Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable ...Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.展开更多
Obtaining a 3D feature description with high descriptiveness and robustness under complicated nuisances is a significant and challenging task in 3D feature matching.This paper proposes a novel feature description cons...Obtaining a 3D feature description with high descriptiveness and robustness under complicated nuisances is a significant and challenging task in 3D feature matching.This paper proposes a novel feature description consisting of a stable local reference frame(LRF)and a feature descriptor based on local spatial voxels.First,an improved LRF was designed by incorporating distance weights into Z-and X-axis calculations.Subsequently,based on the LRF and voxel segmentation,a feature descriptor based on voxel homogenization was proposed.Moreover,uniform segmentation of cube voxels was performed,considering the eigenvalues of each voxel and its neighboring voxels,thereby enhancing the stability of the description.The performance of the descriptor was strictly tested and evaluated on three public datasets,which exhibited high descriptiveness,robustness,and superior performance compared with other current methods.Furthermore,the descriptor was applied to a 3D registration trial,and the results demonstrated the reliability of our approach.展开更多
A fast local reference frame(LRF)construction method based on the signed surface variation is proposed,which can adapt to the real-time applications such as self-driving,face recognition,object detection.The z-axis of...A fast local reference frame(LRF)construction method based on the signed surface variation is proposed,which can adapt to the real-time applications such as self-driving,face recognition,object detection.The z-axis of the LRF is generated based on the concavity of the local surface of keypoint.The x-axis is constructed by the weighted vector sum of a set of projection vectors of the local neighborhoods around keypoint.The performance of the proposed LRF is evaluated on six standard datasets and compared with six state-of-the-art LRF construction methods(e.g.,BOARD,FLARE,SHOT,RoPS and TOLDI).Experimental results validate the high repeatability,robustness,universality and time efficiency of our method.展开更多
We consider Gabor localization operators ?defined by two parameters, the generating function ?of a tight Gabor frame , indexed by a lattice , and a domain ?whose boundary consists of line segments connecting certain p...We consider Gabor localization operators ?defined by two parameters, the generating function ?of a tight Gabor frame , indexed by a lattice , and a domain ?whose boundary consists of line segments connecting certain points of . We provide an explicit formula for the boundary form , the normalized limit of the projection functional , where ?are the eigenvalues of the localization operators ?applied to dilated domains , R is an integer and is the area of the fundamental domain. The boundary form expresses quantitatively the asymptotic interactions between the generating function ?and the oriented boundary ?from the point of view of the projection functional, which measures to what degree a given trace class operator fails to be an orthogonal projection. Keeping the area of the localization domain ?bounded above corresponds to controlling the relative dimensionality of the localization problem.展开更多
According to the issues that the predict errors of chaotic sequences rapidly accumulated in multi-step forecasting which affects the predict accuracy, we proposed a new predict algorithm based on local modeling with v...According to the issues that the predict errors of chaotic sequences rapidly accumulated in multi-step forecasting which affects the predict accuracy, we proposed a new predict algorithm based on local modeling with variable frame length and interpolation points. The core idea is that, using interpolation method to increase the available sample data, then modeling the chaos dynamics system with least square algorithm which based on the Bernstein polynomial to realize the forecasting. We use the local modeling method, looking for the optimum frame length and interpolation points in every frame to improve the predict peformance. The experimental results show that the proposed algorithm can improve the predictive ability effectively, decreasing the accumulation of iterative errors in multi-step prediction.展开更多
In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of po...In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.展开更多
传统的基于形状信息目标定位算法,对目标发生形变及其阻挡的情况下的检测存在较大的困难。为此,本文提出一种基于非齐次FRAME(Inhomogeneous Filters,Random filed,And Maximum Entropy,缩写IFRAME)模型的感兴趣目标检测算法,该模型由...传统的基于形状信息目标定位算法,对目标发生形变及其阻挡的情况下的检测存在较大的困难。为此,本文提出一种基于非齐次FRAME(Inhomogeneous Filters,Random filed,And Maximum Entropy,缩写IFRAME)模型的感兴趣目标检测算法,该模型由能在位置和方向进行局部扰动的基函数组成,是一种可变形模板,因此一定程度上提高定位算法在物体发生形变情况下的鲁棒性。经过多组实验结果表明,本文所提出的算法能较好地解决目标在发生形变、存在遮挡以及复杂背景下的定位问题。展开更多
This paper reports our study of a novel motion estimation algorithm based on global and local compensability analysis. The spatial correlation of motion field is used to reduce the burden of estimation computation and...This paper reports our study of a novel motion estimation algorithm based on global and local compensability analysis. The spatial correlation of motion field is used to reduce the burden of estimation computation and extra bit rate for motion vectors. Experimental results show that this algorithm is more efficient than the conventional methods, especially for temporal activity regions.展开更多
Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ∈ H is called a continuous frame wavelet if there exist A, B 〉 0 such that A｜｜Ф｜｜2≤fG｜...Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ∈ H is called a continuous frame wavelet if there exist A, B 〉 0 such that A｜｜Ф｜｜2≤fG｜〈π（G）ψ,Ф｜2dg≤B｜｜Ф｜｜2（Ф∈H）,in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.展开更多
基金supported by NBHM, Department of Atomic Energy, Government of India (Grant No. 2/48(8)/2016/NBHM(R.P)/R&D II/13924)
文摘Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.
