Two-Sided Matching Decision Making with Multi-Attribute Probabilistic Hesitant Fuzzy Sets

In previous research on two-sided matching(TSM)decision,agents’preferences were often given in the form of exact values of ordinal numbers and linguistic phrase term sets.Nowdays,the matching agent cannot perform the exact evaluation in the TSM situations due to the great fuzziness of human thought and the complexity of reality.Probability hesitant fuzzy sets,however,have grown in popularity due to their advantages in communicating complex information.Therefore,this paper develops a TSM decision-making approach with multi-attribute probability hesitant fuzzy sets and unknown attribute weight information.The agent attribute weight vector should be obtained by using the maximum deviation method and Hamming distance.The probabilistic hesitancy fuzzy information matrix of each agent is then arranged to determine the comprehensive evaluation of two matching agent sets.The agent satisfaction degree is calculated using the technique for order preference by similarity to ideal solution(TOPSIS).Additionally,the multi-object programming technique is used to establish a TSM method with the objective of maximizing the agent satisfaction of two-sided agents,and the matching schemes are then established by solving the built model.The study concludes by providing a real-world supply-demand scenario to illustrate the effectiveness of the proposed method.The proposed method is more flexible than prior research since it expresses evaluation information using probability hesitating fuzzy sets and can be used in scenarios when attribute weight information is unclear.

Two-Sided Stable Matching Decision-Making Method Considering Matching Intention under a Hesitant Fuzzy Environment

In this paper,a stable two-sided matching(TSM)method considering the matching intention of agents under a hesitant fuzzy environment is proposed.The method uses a hesitant fuzzy element(HFE)as its basis.First,the HFE preference matrix is transformed into the normalized HFE preference matrix.On this basis,the distance and the projection of the normalized HFEs on positive and negative ideal solutions are calculated.Then,the normalized HFEs are transformed into agent satisfactions.Considering the stable matching constraints,a multiobjective programming model with the objective of maximizing the satisfactions of two-sided agents is constructed.Based on the agent satisfaction matrix,the matching intention matrix of two-sided agents is built.According to the agent satisfaction matrix and matching intention matrix,the comprehensive satisfaction matrix is set up.Furthermore,the multiobjective programming model based on satisfactions is transformed into a multiobjective programming model based on comprehensive satisfactions.Using the G-S algorithm,the multiobjective programming model based on comprehensive satisfactions is solved,and then the best TSM scheme is obtained.Finally,a terminal distribution example is used to verify the feasibility and effectiveness of the proposed method.

The Aviation Technology Two-Sided Matching with the Expected Time Based on the Probabilistic Linguistic Preference Relations

The two-sided matching has been widely applied to the decision-making problems in the field of management.With the limited working experience,the two-sided agents usually cannot provide the preference order directly for the opposite agent,but rather to provide the preference relations in the form of linguistic information.The preference relations based on probabilistic linguistic term sets(PLTSs)not only allowagents to provide the evaluation with multiple linguistic terms,but also present the different preference degrees for linguistic terms.Considering the diversities of the agents,they may provide their preference relations in the form of the probabilistic linguistic preference relation(PLPR)or the probabilistic linguistic multiplicative preference relation(PLMPR).For two-sided matching with the expected time,we first provide the concept of the time satisfaction degree(TSD).Then,we transform the preference relations in different forms into the unified preference relations(u-PRs).The consistency index to measure the consistency of u-PRs is introduced.Besides,the acceptable consistent u-PRs are constructed,and an algorithm is proposed to modify the unacceptable consistent u-PRs.Furthermore,we present the whole two-sided matching decisionmaking process with the acceptable consistent u-PRs.Finally,a case about aviation technology suppliers and demanders matching is presented to exhibit the rationality and practicality of the proposed method.Some analyses and discussions are provided to further demonstrate the feasibility and effectiveness of the proposed method.

A Portfolio Selection Method Based on Pattern Matching with Dual Information of Direction and Distance

Pattern matching method is one of the classic classifications of existing online portfolio selection strategies. This article aims to study the key aspects of this method—measurement of similarity and selection of similarity sets, and proposes a Portfolio Selection Method based on Pattern Matching with Dual Information of Direction and Distance (PMDI). By studying different combination methods of indicators such as Euclidean distance, Chebyshev distance, and correlation coefficient, important information such as direction and distance in stock historical price information is extracted, thereby filtering out the similarity set required for pattern matching based investment portfolio selection algorithms. A large number of experiments conducted on two datasets of real stock markets have shown that PMDI outperforms other algorithms in balancing income and risk. Therefore, it is suitable for the financial environment in the real world.

