To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical da...To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.展开更多
Traditional deconvolution methods based on single-channel inversion do not consider the spatial structural relation between channels,and hence,they yield high-resolution results with the existing transverse inconsiste...Traditional deconvolution methods based on single-channel inversion do not consider the spatial structural relation between channels,and hence,they yield high-resolution results with the existing transverse inconsistency or discontinuity.Therefore,in this study,the local dip angle was used to obtain the structural information and construct the spatial structurally constraint operator.This operator is then introduced into multichannel deconvolution as a regularization operator to improve the resolution and maintain the transverse continuity of seismic data.Model tests and actual seismic data processing have demonstrated the effectiveness and practicability of this method.展开更多
Non-negative matrix factorization （NMF） is a popular feature encoding method for image understanding due to its non-negative properties in representation, but the learnt basis images are not always local due to the ...Non-negative matrix factorization （NMF） is a popular feature encoding method for image understanding due to its non-negative properties in representation, but the learnt basis images are not always local due to the lack of explicit constraints in its objective. Various algebraic or geometric local constraints are hence proposed to shape the behaviour of the original NMF. Such constraints are usually rigid in the sense that they have to be specified beforehand instead of learning from the data. In this paper, we propose a flexible spatial constraint method for NMF learning based on factor analysis. Particularly, to learn the local spatial structure of the images, we apply a series of transformations such as orthogonal rotation and thresholding to the factor loading matrix obtained through factor analysis. Then we map the transformed loading matrix into a Laplacian matrix and incorporate this into a max-margin non-negative matrix factorization framework as a penalty term, aiming to learn a representation space which is non-negative, discriminative and localstructure-preserving. We verify the feasibility and effectiveness of the proposed method on several real world datasets with encouraging results.展开更多
We present a lightweight and efficient semisupervised video object segmentation network based on the space-time memory framework.To some extent,our method solves the two difficulties encountered in traditional video o...We present a lightweight and efficient semisupervised video object segmentation network based on the space-time memory framework.To some extent,our method solves the two difficulties encountered in traditional video object segmentation:one is that the single frame calculation time is too long,and the other is that the current frame’s segmentation should use more information from past frames.The algorithm uses a global context(GC)module to achieve highperformance,real-time segmentation.The GC module can effectively integrate multi-frame image information without increased memory and can process each frame in real time.Moreover,the prediction mask of the previous frame is helpful for the segmentation of the current frame,so we input it into a spatial constraint module(SCM),which constrains the areas of segments in the current frame.The SCM effectively alleviates mismatching of similar targets yet consumes few additional resources.We added a refinement module to the decoder to improve boundary segmentation.Our model achieves state-of-the-art results on various datasets,scoring 80.1%on YouTube-VOS 2018 and a J&F score of 78.0%on DAVIS 2017,while taking 0.05 s per frame on the DAVIS 2016 validation dataset.展开更多
This paper presents one novel spatial geometric constraints histogram descriptors （SGCHD） based on curvature mesh graph for automatic three-dimensional （3D） pollen particles recognition. In order to reduce high di...This paper presents one novel spatial geometric constraints histogram descriptors （SGCHD） based on curvature mesh graph for automatic three-dimensional （3D） pollen particles recognition. In order to reduce high dimensionality and noise disturbance arising from the abnormal record approach under microscopy, the separated surface curvature voxels are ex- tracted as primitive features to represent the original 3D pollen particles, which can also greatly reduce the computation time for later feature extraction process. Due to the good invariance to pollen rotation and scaling transformation, the spatial geometric constraints vectors are calculated to describe the spatial position correlations of the curvature voxels on the 3D curvature mesh graph. For exact similarity evaluation purpose, the bidirectional histogram algorithm is applied to the spatial geometric constraints vectors to obtain the statistical histogram descriptors with fixed dimensionality, which is invariant to the number and the starting position of the curvature voxels. Our experimental results compared with the traditional methods validate the argument that the presented descriptors are invariant to different pollen particles geometric transformations （such as posing change and spatial rotation）, and high recognition precision and speed can be obtained simultaneously.展开更多
