The quaternion Fourier transform plays a vital role in the representation of two-dimensional signals. This paper characterizes spectrum of quaternion-valued signals on the quaternion Fourier transform domain by the pa...The quaternion Fourier transform plays a vital role in the representation of two-dimensional signals. This paper characterizes spectrum of quaternion-valued signals on the quaternion Fourier transform domain by the partial derivative.展开更多
With the improvement of people’s security awareness,numerous monitoring equipment has been put into use,resulting in the explosive growth of surveillance video data.Key frame extraction technology is a paramount tech...With the improvement of people’s security awareness,numerous monitoring equipment has been put into use,resulting in the explosive growth of surveillance video data.Key frame extraction technology is a paramount technology for improving video storage efficiency and enhancing the accuracy of video retrieval.It can extract key frame sets that can express video content from massive videos.However,the existing key frame extraction algorithms of surveillance video still have deficiencies,such as the destruction of image information integrity and the inability to extract key frames accurately.To this end,this paper proposes a key frame extraction algorithm of surveillance video based on quaternion Fourier saliency detection.Firstly,the algorithm used colors,and intensity features to perform quaternion Fourier transform on surveillance video sequences.Next,the phase spectrum of the quaternion Fourier transformed image was obtained,and he image visual saliency map was obtained according to the quaternion Fourier phase spectrum.Then,the image visual saliency map of two adjacent frames is used to characterize the change of target motion state.Finally,the frames that can accurately express the motion state of the target are selected as key frames.The experimental results show that the method proposed in this paper can accurately capture the changes of the local motion state of the target while maintaining the integrity of the image information.展开更多
This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selec...This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selecting suitable parameters to handle different levels of noise.In particular,the quaternion analytic signal,which is an effective tool in color image processing,can also be produced by quaternion Hardy filtering with specific parameters.Based on the QHF and the improved Di Zenzo gradient operator,a novel color edge detection algorithm is proposed;importantly,it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique.From the experimental results,we conclude that the minimum PSNR improvement rate is 2.3%and the minimum SSIM improvement rate is 30.2%on the CSEE database.The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.展开更多
The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quatern...The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms.In addition,the relationships among different types of sampling formulas under various transforms are discussed.First,if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are identical.If this rectangle is not symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are different from each other.Second,using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform,we derive sampling formulas under various quaternion linear canonical transforms.Third,truncation errors of these sampling formulas are estimated.Finally,some simulations are provided to show how the sampling formulas can be used in applications.展开更多
The Fourier transform for homogeneous vector bundles over quaternion unit disk is studied, and the corresponding inversion formula and Plancherel formula are established.
文摘The quaternion Fourier transform plays a vital role in the representation of two-dimensional signals. This paper characterizes spectrum of quaternion-valued signals on the quaternion Fourier transform domain by the partial derivative.
基金spported by he key-area andevelopment programof Guangdongprovince(Grant No.2019B01013700)National Nature Science Foundation of China(Grant No.61702347)+2 种基金Natural Science Foundation of Hebei Province(Grant No.F2017210161)Science andTechnology Research Project of Higher Education in Hebei Province(Grant No.QN2017132)Graduate Innovation Program(Grant No.YC2022051).
文摘With the improvement of people’s security awareness,numerous monitoring equipment has been put into use,resulting in the explosive growth of surveillance video data.Key frame extraction technology is a paramount technology for improving video storage efficiency and enhancing the accuracy of video retrieval.It can extract key frame sets that can express video content from massive videos.However,the existing key frame extraction algorithms of surveillance video still have deficiencies,such as the destruction of image information integrity and the inability to extract key frames accurately.To this end,this paper proposes a key frame extraction algorithm of surveillance video based on quaternion Fourier saliency detection.Firstly,the algorithm used colors,and intensity features to perform quaternion Fourier transform on surveillance video sequences.Next,the phase spectrum of the quaternion Fourier transformed image was obtained,and he image visual saliency map was obtained according to the quaternion Fourier phase spectrum.Then,the image visual saliency map of two adjacent frames is used to characterize the change of target motion state.Finally,the frames that can accurately express the motion state of the target are selected as key frames.The experimental results show that the method proposed in this paper can accurately capture the changes of the local motion state of the target while maintaining the integrity of the image information.
基金supported in part by the Science and Technology Development Fund,Macao SAR FDCT/085/2018/A2the Guangdong Basic and Applied Basic Research Foundation(2019A1515111185)。
文摘This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selecting suitable parameters to handle different levels of noise.In particular,the quaternion analytic signal,which is an effective tool in color image processing,can also be produced by quaternion Hardy filtering with specific parameters.Based on the QHF and the improved Di Zenzo gradient operator,a novel color edge detection algorithm is proposed;importantly,it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique.From the experimental results,we conclude that the minimum PSNR improvement rate is 2.3%and the minimum SSIM improvement rate is 30.2%on the CSEE database.The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.
基金the Research Development Foundation of Wenzhou Medical UniversityChina(No.QTJ18012)+6 种基金the Wenzhou Science and Technology Bureau of China(No.G2020031)the Guangdong Basic and Applied Basic Research Foundation of China(No.2019A1515111185)the Science and Technology Development FundMacao Special Administrative RegionChina(No.FDCT/085/2018/A2)the University of MacaoChina(No.MYRG2019-00039-FST)。
文摘The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms.In addition,the relationships among different types of sampling formulas under various transforms are discussed.First,if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are identical.If this rectangle is not symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are different from each other.Second,using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform,we derive sampling formulas under various quaternion linear canonical transforms.Third,truncation errors of these sampling formulas are estimated.Finally,some simulations are provided to show how the sampling formulas can be used in applications.
文摘The Fourier transform for homogeneous vector bundles over quaternion unit disk is studied, and the corresponding inversion formula and Plancherel formula are established.