Feature Matching via Topology-Aware Graph Interaction Model

Feature matching plays a key role in computer vision. However, due to the limitations of the descriptors, the putative matches are inevitably contaminated by massive outliers.This paper attempts to tackle the outlier filtering problem from two aspects. First, a robust and efficient graph interaction model,is proposed, with the assumption that matches are correlated with each other rather than independently distributed. To this end, we construct a graph based on the local relationships of matches and formulate the outlier filtering task as a binary labeling energy minimization problem, where the pairwise term encodes the interaction between matches. We further show that this formulation can be solved globally by graph cut algorithm. Our new formulation always improves the performance of previous localitybased method without noticeable deterioration in processing time,adding a few milliseconds. Second, to construct a better graph structure, a robust and geometrically meaningful topology-aware relationship is developed to capture the topology relationship between matches. The two components in sum lead to topology interaction matching(TIM), an effective and efficient method for outlier filtering. Extensive experiments on several large and diverse datasets for multiple vision tasks including general feature matching, as well as relative pose estimation, homography and fundamental matrix estimation, loop-closure detection, and multi-modal image matching, demonstrate that our TIM is more competitive than current state-of-the-art methods, in terms of generality, efficiency, and effectiveness. The source code is publicly available at http://github.com/YifanLu2000/TIM.

Multiple Matching Attenuation Based on Curvelet Domain Extended Filtering

The paper develops a multiple matching attenuation method based on extended filtering in the curvelet domain,which combines the traditional Wiener filtering method with the matching attenuation method in curvelet domain.Firstly,the method uses the predicted multiple data to generate the Hilbert transform records,time derivative records and time derivative records of Hilbert transform.Then,the above records are transformed into the curvelet domain and multiple matching attenuation based on least squares extended filtering is performed.Finally,the attenuation results are transformed back into the time-space domain.Tests on the model data and field data show that the method proposed in the paper effectively suppress the multiples while preserving the primaries well.Furthermore,it has higher accuracy in eliminating multiple reflections,which is more suitable for the multiple attenuation tasks in the areas with complex structures compared to the time-space domain extended filtering method and the conventional curvelet transform method.

A Non-Parametric Scheme for Identifying Data Characteristic Based on Curve Similarity Matching

For accurately identifying the distribution charac-teristic of Gaussian-like noises in unmanned aerial vehicle(UAV)state estimation,this paper proposes a non-parametric scheme based on curve similarity matching.In the framework of the pro-posed scheme,a Parzen window(kernel density estimation,KDE)method on sliding window technology is applied for roughly esti-mating the sample probability density,a precise data probability density function(PDF)model is constructed with the least square method on K-fold cross validation,and the testing result based on evaluation method is obtained based on some data characteristic analyses of curve shape,abruptness and symmetry.Some com-parison simulations with classical methods and UAV flight exper-iment shows that the proposed scheme has higher recognition accuracy than classical methods for some kinds of Gaussian-like data,which provides better reference for the design of Kalman filter(KF)in complex water environment.

Distributed Matching Theory-Based Task Re-Allocating for Heterogeneous Multi-UAV Edge Computing

Many efforts have been devoted to efficient task scheduling in Multi-Unmanned Aerial Vehicle(UAV)edge computing.However,the heterogeneity of UAV computation resource,and the task re-allocating between UAVs have not been fully considered yet.Moreover,most existing works neglect the fact that a task can only be executed on the UAV equipped with its desired service function(SF).In this backdrop,this paper formulates the task scheduling problem as a multi-objective task scheduling problem,which aims at maximizing the task execution success ratio while minimizing the average weighted sum of all tasks’completion time and energy consumption.Optimizing three coupled goals in a realtime manner with the dynamic arrival of tasks hinders us from adopting existing methods,like machine learning-based solutions that require a long training time and tremendous pre-knowledge about the task arrival process,or heuristic-based ones that usually incur a long decision-making time.To tackle this problem in a distributed manner,we establish a matching theory framework,in which three conflicting goals are treated as the preferences of tasks,SFs and UAVs.Then,a Distributed Matching Theory-based Re-allocating(DiMaToRe)algorithm is put forward.We formally proved that a stable matching can be achieved by our proposal.Extensive simulation results show that Di Ma To Re algorithm outperforms benchmark algorithms under diverse parameter settings and has good robustness.