The dynamic parameters of multiple projectiles that are fired using multi-barrel weapons in highfrequency continuous firing modes are important indicators to measure the performance of these weapons.The characteristic...The dynamic parameters of multiple projectiles that are fired using multi-barrel weapons in highfrequency continuous firing modes are important indicators to measure the performance of these weapons.The characteristics of multiple projectiles are high randomness and large numbers launched in a short period of time,making it very difficult to obtain the real dispersion parameters of the projectiles due to the occlusion or coincidence of multiple projectiles.Using six intersecting-screen testing system,in this paper,we propose an association recognition and matching algorithm of multiple projectiles using a temporal and spatial information constraint mechanism.We extract the output signal from each detection screen and then use the wavelet transform to process the output signal.We present a method to identify and extract the time values on which the projectiles pass through the detection screens using the wavelet transform modulus maximum theory.We then use the correlation of the output signals of three parallel detection screens to establish a correlation coefficient recognition constraint function for the multiple projectiles.Based on the premise of linear projectile motion,we establish a temporal and spatial constraint matching model using the projectile’s position coordinates in each detection screen and the projectile’s time constraints within the multiple intersecting-screen geometry.We then determine the time values of the multiple projectiles in each detection screen using an iterative search cycle registration,and finally obtain the flight parameters for the multiple projectiles in the presence of uncertainty.The proposed method and algorithm were verified experimentally and can solve the problem of uncertainty in projectiles flight parameter under different multiple projectile firing states.展开更多
The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modem parallel mechanisms. However its range of ap...The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modem parallel mechanisms. However its range of application needs to further extend to general multi-loop spatial mechanism. This kind of mechanism is not only more complex in structure but also with strong motion coupling among loops, making the mobility analysis even more complicated, and the relevant research has long been ignored. It is focused on how to apply the new principle for general spatial mechanism to those various multi-loop spatial mechanisms, and some new meaningful knowledge is further found. Several typical examples of the genera/multi-loop spatial mechanisms with motion couple even strong motion couple are considered. These spatial mechanisms include different closing way： over-constraint appearing in rigid closure, in movable closure, and in dynamic closure as well; these examples also include two different new methods to solve this kind of issue： the way to recognize over-constraints by analyzing relative movement between two connected links and by constructing a virtual loop to recognize over-constraints. In addition, over-constraint determination tabulation is brought to analyze the motion couple. The researches above are all based upon the screw theory. All these multi-loop spatial mechanisms with different kinds of structures can completely be solved by following the directions and examples, and the new mobility theory based on the screw theory is also proved to be valid. This study not only enriches and develops the theory and makes the theory more universal, but also has a special meaning for innovation in mechanical engineering.展开更多
Since its inception,the Internet has been rapidly evolving.With the advancement of science and technology and the explosive growth of the population,the demand for the Internet has been on the rise.Many applications i...Since its inception,the Internet has been rapidly evolving.With the advancement of science and technology and the explosive growth of the population,the demand for the Internet has been on the rise.Many applications in education,healthcare,entertainment,science,and more are being increasingly deployed based on the internet.Concurrently,malicious threats on the internet are on the rise as well.Distributed Denial of Service(DDoS)attacks are among the most common and dangerous threats on the internet today.The scale and complexity of DDoS attacks are constantly growing.Intrusion Detection Systems(IDS)have been deployed and have demonstrated their effectiveness in defense against those threats.In addition,the research of Machine Learning(ML)and Deep Learning(DL)in IDS has gained effective results and significant attention.However,one of the challenges when applying ML and DL techniques in intrusion detection is the identification of unknown attacks.These attacks,which are not encountered during the system’s training,can lead to misclassification with significant errors.In this research,we focused on addressing the issue of Unknown Attack Detection,combining two methods:Spatial Location Constraint Prototype Loss(SLCPL)and Fuzzy C-Means(FCM).With the proposed method,we achieved promising results compared to traditional methods.The proposed method demonstrates a very high accuracy of up to 99.8%with a low false positive rate for known attacks on the Intrusion Detection Evaluation Dataset(CICIDS2017)dataset.Particularly,the accuracy is also very high,reaching 99.7%,and the precision goes up to 99.9%for unknown DDoS attacks on the DDoS Evaluation Dataset(CICDDoS2019)dataset.The success of the proposed method is due to the combination of SLCPL,an advanced Open-Set Recognition(OSR)technique,and FCM,a traditional yet highly applicable clustering technique.This has yielded a novel method in the field of unknown attack detection.This further expands the trend of applying DL and ML techniques in the development of intrusion detection systems and cybersecurity.Finally,implementing the proposed method in real-world systems can enhance the security capabilities against increasingly complex threats on computer networks.展开更多
