In the digital world,a wide range of handwritten and printed documents should be converted to digital format using a variety of tools,including mobile phones and scanners.Unfortunately,this is not an optimal procedure...In the digital world,a wide range of handwritten and printed documents should be converted to digital format using a variety of tools,including mobile phones and scanners.Unfortunately,this is not an optimal procedure,and the entire document image might be degraded.Imperfect conversion effects due to noise,motion blur,and skew distortion can lead to significant impact on the accuracy and effectiveness of document image segmentation and analysis in Optical Character Recognition(OCR)systems.In Document Image Analysis Systems(DIAS),skew estimation of images is a crucial step.In this paper,a novel,fast,and reliable skew detection algorithm based on the Radon Transform and Curve Length Fitness Function(CLF),so-called Radon CLF,was proposed.The Radon CLF model aims to take advantage of the properties of Radon spaces.The Radon CLF explores the dominating angle more effectively for a 1D signal than it does for a 2D input image due to an innovative fitness function formulation for a projected signal of the Radon space.Several significant performance indicators,including Mean Square Error(MSE),Mean Absolute Error(MAE),Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Measure(SSIM),Accuracy,and run-time,were taken into consideration when assessing the performance of our model.In addition,a new dataset named DSI5000 was constructed to assess the accuracy of the CLF model.Both two-dimensional image signal and the Radon space have been used in our simulations to compare the noise effect.Obtained results show that the proposed method is more effective than other approaches already in use,with an accuracy of roughly 99.87%and a run-time of 0.048(s).The introduced model is far more accurate and timeefficient than current approaches in detecting image skew.展开更多
A novel and efficient approach for detecting wood texture orientation by computer was presented. Four Matlab functions were tried to describe the relative position and orientation of wood texture pixels, to detect tex...A novel and efficient approach for detecting wood texture orientation by computer was presented. Four Matlab functions were tried to describe the relative position and orientation of wood texture pixels, to detect texture shape and to create skeletal lines image of wood texture, and BWMORPH function was found the best one. Then by Radon transform, it generated a signature composed of 180 values, each value summing up the size of texture lines that are shaped along that angle, and a two dimensional curve plot was drawn to represent the texture orientation of wood. Furthermore, it analyzed texture orientations of forty species as well as their general statistic laws, classified by softwood, hardwood, radial section and tangential section, and the results showed that texture orientation laws described by Radon trans- form plot and their extracting datum were in accord with the impression of wood texture that people possessed in daily life, which con- firmed the validity of this new approach and their appealing utilization potentials.展开更多
The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means ...The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.展开更多
The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads...The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.展开更多
In this work, the image reconstruction in π-scheme short-scan single-photon emission computed tomography （SPECT） with nonuniform attenuation is derived in its most general form when π-scheme short-scan SPECT entai...In this work, the image reconstruction in π-scheme short-scan single-photon emission computed tomography （SPECT） with nonuniform attenuation is derived in its most general form when π-scheme short-scan SPECT entails data acquisition over disjoint angular intervals without conjugate views totaling to π radians. The reconstruction results are based on decomposition of Novikov＇s inversion operator into three parts bounded in the L2 sense. The first part involves the measured partial data; the second part is a skew-symmetric operator; the third part is a symmetric and compact contribution. It is showed firstly that the operators involved belong to L（L^2（B）. Furthermore numerical simulations are conducted to demonstrate the effectiveness of the developed method.展开更多
This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates th...This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.展开更多
The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-bac...The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-backprojection （FBP） algorithm based on the Radon inversion transform is presented to deal with the three-dimensional （3D） local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography （ATRACT）, not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.展开更多
The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction ...The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction of a singular value decomposition for R. This immediately leads to an inversion formula by series expansion and range characterizations.展开更多
The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new image- watermarking method is presented to resist ...The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new image- watermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually. Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.展开更多