A Time Series Short-Term Prediction Method Based on Multi-Granularity Event Matching and Alignment

Accurate forecasting of time series is crucial across various domains.Many prediction tasks rely on effectively segmenting,matching,and time series data alignment.For instance,regardless of time series with the same granularity,segmenting them into different granularity events can effectively mitigate the impact of varying time scales on prediction accuracy.However,these events of varying granularity frequently intersect with each other,which may possess unequal durations.Even minor differences can result in significant errors when matching time series with future trends.Besides,directly using matched events but unaligned events as state vectors in machine learning-based prediction models can lead to insufficient prediction accuracy.Therefore,this paper proposes a short-term forecasting method for time series based on a multi-granularity event,MGE-SP(multi-granularity event-based short-termprediction).First,amethodological framework for MGE-SP established guides the implementation steps.The framework consists of three key steps,including multi-granularity event matching based on the LTF(latest time first)strategy,multi-granularity event alignment using a piecewise aggregate approximation based on the compression ratio,and a short-term prediction model based on XGBoost.The data from a nationwide online car-hailing service in China ensures the method’s reliability.The average RMSE(root mean square error)and MAE(mean absolute error)of the proposed method are 3.204 and 2.360,lower than the respective values of 4.056 and 3.101 obtained using theARIMA(autoregressive integratedmoving average)method,as well as the values of 4.278 and 2.994 obtained using k-means-SVR(support vector regression)method.The other experiment is conducted on stock data froma public data set.The proposed method achieved an average RMSE and MAE of 0.836 and 0.696,lower than the respective values of 1.019 and 0.844 obtained using the ARIMA method,as well as the values of 1.350 and 1.172 obtained using the k-means-SVR method.

CMMCAN:Lightweight Feature Extraction and Matching Network for Endoscopic Images Based on Adaptive Attention

In minimally invasive surgery,endoscopes or laparoscopes equipped with miniature cameras and tools are used to enter the human body for therapeutic purposes through small incisions or natural cavities.However,in clinical operating environments,endoscopic images often suffer from challenges such as low texture,uneven illumination,and non-rigid structures,which affect feature observation and extraction.This can severely impact surgical navigation or clinical diagnosis due to missing feature points in endoscopic images,leading to treatment and postoperative recovery issues for patients.To address these challenges,this paper introduces,for the first time,a Cross-Channel Multi-Modal Adaptive Spatial Feature Fusion(ASFF)module based on the lightweight architecture of EfficientViT.Additionally,a novel lightweight feature extraction and matching network based on attention mechanism is proposed.This network dynamically adjusts attention weights for cross-modal information from grayscale images and optical flow images through a dual-branch Siamese network.It extracts static and dynamic information features ranging from low-level to high-level,and from local to global,ensuring robust feature extraction across different widths,noise levels,and blur scenarios.Global and local matching are performed through a multi-level cascaded attention mechanism,with cross-channel attention introduced to simultaneously extract low-level and high-level features.Extensive ablation experiments and comparative studies are conducted on the HyperKvasir,EAD,M2caiSeg,CVC-ClinicDB,and UCL synthetic datasets.Experimental results demonstrate that the proposed network improves upon the baseline EfficientViT-B3 model by 75.4%in accuracy(Acc),while also enhancing runtime performance and storage efficiency.When compared with the complex DenseDescriptor feature extraction network,the difference in Acc is less than 7.22%,and IoU calculation results on specific datasets outperform complex dense models.Furthermore,this method increases the F1 score by 33.2%and accelerates runtime by 70.2%.It is noteworthy that the speed of CMMCAN surpasses that of comparative lightweight models,with feature extraction and matching performance comparable to existing complex models but with faster speed and higher cost-effectiveness.