The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into accou...The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into account not only the objects and relationships among objects but also spatial data schema (classification and aggregation hierarchy) associated with the final existing database.The operations perform the actions of generalization in support of data reduction in the database.The constraints in database generalization are still lack of research.There is still the lack of frameworks to express the constraints and the operations on the basis of object_oriented data structure in database generalization.This paper focuses on the frameworks for generalization operations and constraints on the basis of object_oriented data structure in database generalization.The constraints as the attributes of the object and the operations as the methods of the object can be encapsulated in classes.They have the inheritance and polymorphism property.So the framework of the constraints and the operations which are based on object_oriented data structure can be easily understood and implemented.The constraint and the operations based on object_oriented database are proposed based on object_oriented database.The frameworks for generalization operations,constraints and relations among objects based on object_oriented data structure in database generalization are designed.The categorical database generalization is concentrated on in this paper.展开更多
离轴非球面形状不对称且其表面曲率变化非线性,给面形高精度测量带来挑战。为解决现有离轴非球面面形测量方法高度依赖待测件初始调整位姿和曲率变化难适应的问题,本文提出了一种基于空间约束的差动共焦离轴非球面自适应测量方法,以实...离轴非球面形状不对称且其表面曲率变化非线性,给面形高精度测量带来挑战。为解决现有离轴非球面面形测量方法高度依赖待测件初始调整位姿和曲率变化难适应的问题,本文提出了一种基于空间约束的差动共焦离轴非球面自适应测量方法,以实现对离轴非球面的无初始位姿依赖、曲率变化自适应、高精度测量。首先,根据平移-回转扫描测量原理和差动共焦技术抗表面倾角精准定焦的性能,从规划测量点和待测点之间的距离和倾角两个维度出发,构建了空间约束模型,基于该模型,对等面积准则下的螺旋扫描路径规划算法进行优化,实现对离轴非球面测量路径的曲率自适应动态调整。使用该方法对离轴非球面和20°倾斜平面进行测量实验,将测量结果与Zygo干涉仪的测量结果点对点作差,面形差别的均方根(Root Mean Square,RMS)值均优于10 nm,对应3σ优于5 nm,满足离轴非球面的高精度测量要求。展开更多
基金supported by the National Program on Key Basic Research Project of China(973 Program)(No.2013CB036002,No.2014CB046901)the National Major Scientific Equipment Developed Special Project(No.51327802)+3 种基金National Natural Science Foundation of China(No.51139004,No.41102183)the Research Fund for the Doctoral Program of Higher Education of China(No.20110131120070)Natural Science Foundation of Shandong Province(No.ZR2011EEQ013)the Graduate Innovation Fund of Shandong University(No.YZC12083)
文摘To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.
基金supported by the basic and forward-looking project(No.2023YQX302)。
文摘Traditional deconvolution methods based on single-channel inversion do not consider the spatial structural relation between channels,and hence,they yield high-resolution results with the existing transverse inconsistency or discontinuity.Therefore,in this study,the local dip angle was used to obtain the structural information and construct the spatial structurally constraint operator.This operator is then introduced into multichannel deconvolution as a regularization operator to improve the resolution and maintain the transverse continuity of seismic data.Model tests and actual seismic data processing have demonstrated the effectiveness and practicability of this method.
文摘Non-negative matrix factorization （NMF） is a popular feature encoding method for image understanding due to its non-negative properties in representation, but the learnt basis images are not always local due to the lack of explicit constraints in its objective. Various algebraic or geometric local constraints are hence proposed to shape the behaviour of the original NMF. Such constraints are usually rigid in the sense that they have to be specified beforehand instead of learning from the data. In this paper, we propose a flexible spatial constraint method for NMF learning based on factor analysis. Particularly, to learn the local spatial structure of the images, we apply a series of transformations such as orthogonal rotation and thresholding to the factor loading matrix obtained through factor analysis. Then we map the transformed loading matrix into a Laplacian matrix and incorporate this into a max-margin non-negative matrix factorization framework as a penalty term, aiming to learn a representation space which is non-negative, discriminative and localstructure-preserving. We verify the feasibility and effectiveness of the proposed method on several real world datasets with encouraging results.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.61802197,62072449,and 61632003)the Science and Technology Development Fund,Macao SAR(Grant Nos.0018/2019/AKP and SKL-IOTSC(UM)-2021-2023)+1 种基金the Guangdong Science and Technology Department(Grant No.2020B1515130001)University of Macao(Grant Nos.MYRG2020-00253-FST and MYRG2022-00059-FST).
