Search Results (78)

The extraction of the light stripe center is a pivotal step in line-structured light vision measurement. This paper addresses a key challenge in the online measurement of train wheel treads, where the diverse and complex profile characteristics of the tread surface lead to uneven gray-level distribution and varying width features in the stripe image, ultimately degrading the accuracy of center extraction. To solve this problem, a region-adaptive multiscale method for light stripe center extraction is proposed. First, potential light stripe regions are identified and enhanced based on the gray-gradient features of the image, enabling precise segmentation. Subsequently, by normalizing the feature responses under Gaussian kernels with different scales, the locally optimal scale parameter (σ) is determined adaptively for each stripe region. Sub-pixel center extraction is then performed using the Hessian matrix corresponding to this optimal σ. Experimental results demonstrate that under on-site conditions featuring uneven wheel surface reflectivity, the proposed method can reliably extract light stripe centers with high stability. It achieves a repeatability of 0.10 mm, with mean measurement errors of 0.12 mm for flange height and 0.10 mm for flange thickness, thereby enhancing both stability and accuracy in industrial measurement environments. The repeatability and reproducibility of the method were further validated through repeated testing of multiple wheels. Full article

This mini-review discusses recent advances in the rigorous application of Bonding Evolution Theory (BET) to elucidate electron rearrangements in cycloaddition reactions occurring in both ground and electronically excited states. Computational studies reveal that describing bond formation and cleavage through parametric polynomials derived from the Catastrophe Theory (CT) provides a deeper and more coherent understanding of chemical bonding and reactivity. However, several existing BET applications have adopted CT concepts without fully incorporating the mathematical rigor on which BET is based, resulting in conceptual ambiguities and inaccurate interpretations. A proper implementation of BET requires evaluating the Hessian matrix at potentially degenerate critical points (CPs) of the Electron Localization Function (ELF) and assessing their relative evolution along the reaction coordinate. This systematic protocol integrates key CT principles within BET’s original framework, restoring its formal consistency. The resulting analyses have revealed correlations between electron-density symmetry and CT polynomials, relationships between these polynomials and the homolytic or heterolytic character of bond dissociation, and the development of a CT-based model for scaling bond polarity. These findings demonstrate that incorporating CT-derived functions into BET is not merely a formal refinement but a fundamental step toward achieving a more rigorous and predictive understanding of electron rearrangements in cycloadditions. Full article

We introduce a new method for estimating gravitational wave parameters. This approach uses a second-order likelihood optimization framework built into a machine learning system (JimGW). Current methods often rely on first-order approximations, which can miss important details, while our method incorporates the full Hessian matrix of the likelihood function. This allows us to better capture the shape of the parameter space for gravitational waves. Our theoretical framework demonstrates that the trace of the Hessian matrix, when properly normalized, provides a coordinate-invariant measure of the local likelihood geometry that significantly enhances parameter recovery accuracy for gravitational wave sources. We test our second-order method using data from the three gravitational wave events. Take GW150914 as an example; the results show large gains in precision for parameter estimation, with accuracy gains exceeding 93% across all inferred parameters compared to standard first-order implementations. We use Jensen–Shannon divergence to compare the resulting posterior distributions. The JSD values range from 0.366 to 0.948, which correlate directly with improved parameter recovery as validated through injection studies. The method remains computationally efficient with only a 20% increase in runtime. At the same time, it produces seven times more effective samples. Our results show that machine learning methods using only first-order information can lead to systematic errors in gravitational wave parameter estimation. The incorporation of second-order corrections emerges not as an optional refinement but as a necessary component for achieving theoretically optimal inference. It also matters for ongoing gravitational wave analyses, future detector networks, and the broader application of machine learning methods in precision scientific measurement. Full article