Using the technique of integration within an ordered product of operators, we reveal that a new quantum mechanical representation |x,μ,v > exsit, the eigenvector of operator μQ+vP (linear combination of coordinat...Using the technique of integration within an ordered product of operators, we reveal that a new quantum mechanical representation |x,μ,v > exsit, the eigenvector of operator μQ+vP (linear combination of coordinate Q and momentum P) with eigenvalue x, which is inherent to the two-parameter(μ,v) Radon transformation of the Wigner operator. It turns out that the projection operator |x,μ,v > < x,μ,v | is just the Radon transformation of the Wigner operator. The inverse of operator Radon transformation is also derived which indicates tomography in operator version.展开更多
The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transf...The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.展开更多
In multi-LFM signal condition, Radon-Ambiguity Transform (RAT) of the strongLFM component has strong suppression effect on that of the weak LFM component. A methodnamed as Recursive Filtering RAT (RFRAT) Mgorithm is p...In multi-LFM signal condition, Radon-Ambiguity Transform (RAT) of the strongLFM component has strong suppression effect on that of the weak LFM component. A methodnamed as Recursive Filtering RAT (RFRAT) Mgorithm is proposed for solving this problem. Byfully using of the Maximum Likelihood (ML) estimation value of the frequency modulation rategot by RAT. RFRAT can detect the noisy multi-LFM signals out step by step. The merit of thisnew method is validated by an illustrative example in low Signal-to-Noise-Ratio (SNR) condition.展开更多
Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin...Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.展开更多
The Radon-ambiguity transform （RAT）, although efficient for detecting the linear frequency modulated signals （LFMs）, is troubled by the energy accumulation of noise in low signal-to-noise ratio （SNR）. A secondor...The Radon-ambiguity transform （RAT）, although efficient for detecting the linear frequency modulated signals （LFMs）, is troubled by the energy accumulation of noise in low signal-to-noise ratio （SNR）. A secondorder difference （SOD） method is proposed to treat with this problem. In the SOD method, the optimal search step and difference step are derived from the LFM rate resolution formula. The sharpness of the peaks of RAT is measured by curvature, and the sharpness, but not the magnitude of the peaks, is used to detect the LFMs. The SOD method removes the noise energy accumulation and reserves the drastically changing components integrally; thus, it improves the detection probability of LFMs in low SNR. The expected performance of the new method is verified by 100 Monte Carlo simulations.展开更多
A novel method of rotated window Radon transform is developed for identifying the linear texture in SAR image.It is applied to automatic detection of the ship wakes of SEASAT SAR image.The location and direction of th...A novel method of rotated window Radon transform is developed for identifying the linear texture in SAR image.It is applied to automatic detection of the ship wakes of SEASAT SAR image.The location and direction of the traveling ship can be quickly and accurately detectec,In some cases, the ship velocity can also be obtained.展开更多
基金funded by the Basic Research and Strategic Reserve Technology Research Fund Project of CNPC (2019D-500803)the national oil and gas project (2016zx05007-006)。
文摘In the digital world,a wide range of handwritten and printed documents should be converted to digital format using a variety of tools,including mobile phones and scanners.Unfortunately,this is not an optimal procedure,and the entire document image might be degraded.Imperfect conversion effects due to noise,motion blur,and skew distortion can lead to significant impact on the accuracy and effectiveness of document image segmentation and analysis in Optical Character Recognition(OCR)systems.In Document Image Analysis Systems(DIAS),skew estimation of images is a crucial step.In this paper,a novel,fast,and reliable skew detection algorithm based on the Radon Transform and Curve Length Fitness Function(CLF),so-called Radon CLF,was proposed.The Radon CLF model aims to take advantage of the properties of Radon spaces.The Radon CLF explores the dominating angle more effectively for a 1D signal than it does for a 2D input image due to an innovative fitness function formulation for a projected signal of the Radon space.Several significant performance indicators,including Mean Square Error(MSE),Mean Absolute Error(MAE),Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Measure(SSIM),Accuracy,and run-time,were taken into consideration when assessing the performance of our model.In addition,a new dataset named DSI5000 was constructed to assess the accuracy of the CLF model.Both two-dimensional image signal and the Radon space have been used in our simulations to compare the noise effect.Obtained results show that the proposed method is more effective than other approaches already in use,with an accuracy of roughly 99.87%and a run-time of 0.048(s).The introduced model is far more accurate and timeefficient than current approaches in detecting image skew.
文摘A novel and efficient approach for detecting wood texture orientation by computer was presented. Four Matlab functions were tried to describe the relative position and orientation of wood texture pixels, to detect texture shape and to create skeletal lines image of wood texture, and BWMORPH function was found the best one. Then by Radon transform, it generated a signature composed of 180 values, each value summing up the size of texture lines that are shaped along that angle, and a two dimensional curve plot was drawn to represent the texture orientation of wood. Furthermore, it analyzed texture orientations of forty species as well as their general statistic laws, classified by softwood, hardwood, radial section and tangential section, and the results showed that texture orientation laws described by Radon trans- form plot and their extracting datum were in accord with the impression of wood texture that people possessed in daily life, which con- firmed the validity of this new approach and their appealing utilization potentials.