Artificial Immune Detection for Network Intrusion Data Based on Quantitative Matching Method

Artificial immune detection can be used to detect network intrusions in an adaptive approach and proper matching methods can improve the accuracy of immune detection methods.This paper proposes an artificial immune detection model for network intrusion data based on a quantitative matching method.The proposed model defines the detection process by using network data and decimal values to express features and artificial immune mechanisms are simulated to define immune elements.Then,to improve the accuracy of similarity calculation,a quantitative matching method is proposed.The model uses mathematical methods to train and evolve immune elements,increasing the diversity of immune recognition and allowing for the successful detection of unknown intrusions.The proposed model’s objective is to accurately identify known intrusions and expand the identification of unknown intrusions through signature detection and immune detection,overcoming the disadvantages of traditional methods.The experiment results show that the proposed model can detect intrusions effectively.It has a detection rate of more than 99.6%on average and a false alarm rate of 0.0264%.It outperforms existing immune intrusion detection methods in terms of comprehensive detection performance.

Reshaping Li–Mg hybrid batteries:Epitaxial electrodeposition and spatial confinement on MgMOF substrates via the lattice‐matching strategy

The emergence of Li–Mg hybrid batteries has been receiving attention,owing to their enhanced electrochemical kinetics and reduced overpotential.Nevertheless,the persistent challenge of uneven Mg electrodeposition remains a significant impediment to their practical integration.Herein,we developed an ingenious approach that centered around epitaxial electrocrystallization and meticulously controlled growth of magnesium crystals on a specialized MgMOF substrate.The chosen MgMOF substrate demonstrated a robust affinity for magnesium and showed minimal lattice misfit with Mg,establishing the crucial prerequisites for successful heteroepitaxial electrocrystallization.Moreover,the incorporation of periodic electric fields and successive nanochannels within the MgMOF structure created a spatially confined environment that considerably promoted uniform magnesium nucleation at the molecular scale.Taking inspiration from the“blockchain”concept prevalent in the realm of big data,we seamlessly integrated a conductive polypyrrole framework,acting as a connecting“chain,”to interlink the“blocks”comprising the MgMOF cavities.This innovative design significantly amplified charge‐transfer efficiency,thereby increasing overall electrochemical kinetics.The resulting architecture(MgMOF@PPy@CC)served as an exceptional host for heteroepitaxial Mg electrodeposition,showcasing remarkable electrostripping/plating kinetics and excellent cycling performance.Surprisingly,a symmetrical cell incorporating the MgMOF@PPy@CC electrode demonstrated impressive stability even under ultrahigh current density conditions(10mAcm–2),maintaining operation for an extended 1200 h,surpassing previously reported benchmarks.Significantly,on coupling the MgMOF@PPy@CC anode with a Mo_(6)S_(8) cathode,the assembled battery showed an extended lifespan of 10,000 cycles at 70 C,with an outstanding capacity retention of 96.23%.This study provides a fresh perspective on the rational design of epitaxial electrocrystallization driven by metal–organic framework(MOF)substrates,paving the way toward the advancement of cuttingedge batteries.

Matching Dyeing and Properties of Silk Fabrics with Natural Edible Pigments

The silk fabrics were matching dyed with three natural edible pigments(red rice red,ginger yellow and gardenia blue).By investigating the dyeing rates and lifting properties of these pigments,it was observed that their compatibilities were excellent in the dyeing process:dye dosage 2.5%(omf),mordant alum dosage 2.0%(omf),dyeing temperature 80℃and dyeing time 40 min.The silk fabrics dyed with secondary colors exhibited vibrant and vivid color owing to the remarkable lightness and chroma of ginger yellow.However,gardenia blue exhibited multiple absorption peaks in the visible light range,resulting in significantly lower lightness and chroma for the silk fabrics dyed with tertiary colors,thus making it suitable only for matte-colored fabrics with low chroma levels.In addition,the silk fabrics dyed with these three pigments had a color fastness that exceeded grade 3 in resistance to perspiration,soap washing and light exposure,indicating acceptable wearing properties.The dyeing process described in this research exhibited a wide range of potential applications in matching dyeing of protein-based textiles with natural colorants.

Inversion of Seabed Geotechnical Properties in the Arctic Chukchi Deep Sea Basin Based on Time Domain Adaptive Search Matching Algorithm

The chirp sub-bottom profiler,for its high resolution,easy accessibility and cost-effectiveness,has been widely used in acoustic detection.In this paper,the acoustic impedance and grain size compositions were obtained based on the chirp sub-bottom profiler data collected in the Chukchi Plateau area during the 11th Arctic Expedition of China.The time-domain adaptive search matching algorithm was used and validated on our established theoretical model.The misfit between the inversion result and the theoretical model is less than 0.067%.The grain size was calculated according to the empirical relationship between the acoustic impedance and the grain size of the sediment.The average acoustic impedance of sub-seafloor strata is 2.5026×10^(6) kg(s m^(2))^(-1)and the average grain size(θvalue)of the seafloor surface sediment is 7.1498,indicating the predominant occurrence of very fine silt sediment in the study area.Comparison of the inversion results and the laboratory measurements of nearby borehole samples shows that they are in general agreement.