Accurate and efficient simulation of airflows in human airways is critical for advancing the understanding of respiratory physiology, disease diagnostics, and inhalation drug delivery. Traditional computational fluid dynamics (CFD) provides detailed predictions but is often mesh-sensitive and computationally expensive for complex geometries. In this study, we explored the usage of physics-informed neural networks (PINNs) to simulate airflows in three geometries with increasing complexity: a duct, a simplified mouth–lung model, and a patient-specific upper airway. Key procedures to implement PINN training and testing were presented, including geometry preparation/scaling, boundary/constraint specification, training diagnostics, nondimensionalization, and inference mapping. Both the laminar PINN and SDF–mixing-length PINN were tested. PINN predictions were validated against high-fidelity CFD simulations to assess accuracy, efficiency, and generalization. The results demonstrated that nondimensionalization of the governing equations was essential to ensure training accuracy for respiratory flows at 1 m/s and above. Hessian-matrix-based diagnosis revealed a quick increase in training challenges with flow speed and geometrical complexity. Both the laminar and SDF–mixing-length PINNs achieved comparable accuracy to corresponding CFD predictions in the duct and simplified mouth–lung geometry. However, only the SDF–mixing-length PINN adequately captured flow details unique to respiratory morphology, such as obstruction-induced flow diversion, recirculating flows, and laryngeal jet decay. The results of this study highlight the potential of PINNs as a flexible alternative to conventional CFD for modeling respiratory airflows, with adaptability to patient-specific geometries and promising integration with static or real-time imaging (e.g., 4D CT/MRI). Full article

To address the ill-posedness of the Hessian matrix in monocular visual-inertial SLAM (Simultaneous Localization and Mapping) caused by unobservable depth of feature points, which leads to convergence difficulties and reduced robustness, this paper proposes a Pre-Dog-Leg feature optimization method based on an adaptive preconditioner. First, we propose a multi-candidate initialization method with robust characteristics. This method effectively circumvents erroneous depth initialization by introducing multiple depth assumptions and geometric consistency constraints. Second, we address the pathology of the Hessian matrix of the feature points by constructing a hybrid SPAI-Jacobi adaptive preconditioner. This preconditioner is capable of identifying matrix pathology and dynamically enabling preconditioning as a strategy. Finally, we construct a hybrid adaptive preconditioner for the traditional Dog-Leg numerical optimization method. To address the issue of degraded convergence performance when solving pathological problems, we map the pathological optimization problem from the original parameter space to a well-conditioned preconditioned space. The optimization equivalence is maintained by variable recovery. The experiments on the EuRoC dataset show that the method reduces the number of Hessian matrix conditionals by a factor of 7.9, effectively suppresses outliers, and significantly improves the overall convergence time. From the analysis of trajectory error, the absolute trajectory error is reduced by up to 16.48% relative to RVIO2 on the MH_01 sequence, 20.83% relative to VINS-mono on the MH_02 sequence, and up to 14.73% relative to VINS-mono and 34.0% relative to OpenVINS on the highly dynamic MH_05 sequence, indicating that the algorithm achieves higher localization accuracy and stronger system robustness. Full article

Deep learning models are often perceived as black boxes, making it challenging to analyze the causal relationships between inputs and outputs. For this reason, the explainability of model learning has garnered increasing attention in recent years. Some previous studies proposed influence functions, which evaluate how the weighting of data impacts the model by mathematical analysis, thereby explaining how it realizes the data. This inspires us to suggest that when data in an upstream task is affected by varying levels of noise interference, it is practical to set up a downstream model to apply Taylor expansion in conjunction with the Hessian matrix to estimate perturbations that each data point cause in the model. Additionally, utilizing Integrated Gradients to compute the loss difference between the original data instances and a baseline instance which does not affect the model is powerful to yield a memorization matrix that allows researchers to observe the changes in model reasoning before and after noise interference, helping to analyze the causes of erroneous inference. Full article

Accurate liver segmentation from computed tomography (CT) scans is essential for liver cancer diagnosis and liver surgery planning. Convolutional neural network (CNN)-based models have limited segmentation performance due to their localized receptive fields. Hybrid models incorporating CNNs and transformers that can capture long-range dependencies have shown promising performance in liver segmentation with the cost of high model complexity. Therefore, a new network architecture named G-UNETR++ is proposed to improve accuracy in liver segmentation with moderate model complexity. Two gradient-based encoders that take the second-order partial derivatives (the first two elements from the last column of the Hessian matrix of a CT scan) as inputs are proposed to learn the 3D geometric features such as the boundaries between different organs and tissues. In addition, a hybrid loss function that combines dice loss, cross-entropy loss, and Hausdorff distance loss is designed to address class imbalance and improve segmentation performance in challenging cases. The proposed method was evaluated on three public datasets, the Liver Tumor Segmentation (LiTS) dataset, the 3D Image Reconstruction for Comparison of Algorithms Database (3D-IRCADb), and the Segmentation of the Liver Competition 2007 (Sliver07) dataset, and achieved 97.38%, 97.50%, and 97.32% in terms of the dice similarity coefficient for liver segmentation on the three datasets, respectively. The proposed method outperformed the other state-of-the-art models on the three datasets, which demonstrated the strong effectiveness, robustness, and generalizability of the proposed method in liver segmentation. Full article