基金the National Natural Science Foundation of China,No.51705469the Zhengzhou University Youth Talent Enterprise Cooperative Innovation Team Support Program Project(2021,2022).
文摘Obtaining a 3D feature description with high descriptiveness and robustness under complicated nuisances is a significant and challenging task in 3D feature matching.This paper proposes a novel feature description consisting of a stable local reference frame(LRF)and a feature descriptor based on local spatial voxels.First,an improved LRF was designed by incorporating distance weights into Z-and X-axis calculations.Subsequently,based on the LRF and voxel segmentation,a feature descriptor based on voxel homogenization was proposed.Moreover,uniform segmentation of cube voxels was performed,considering the eigenvalues of each voxel and its neighboring voxels,thereby enhancing the stability of the description.The performance of the descriptor was strictly tested and evaluated on three public datasets,which exhibited high descriptiveness,robustness,and superior performance compared with other current methods.Furthermore,the descriptor was applied to a 3D registration trial,and the results demonstrated the reliability of our approach.
基金Youth Program of National Natural Science Foundation of China(Nos.41901415,61801481)。
文摘A fast local reference frame(LRF)construction method based on the signed surface variation is proposed,which can adapt to the real-time applications such as self-driving,face recognition,object detection.The z-axis of the LRF is generated based on the concavity of the local surface of keypoint.The x-axis is constructed by the weighted vector sum of a set of projection vectors of the local neighborhoods around keypoint.The performance of the proposed LRF is evaluated on six standard datasets and compared with six state-of-the-art LRF construction methods(e.g.,BOARD,FLARE,SHOT,RoPS and TOLDI).Experimental results validate the high repeatability,robustness,universality and time efficiency of our method.
文摘We consider Gabor localization operators ?defined by two parameters, the generating function ?of a tight Gabor frame , indexed by a lattice , and a domain ?whose boundary consists of line segments connecting certain points of . We provide an explicit formula for the boundary form , the normalized limit of the projection functional , where ?are the eigenvalues of the localization operators ?applied to dilated domains , R is an integer and is the area of the fundamental domain. The boundary form expresses quantitatively the asymptotic interactions between the generating function ?and the oriented boundary ?from the point of view of the projection functional, which measures to what degree a given trace class operator fails to be an orthogonal projection. Keeping the area of the localization domain ?bounded above corresponds to controlling the relative dimensionality of the localization problem.
文摘According to the issues that the predict errors of chaotic sequences rapidly accumulated in multi-step forecasting which affects the predict accuracy, we proposed a new predict algorithm based on local modeling with variable frame length and interpolation points. The core idea is that, using interpolation method to increase the available sample data, then modeling the chaos dynamics system with least square algorithm which based on the Bernstein polynomial to realize the forecasting. We use the local modeling method, looking for the optimum frame length and interpolation points in every frame to improve the predict peformance. The experimental results show that the proposed algorithm can improve the predictive ability effectively, decreasing the accumulation of iterative errors in multi-step prediction.
文摘In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.
文摘传统的基于形状信息目标定位算法,对目标发生形变及其阻挡的情况下的检测存在较大的困难。为此,本文提出一种基于非齐次FRAME(Inhomogeneous Filters,Random filed,And Maximum Entropy,缩写IFRAME)模型的感兴趣目标检测算法,该模型由能在位置和方向进行局部扰动的基函数组成,是一种可变形模板,因此一定程度上提高定位算法在物体发生形变情况下的鲁棒性。经过多组实验结果表明,本文所提出的算法能较好地解决目标在发生形变、存在遮挡以及复杂背景下的定位问题。
文摘This paper reports our study of a novel motion estimation algorithm based on global and local compensability analysis. The spatial correlation of motion field is used to reduce the burden of estimation computation and extra bit rate for motion vectors. Experimental results show that this algorithm is more efficient than the conventional methods, especially for temporal activity regions.
文摘Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ∈ H is called a continuous frame wavelet if there exist A, B 〉 0 such that A｜｜Ф｜｜2≤fG｜〈π（G）ψ,Ф｜2dg≤B｜｜Ф｜｜2（Ф∈H）,in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.