Automatic depth matching method of well log based on deep reinforcement learning

In the traditional well log depth matching tasks,manual adjustments are required,which means significantly labor-intensive for multiple wells,leading to low work efficiency.This paper introduces a multi-agent deep reinforcement learning(MARL)method to automate the depth matching of multi-well logs.This method defines multiple top-down dual sliding windows based on the convolutional neural network(CNN)to extract and capture similar feature sequences on well logs,and it establishes an interaction mechanism between agents and the environment to control the depth matching process.Specifically,the agent selects an action to translate or scale the feature sequence based on the double deep Q-network(DDQN).Through the feedback of the reward signal,it evaluates the effectiveness of each action,aiming to obtain the optimal strategy and improve the accuracy of the matching task.Our experiments show that MARL can automatically perform depth matches for well-logs in multiple wells,and reduce manual intervention.In the application to the oil field,a comparative analysis of dynamic time warping(DTW),deep Q-learning network(DQN),and DDQN methods revealed that the DDQN algorithm,with its dual-network evaluation mechanism,significantly improves performance by identifying and aligning more details in the well log feature sequences,thus achieving higher depth matching accuracy.

Road Traffic Monitoring from Aerial Images Using Template Matching and Invariant Features

Road traffic monitoring is an imperative topic widely discussed among researchers.Systems used to monitor traffic frequently rely on cameras mounted on bridges or roadsides.However,aerial images provide the flexibility to use mobile platforms to detect the location and motion of the vehicle over a larger area.To this end,different models have shown the ability to recognize and track vehicles.However,these methods are not mature enough to produce accurate results in complex road scenes.Therefore,this paper presents an algorithm that combines state-of-the-art techniques for identifying and tracking vehicles in conjunction with image bursts.The extracted frames were converted to grayscale,followed by the application of a georeferencing algorithm to embed coordinate information into the images.The masking technique eliminated irrelevant data and reduced the computational cost of the overall monitoring system.Next,Sobel edge detection combined with Canny edge detection and Hough line transform has been applied for noise reduction.After preprocessing,the blob detection algorithm helped detect the vehicles.Vehicles of varying sizes have been detected by implementing a dynamic thresholding scheme.Detection was done on the first image of every burst.Then,to track vehicles,the model of each vehicle was made to find its matches in the succeeding images using the template matching algorithm.To further improve the tracking accuracy by incorporating motion information,Scale Invariant Feature Transform(SIFT)features have been used to find the best possible match among multiple matches.An accuracy rate of 87%for detection and 80%accuracy for tracking in the A1 Motorway Netherland dataset has been achieved.For the Vehicle Aerial Imaging from Drone(VAID)dataset,an accuracy rate of 86%for detection and 78%accuracy for tracking has been achieved.

Ground target localization of unmanned aerial vehicle based on scene matching

In order to improve target localization precision,accuracy,execution efficiency,and application range of the unmanned aerial vehicle(UAV)based on scene matching,a ground target localization method for unmanned aerial vehicle based on scene matching(GTLUAVSM)is proposed.The sugges-ted approach entails completing scene matching through a feature matching algorithm.Then,multi-sensor registration is optimized by robust estimation based on homologous registration.Finally,basemap generation and model solution are utilized to improve basemap correspondence and accom-plish aerial image positioning.Theoretical evidence and experimental verification demonstrate that GTLUAVSM can improve localization accuracy,speed,and precision while minimizing reliance on task equipment.

Can propensity score matching replace randomized controlled trials?