文摘We present a lightweight and efficient semisupervised video object segmentation network based on the space-time memory framework.To some extent,our method solves the two difficulties encountered in traditional video object segmentation:one is that the single frame calculation time is too long,and the other is that the current frame’s segmentation should use more information from past frames.The algorithm uses a global context(GC)module to achieve highperformance,real-time segmentation.The GC module can effectively integrate multi-frame image information without increased memory and can process each frame in real time.Moreover,the prediction mask of the previous frame is helpful for the segmentation of the current frame,so we input it into a spatial constraint module(SCM),which constrains the areas of segments in the current frame.The SCM effectively alleviates mismatching of similar targets yet consumes few additional resources.We added a refinement module to the decoder to improve boundary segmentation.Our model achieves state-of-the-art results on various datasets,scoring 80.1%on YouTube-VOS 2018 and a J&F score of 78.0%on DAVIS 2017,while taking 0.05 s per frame on the DAVIS 2016 validation dataset.
基金supported by the National Natural Science Foundation of China(Grant No.61375030)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20090149)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province,China(Grant No.08KJD520019)
文摘This paper presents one novel spatial geometric constraints histogram descriptors （SGCHD） based on curvature mesh graph for automatic three-dimensional （3D） pollen particles recognition. In order to reduce high dimensionality and noise disturbance arising from the abnormal record approach under microscopy, the separated surface curvature voxels are ex- tracted as primitive features to represent the original 3D pollen particles, which can also greatly reduce the computation time for later feature extraction process. Due to the good invariance to pollen rotation and scaling transformation, the spatial geometric constraints vectors are calculated to describe the spatial position correlations of the curvature voxels on the 3D curvature mesh graph. For exact similarity evaluation purpose, the bidirectional histogram algorithm is applied to the spatial geometric constraints vectors to obtain the statistical histogram descriptors with fixed dimensionality, which is invariant to the number and the starting position of the curvature voxels. Our experimental results compared with the traditional methods validate the argument that the presented descriptors are invariant to different pollen particles geometric transformations （such as posing change and spatial rotation）, and high recognition precision and speed can be obtained simultaneously.
基金been supported by Project of the National Natural Science Foundation of China(No.62073256)the Shaanxi Provincial Science and Technology Department(No.2020GY-125)Xi’an Science and Technology Innovation talent service enterprise project(No.2020KJRC0041)。
文摘The dynamic parameters of multiple projectiles that are fired using multi-barrel weapons in highfrequency continuous firing modes are important indicators to measure the performance of these weapons.The characteristics of multiple projectiles are high randomness and large numbers launched in a short period of time,making it very difficult to obtain the real dispersion parameters of the projectiles due to the occlusion or coincidence of multiple projectiles.Using six intersecting-screen testing system,in this paper,we propose an association recognition and matching algorithm of multiple projectiles using a temporal and spatial information constraint mechanism.We extract the output signal from each detection screen and then use the wavelet transform to process the output signal.We present a method to identify and extract the time values on which the projectiles pass through the detection screens using the wavelet transform modulus maximum theory.We then use the correlation of the output signals of three parallel detection screens to establish a correlation coefficient recognition constraint function for the multiple projectiles.Based on the premise of linear projectile motion,we establish a temporal and spatial constraint matching model using the projectile’s position coordinates in each detection screen and the projectile’s time constraints within the multiple intersecting-screen geometry.We then determine the time values of the multiple projectiles in each detection screen using an iterative search cycle registration,and finally obtain the flight parameters for the multiple projectiles in the presence of uncertainty.The proposed method and algorithm were verified experimentally and can solve the problem of uncertainty in projectiles flight parameter under different multiple projectile firing states.
基金Supported by National Natural Science Foundation of China(Grant No.51005195)Natural Science Research Fund for Youth in Higher Education Institutions of Hebei Province,China(Grant No.QN2014175)
文摘The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modem parallel mechanisms. However its range of application needs to further extend to general multi-loop spatial mechanism. This kind of mechanism is not only more complex in structure but also with strong motion coupling among loops, making the mobility analysis even more complicated, and the relevant research has long been ignored. It is focused on how to apply the new principle for general spatial mechanism to those various multi-loop spatial mechanisms, and some new meaningful knowledge is further found. Several typical examples of the genera/multi-loop spatial mechanisms with motion couple even strong motion couple are considered. These spatial mechanisms include different closing way： over-constraint appearing in rigid closure, in movable closure, and in dynamic closure as well; these examples also include two different new methods to solve this kind of issue： the way to recognize over-constraints by analyzing relative movement between two connected links and by constructing a virtual loop to recognize over-constraints. In addition, over-constraint determination tabulation is brought to analyze the motion couple. The researches above are all based upon the screw theory. All these multi-loop spatial mechanisms with different kinds of structures can completely be solved by following the directions and examples, and the new mobility theory based on the screw theory is also proved to be valid. This study not only enriches and develops the theory and makes the theory more universal, but also has a special meaning for innovation in mechanical engineering.