文摘The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.
基金Supported by the National Natural Science F oundation of China( No.199710 6 4) ,Key Project of Science and Tech-nology of Hubei Province Education Com mittee
文摘The exponential Radon transform, a generalization of the Radon transform, is defined and studied as a mapping of function spaces. It is represented in terms of Fourier transform of its domain and range, and this leads to the harmonic decomposition reconstruction. The results are similar results of Tretiak and Metz.
基金supported by the National Natural Science Foundation of China(61271398)K.C.Wong Magna Fund in Ningbo University
文摘In this work, the image reconstruction in π-scheme short-scan single-photon emission computed tomography （SPECT） with nonuniform attenuation is derived in its most general form when π-scheme short-scan SPECT entails data acquisition over disjoint angular intervals without conjugate views totaling to π radians. The reconstruction results are based on decomposition of Novikov＇s inversion operator into three parts bounded in the L2 sense. The first part involves the measured partial data; the second part is a skew-symmetric operator; the third part is a symmetric and compact contribution. It is showed firstly that the operators involved belong to L（L^2（B）. Furthermore numerical simulations are conducted to demonstrate the effectiveness of the developed method.
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603)
文摘The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography （CT）, which creates the possibility for dose reduction. In this paper, a filtered-backprojection （FBP） algorithm based on the Radon inversion transform is presented to deal with the three-dimensional （3D） local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography （ATRACT）, not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.
基金Supported by the Foundation of the Ministry of Education of China and the Science Foundation of Wuhan University
文摘The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL 2-spaces. Our result is the explicit construction of a singular value decomposition for R. This immediately leads to an inversion formula by series expansion and range characterizations.
文摘The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new image- watermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually. Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.
基金Supported by the National Natural Sciences Foundation of China and President Foundation of Chinese Academy of Sciences.
文摘Using the technique of integration within an ordered product of operators, we reveal that a new quantum mechanical representation |x,μ,v > exsit, the eigenvector of operator μQ+vP (linear combination of coordinate Q and momentum P) with eigenvalue x, which is inherent to the two-parameter(μ,v) Radon transformation of the Wigner operator. It turns out that the projection operator |x,μ,v > < x,μ,v | is just the Radon transformation of the Wigner operator. The inverse of operator Radon transformation is also derived which indicates tomography in operator version.
基金supported by the National Natural Science Foundation of China(61271398)K.C.Wong Magna Fund in Ningbo UniversityNatural Science Foundation of Ningbo City(2010A610102)
文摘The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.
基金Supported by the National 973 Program(No.973-1-12)
文摘In multi-LFM signal condition, Radon-Ambiguity Transform (RAT) of the strongLFM component has strong suppression effect on that of the weak LFM component. A methodnamed as Recursive Filtering RAT (RFRAT) Mgorithm is proposed for solving this problem. Byfully using of the Maximum Likelihood (ML) estimation value of the frequency modulation rategot by RAT. RFRAT can detect the noisy multi-LFM signals out step by step. The merit of thisnew method is validated by an illustrative example in low Signal-to-Noise-Ratio (SNR) condition.
基金Supported by the Foundation of the National Natural Science of China( No.1 0 0 71 0 39) and the Foundation of Edu-cation Commission of Jiangsu Province
文摘Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
基金supported by the Program for New Century Excellent Talents in University, Ministry of Education (NCET-05-0803)
文摘The Radon-ambiguity transform （RAT）, although efficient for detecting the linear frequency modulated signals （LFMs）, is troubled by the energy accumulation of noise in low signal-to-noise ratio （SNR）. A secondorder difference （SOD） method is proposed to treat with this problem. In the SOD method, the optimal search step and difference step are derived from the LFM rate resolution formula. The sharpness of the peaks of RAT is measured by curvature, and the sharpness, but not the magnitude of the peaks, is used to detect the LFMs. The SOD method removes the noise energy accumulation and reserves the drastically changing components integrally; thus, it improves the detection probability of LFMs in low SNR. The expected performance of the new method is verified by 100 Monte Carlo simulations.
基金Supported by the National Natural Science Foundation of China(No.49831060,No.69771007),and National Defense Foundation
文摘A novel method of rotated window Radon transform is developed for identifying the linear texture in SAR image.It is applied to automatic detection of the ship wakes of SEASAT SAR image.The location and direction of the traveling ship can be quickly and accurately detectec,In some cases, the ship velocity can also be obtained.