Randomized controlled trials(RCTs)have long been recognized as the gold standard for establishing causal relationships in clinical research.Despite that,various limitations of RCTs prevent its widespread implementation,ranging from the ethicality of withholding potentially-lifesaving treatment from a group to relatively poor external validity due to stringent inclusion criteria,amongst others.However,with the introduction of propensity score matching(PSM)as a retrospective statistical tool,new frontiers in establishing causation in clinical research were opened up.PSM predicts treatment effects using observational data from existing sources such as registries or electronic health records,to create a matched sample of participants who received or did not receive the intervention based on their propensity scores,which takes into account characteristics such as age,gender and comorbidities.Given its retrospective nature and its use of observational data from existing sources,PSM circumvents the aforementioned ethical issues faced by RCTs.Majority of RCTs exclude elderly,pregnant women and young children;thus,evidence of therapy efficacy is rarely proven by robust clinical research for this population.On the other hand,by matching study patient characteristics to that of the population of interest,including the elderly,pregnant women and young children,PSM allows for generalization of results to the wider population and hence greatly increases the external validity.Instead of replacing RCTs with PSM,the synergistic integration of PSM into RCTs stands to provide better research outcomes with both methods complementing each other.For example,in an RCT investigating the impact of mannitol on outcomes among participants of the Intensive Blood Pressure Reduction in Acute Cerebral Hemorrhage Trial,the baseline characteristics of comorbidities and current medications between treatment and control arms were significantly different despite the randomization protocol.Therefore,PSM was incorporated in its analysis to create samples from the treatment and control arms that were matched in terms of these baseline characteristics,thus providing a fairer comparison for the impact of mannitol.This literature review reports the applications,advantages,and considerations of using PSM with RCTs,illustrating its utility in refining randomization,improving external validity,and accounting for non-compliance to protocol.Future research should consider integrating the use of PSM in RCTs to better generalize outcomes to target populations for clinical practice and thereby benefit a wider range of patients,while maintaining the robustness of randomization offered by RCTs.

A Study of the TPS Based Beam-Matching Concept for Medical Linear Accelerators at a Tertiary Hospital

The flexibility in radiotherapy can be improved if patients can be moved between any one of the department’s medical linear accelerators (LINACs) without the need to change anything in the patient’s treatment plan. For this to be possible, the dosimetric characteristics of the various accelerators must be the same, or nearly the same. The purpose of this work is to describe further and compare measurements and parameters after the initial vendor-recommended beam matching of the five LINACs. Deviations related to dose calculations and to beam matched accelerators may compromise treatment accuracy. The safest and most practical way to ensure that all accelerators are within clinical acceptable accuracy is to include TPS calculations in the LINACs matching evaluation. Treatment planning system (TPS) was used to create three photons plans with different field sizes 3 × 3 cm, 10 × 10 cm and 25 × 25 cm at a depth of 4.5 cm in Perspex. Calculated TPS plans were sent to Mosaiq to be delivered by five LINACs. TPS plans were compared with five LINACs measurements data using Gamma analyses of 2% and 2 mm. The results suggest that for four out of the five LINACs, there was generally good agreement, less than a 2% deviation between the planned dose distribution and the measured dose distribution. However, one specific LINAC named “Asterix” exhibited a deviation of 2.121% from the planned dose. The results show that all of the LINACs’ performance were within the acceptable deviation and delivering radiation dose consistently and accurately.

Loop Closure Detection via Locality Preserving Matching With Global Consensus

A critical component of visual simultaneous localization and mapping is loop closure detection(LCD),an operation judging whether a robot has come to a pre-visited area.Concretely,given a query image(i.e.,the latest view observed by the robot),it proceeds by first exploring images with similar semantic information,followed by solving the relative relationship between candidate pairs in the 3D space.In this work,a novel appearance-based LCD system is proposed.Specifically,candidate frame selection is conducted via the combination of Superfeatures and aggregated selective match kernel(ASMK).We incorporate an incremental strategy into the vanilla ASMK to make it applied in the LCD task.It is demonstrated that this setting is memory-wise efficient and can achieve remarkable performance.To dig up consistent geometry between image pairs during loop closure verification,we propose a simple yet surprisingly effective feature matching algorithm,termed locality preserving matching with global consensus(LPM-GC).The major objective of LPM-GC is to retain the local neighborhood information of true feature correspondences between candidate pairs,where a global constraint is further designed to effectively remove false correspondences in challenging sceneries,e.g.,containing numerous repetitive structures.Meanwhile,we derive a closed-form solution that enables our approach to provide reliable correspondences within only a few milliseconds.The performance of the proposed approach has been experimentally evaluated on ten publicly available and challenging datasets.Results show that our method can achieve better performance over the state-of-the-art in both feature matching and LCD tasks.We have released our code of LPM-GC at https://github.com/jiayi-ma/LPM-GC.