The trust region method is an effective method for solving unconstrained optimization problems. Incorrectly updating the rules of the trust region radius will increase the number of iterations and affect the calculation efficiency. In order to obtain an effective radius for the trust region, an adaptive radius updating criterion is proposed based on the gradient of the current iteration point and the eigenvalue of the Hessian matrix which avoids calculating the inverse of the Hessian matrix during radius updating. This approach reduces the computation time and enhances the algorithm’s performance. On this basis, we apply adaptive radius and non-monotonic techniques to the trust region algorithm and propose an improved non-monotonic adaptive trust region algorithm. Under proper assumptions, the convergence of the algorithm is analyzed. Numerical experiments confirm that the suggested algorithm is effective. Full article

The numerical solution of optimal control problems through second-order methods is examined in this paper. Controlled processes are described by a system of nonlinear ordinary differential equations. There are two specific characteristics of the class of control actions used. The first one is that controls are searched for in a given class of functions, which depend on unknown parameters to be found by minimizing an objective functional. The parameter values, in general, may be different at different time intervals. The second feature of the considered problem is that the boundaries of time intervals are also optimized with fixed values of the parameters of the control actions in each of the intervals. The special cases of the problem under study are relay control problems with optimized switching moments. In this work, formulas for the gradient and the Hessian matrix of the objective functional with respect to the optimized parameters are obtained. For this, the technique of fast differentiation is used. A comparison of numerical experiment results obtained with the use of first- and second-order optimization methods is presented. Full article

Domain generalization (DG) aims to learn knowledge from multiple related domains to achieve a robust generalization performance in unseen target domains, which is an effective approach to mitigate domain shift in remote sensing image classification. Although the sharpness-aware minimization (SAM) method enhances DG capability and improves remote sensing image classification performance by promoting the convergence of the loss minimum to a flatter loss surface, the perturbation loss (maximum loss within the neighborhood of a local minimum) of SAM fails to accurately measure the true sharpness of the loss landscape. Furthermore, its variants often overlook gradient conflicts, thereby limiting further improvement in DG performance. In this paper, we introduce implicit sharpness-aware minimization (ISAM), a novel method that addresses the deficiencies of SAM and mitigates gradient conflicts. Specifically, we demonstrate that the discrepancy in training loss during gradient ascent or descent serves as an equivalent measure of the dominant eigenvalue of the Hessian matrix. This discrepancy provides a reliable measure for sharpness. ISAM effectively reduces sharpness and mitigates potential conflicts between gradients by implicitly minimizing the discrepancy between training losses while ensuring a sufficiently low minimum through minimizing perturbation loss. Extensive experiments and analyses demonstrate that ISAM significantly enhances the model’s generalization ability on remote sensing and DG datasets, outperforming existing state-of-the-art methods. Full article

The measurement precision of a line-structured light measurement system is directly affected by the accuracy of extracting the center points of the laser stripes. When the measured object’s surface has significant undulations and severe reflections, existing algorithms are prone to issues such as significant susceptibility to noise and the extraction of false center points. To address these issues, an improved unilateral tracing-based structured light centerline extraction algorithm is proposed. The algorithm first performs unilateral and bidirectional tracing on the upper boundary of the preprocessed laser stripes, then uses the grayscale centroid method to extract the initial coordinates of the center points, and finally corrects them by calculating the stripe’s normal direction using the Hessian matrix. Experimental results show that the proposed algorithm can still extract the stripe center points well under strong interference, with the RMSE reduced by 37% compared to the Steger method and the running speed increased by almost 4 times compared to the grayscale centroid method. The algorithm’s strong robustness, high accuracy, and efficiency provide a viable solution for real-time measurement of line-structured light and high-precision three-dimensional reconstruction. Full article