基金This research was partly supported by the National Science and Technology Council,Taiwan with Grant Numbers 112-2221-E-992-045,112-2221-E-992-057-MY3 and 112-2622-8-992-009-TD1.
文摘Since its inception,the Internet has been rapidly evolving.With the advancement of science and technology and the explosive growth of the population,the demand for the Internet has been on the rise.Many applications in education,healthcare,entertainment,science,and more are being increasingly deployed based on the internet.Concurrently,malicious threats on the internet are on the rise as well.Distributed Denial of Service(DDoS)attacks are among the most common and dangerous threats on the internet today.The scale and complexity of DDoS attacks are constantly growing.Intrusion Detection Systems(IDS)have been deployed and have demonstrated their effectiveness in defense against those threats.In addition,the research of Machine Learning(ML)and Deep Learning(DL)in IDS has gained effective results and significant attention.However,one of the challenges when applying ML and DL techniques in intrusion detection is the identification of unknown attacks.These attacks,which are not encountered during the system’s training,can lead to misclassification with significant errors.In this research,we focused on addressing the issue of Unknown Attack Detection,combining two methods:Spatial Location Constraint Prototype Loss(SLCPL)and Fuzzy C-Means(FCM).With the proposed method,we achieved promising results compared to traditional methods.The proposed method demonstrates a very high accuracy of up to 99.8%with a low false positive rate for known attacks on the Intrusion Detection Evaluation Dataset(CICIDS2017)dataset.Particularly,the accuracy is also very high,reaching 99.7%,and the precision goes up to 99.9%for unknown DDoS attacks on the DDoS Evaluation Dataset(CICDDoS2019)dataset.The success of the proposed method is due to the combination of SLCPL,an advanced Open-Set Recognition(OSR)technique,and FCM,a traditional yet highly applicable clustering technique.This has yielded a novel method in the field of unknown attack detection.This further expands the trend of applying DL and ML techniques in the development of intrusion detection systems and cybersecurity.Finally,implementing the proposed method in real-world systems can enhance the security capabilities against increasingly complex threats on computer networks.
文摘The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into account not only the objects and relationships among objects but also spatial data schema (classification and aggregation hierarchy) associated with the final existing database.The operations perform the actions of generalization in support of data reduction in the database.The constraints in database generalization are still lack of research.There is still the lack of frameworks to express the constraints and the operations on the basis of object_oriented data structure in database generalization.This paper focuses on the frameworks for generalization operations and constraints on the basis of object_oriented data structure in database generalization.The constraints as the attributes of the object and the operations as the methods of the object can be encapsulated in classes.They have the inheritance and polymorphism property.So the framework of the constraints and the operations which are based on object_oriented data structure can be easily understood and implemented.The constraint and the operations based on object_oriented database are proposed based on object_oriented database.The frameworks for generalization operations,constraints and relations among objects based on object_oriented data structure in database generalization are designed.The categorical database generalization is concentrated on in this paper.
基金Acknowledgements： This work is supported by Youth Foundation of Jilin University （No. 419070100102）, NSFC of China Major Research Program 60496321, Basic Theory and Core Techniques of Non Canonical Knowledge National Natural Science Foundation of China under Grant No. 60373098 and No. 60173006, the National High-Tech Research and Development Plan of China under Grant No.2003AA118020, the Major Program of Science and Technology Development Plan of Jilin Province under Grant No. 20020303, the Science and Technology Development Plan of Jilin Province under Grant No. 20030523.
文摘离轴非球面形状不对称且其表面曲率变化非线性,给面形高精度测量带来挑战。为解决现有离轴非球面面形测量方法高度依赖待测件初始调整位姿和曲率变化难适应的问题,本文提出了一种基于空间约束的差动共焦离轴非球面自适应测量方法,以实现对离轴非球面的无初始位姿依赖、曲率变化自适应、高精度测量。首先,根据平移-回转扫描测量原理和差动共焦技术抗表面倾角精准定焦的性能,从规划测量点和待测点之间的距离和倾角两个维度出发,构建了空间约束模型,基于该模型,对等面积准则下的螺旋扫描路径规划算法进行优化,实现对离轴非球面测量路径的曲率自适应动态调整。使用该方法对离轴非球面和20°倾斜平面进行测量实验,将测量结果与Zygo干涉仪的测量结果点对点作差,面形差别的均方根(Root Mean Square,RMS)值均优于10 nm,对应3σ优于5 nm,满足离轴非球面的高精度测量要求。
