affect the detection performance, making the problem more challenging. In this article, we address this issue by first discussing why recovering curvature information matters for HT detection and then proposing a novel MCI super-resolution (SR) method via a curvature consistent network (CCN). It consists of a homogeneous workflow and a heterogeneous workflow, where the former learns a mapping between homogeneous images, i.e., LR and HR MCIs, and the latter learns a mapping between heterogeneous images, i.e., MCIs and curvature images. Besides, a collaborative fusion strategy is used to leverage features learned from both workflows level-by-level by recovering the HR image eventually. To mitigate the issue of lacking an MCI dataset, we construct a new benchmark consisting of realistic MCIs at different resolutions, called MCI. Experiments on MCI demonstrate that the proposed CCN outperforms representative SR methods by recovering more delicate circuit lines and yields higher HT detection performance. The dataset is available at github.com/RuiZhang97/CCN.

Clustering and Segmentation of Adhesive Pests in Apple Orchards Based on GMM-DC

The segmentation of individual pests is a prerequisite for pest feature extraction and identification. To address the issue of pest adhesion in the apple orchard pest identification process, this research proposed a pest adhesion image segmentation method based on Gaussian Mixture Model with Density and Curvature Weighting (GMM-DC). First, in the HSV color space, an image was desaturated by adjusting the hue and inverting to mitigate threshold crossing points. Subsequently, threshold segmentation and contour selection methods were used to separate the image background. Next, a shape factor was introduced to determine the regions and quantities of adhering pests, thereby determining the number of model clustering clusters. Then, point cloud reconstruction was performed based on the color and spatial distribution features of the pests. To construct the GMM-DC segmentation model, a spatial density (SD) and spatial curvature (SC) information function were designed and embedded in the GMM. Finally, experimental analysis was conducted on the collected apple orchard pest images. The results showed that GMM-DC achieved an average accurate segmentation rate of 95.75%, an average over-segmentation rate of 2.83%, and an average under-segmentation rate of 1.42%. These results significantly outperformed traditional image segmentation methods. In addition, the original and improved Mask R-CNN models were used as recognition models, and the mean Average Precision was used as the evaluation metric. Recognition experiments were conducted on pest images with and without the proposed method. The results show the mean Average Precision for pest images segmented with the proposed method as 92.43% and 96.75%. This indicates an improvement of 13.01% and 12.18% in average recognition accuracy, respectively. The experimental results demonstrate that this method provides a theoretical and methodological foundation for accurate pest identification in orchards.

An adaptive B-spline representation of topology optimization design for Additive Manufacturing

Topology optimization is a renowned structural optimization approach used to compute the optimal topology for the enhancement of structural performance. It has been in common practice in different engineering fields such as automobile and aerospace. However, there still exist gaps between topology optimization and its engineering operations, which considerably impedes topology optimization’s applications. One of these gaps is how to make (especially finite element-based) topology optimization results machine-readable, which means, how to transform these into computer-aided design (CAD) models, which are ready-to-use models for manufacturing. In the proposed work the authors adopted a unique methodology that plugs the gap between topology optimization and manufacturing. This methodology seamlessly integrates the structural analysis tool, boundary description tool and standard CAD geometry representation; equipped with the Hausdorff distance approach for 3D printing/additive manufacturing of optimal structures. Initially, we extract the skeleton of the optimal design (in the form of a points cloud) using the level set method, followed by an interpolation technique with shape preservation property, the extracted skeleton is made dense. Incorporating the shape and curvature information of the data set, an adaptive B-spline approximation is devised for fitting a smooth curve through the points cloud. This approach interprets topology optimization results as a parametric CAD model with minimum possible control points and minimum approximation error. The CAD-based optimal designs are then used for additive manufacturing. The numerical results exhibit in detail the validity and accuracy of the proposed method.

Accelerated Distributed Approximate Newton Method.

Distributed second-order optimization, as an effective strategy for training large-scale machine learning systems, has been widely investigated due to its low communication complexity. However, the existing distributed second-order optimization algorithms, including distributed approximate Newton (DANE), accelerated inexact DANE (AIDE), and statistically preconditioned accelerated gradient (SPAG), are all required to precisely solve an expensive subproblem up to the target precision. Therefore, this causes these algorithms to suffer from high computation costs and this hinders their development. In this article, we design a novel distributed second-order algorithm called the accelerated distributed approximate Newton (ADAN) method to overcome the high computation costs of the existing ones. Compared with DANE, AIDE, and SPAG, which are constructed based on the relative smooth theory, ADAN's theoretical foundation is built upon the inexact Newton theory. The different theoretical foundations lead to handle the expensive subproblem efficiently, and steps required to solve the subproblem are independent of the target precision. At the same time, ADAN resorts to the acceleration and can effectively exploit the objective function's curvature information, making ADAN to achieve a low communication complexity. Thus, ADAN can achieve both the communication and computation efficiencies, while DANE, AIDE, and SPAG can achieve only the communication efficiency. Our empirical study also validates the advantages of ADAN over extant distributed second-order algorithms.

Communication Efficient Curvature Aided Primal-Dual Algorithms for Decentralized Optimization

This paper presents a family of algorithms for decentralized convex composite problems. We consider the setting of a network of agents that cooperatively minimize a global objective function composed of a sum of local functions plus a regularizer. Through the use of intermediate consensus variables, we remove the need for inner communication loops between agents when computing curvature-guided updates. A general scheme is presented which unifies the analysis for a plethora of computing choices, including gradient descent, Newton updates, and BFGS updates. Our analysis establishes sublinear convergence rates under convex objective functions with Lipschitz continuous gradients, as well as linear convergence rates when the local functions are further assumed to be strongly convex. Moreover, we explicitly characterize the acceleration due to curvature information. Last but not the least, we present an asynchronous implementation for the proposed algorithms, which removes the need for a central clock, with linear convergence rates established in expectation under strongly convex objectives. We ascertain the effectiveness of the proposed methods with numerical experiments on benchmark datasets.