The field of sensorless control of permanent magnet synchronous motor (PMSM) systems has been the subject of extensive research. The accuracy of sensorless controllers depends on the precise estimation of PMSM state quantities, including rotational speed and rotor position. In order to enhance state estimation accuracy, this paper proposes a moving horizon estimator that can be utilized in the sensorless control system of PMSM. Considering the parameter variations observed in PMSM, a nonlinear mathematical model of PMSM is established. A model reference adaptive system (MRAS) is employed to identify parameters such as resistance, inductance, and magnetic chain in real time. This approach can mitigate the impact of parameter fluctuations. Moving horizon estimation (MHE) is an estimation method based on optimization that can directly handle nonlinear system models. In order to eliminate the influence of external interference and improve the robustness of state estimation, a method based on MHE has been designed for PMSM, and a sensorless observer has been established. Considering the traditional MHE with large computation and high memory occupation, the calculation of MHE is optimized by utilizing a Hessian matrix and gradient vector. The speed and position of the PMSM are estimated within constraints during a single-step iteration. The results of the simulation demonstrate that in comparison to the traditional control structure, the estimation error of rotational speed and rotor position can be reduced by utilizing the proposed method. A more accurate estimation can be achieved with good adaptability and computational speed, which can enhance the robustness of the control system of PMSM. Full article

The present study aims to propose a general framework of modeling rigid body potentials (RBPs) suitable for analyzing the orbit–attitude coupled motion of a spacecraft (S/C) near small celestial bodies, regardless of gravity estimation models. Here, ‘rigid body potential’ refers to the potential of a small celestial body integrated across the finite volume of an S/C, assuming that the mass of the S/C has no influence on the motion of the small celestial body. First proposed is a comprehensive formulation for modeling the RBP including its associated force, torque, and Hessian matrix, which is then applied to three gravity estimation models. The Hessian of potential plays a crucial role in calculating the RBP. This study assesses the RBP via numerical simulations for the purpose of determining proper gravity estimation models and seeking modeling conditions. The gravity estimation models and the associated RBP are tested for eight small celestial bodies. In this study, we utilize distance units (DUs) instead of SI units, where the DU is defined as the mean radius of the given small celestial body. For a given specific distance in Dus, the relative error of the gravity estimation model at this distance has a similar value regardless of the small celestial body. However, the difference value between the potential and RBP depends on the DU; in other words, it depends on the size of the small celestial body. This implies that accurate gravity estimation models are imperative for conducting RBP analysis. The overall results can help develop a propagation system for orbit–attitude coupled motions of an S/C in the vicinity of small celestial bodies. Full article

Primary dendrite information is one of the most important metrics to measure the quality of continuous cast slabs. The contrast of low magnification images is very low under the influence of illumination and sampling devices, so the traditional dendrite detection method has the problem of missed detections. We propose an automatic dendrite detection method based on an improved Hough transform, which effectively improves the accuracy and efficiency of primary dendrite detection. By using the local grayscale features of the image, a genetic algorithm-based local contrast enhancement algorithm is proposed. Compared with the traditional contrast enhancement algorithm, it can retain all the information of the dendrites. Combined with the image binarization method based on Hessian matrix, we can obtain more detailed information about the dendrites. According to the continuity and solidification characteristics of dendrites, the Hough transform is improved to extract dendrite information, which effectively reduces the computational cost of the Hough transform. The experimental results show that the method of this paper has versatility, and the error is four pixels compared with the manual method, which can provide a reliable basis for the subsequent judgement of the quality of cast billets. Full article

This paper is dedicated to the development of a novel class of quasi-Newton techniques tailored to address computational challenges posed by memory constraints. Such methodologies are commonly referred to as “limited” memory methods. The method proposed herein showcases adaptability by introducing a customizable memory parameter governing the retention of historical data in constructing the Hessian estimate matrix at each iterative stage. The search directions generated through this novel approach are derived from a modified version closely resembling the full memory multi-step BFGS update, incorporating limited memory computation for a singular term to approximate matrix–vector multiplication. Results from numerical experiments, exploring various parameter configurations, substantiate the enhanced efficiency of the proposed algorithm within the realm of limited memory quasi-Newton methodologies category. Full article