Background:This retrospective study was designed to investigate the sole influence of orthokeratology(OK)lens fitting decentration on the Zernike coefficients of the reshaped anterior corneal surface.Methods:This stud...Background:This retrospective study was designed to investigate the sole influence of orthokeratology(OK)lens fitting decentration on the Zernike coefficients of the reshaped anterior corneal surface.Methods:This study comprised a review of 106 right eyes and measurements of corneal topography both before OK and at 1-month follow-up visit.A routine was designed to calculate local corneal surface astigmatism and assist the determination of OK lens fitting decentration from pupil center.The pupil-centered corneal Zernike coefficients of baseline(PCCB)and post-treatment(PCCP)were calculated.Meanwhile,the OK-lens-centered corneal Zernike coefficients of post-treatment(OCCP)were also calculated and considered as the presumptive ideal fitting group without decentration.Relationships between lens fitting decentration and the change of Zernike coefficients including(PCCP−PCCB)and(PCCP−OCCP)were analyzed.Results:Patients with a mean age of 11±2.36 years old had an average spherical equivalent refractive error of−3.52±1.06 D before OK.One month after treatment,OK lens fitting decentration from pupil center was 0.68±0.35 mm.RMS of 3rd-order(P<0.05),RMS of 4th-order(P<0.001)and RMS of total high order(P<0.001)corneal Zernike coefficients were increased in PCCP by comparing with OCCP,which was solely caused by lens fitting decentration.Nevertheless,no significant difference was observed in C^(0)_(2)(P>0.05).For the high order corneal Zernike coefficients in(PCCP–OCCP),radial distance of decentration was correlated with C^(−1)_(3)(r=−0.296,P<0.05),C^(1)_(3)(r=−0.396,P<0.001),and C^(0)_(4)(r=0.449,P<0.001),horizontal decentration was significantly correlated with C^(1)_(3)(r=0.901,P<0.001)and C^(1)_(5)(r=0.340,P<0.001),and vertical decentration was significantly correlated with C^(−1)_(3)(r=0.904,P<0.001).Conclusions:OK lens fitting decentration within 1.5 mm hardly influenced the change of corneal spherical power for myopia correction,but significantly induced additional corneal high order Zernike coefficien展开更多
Conformal domes that are shaped to meet aerodynamic requirements can increase range and speed for the host platform. Because these domes typically deviate greatly from spherical surface descriptions, a variety of aber...Conformal domes that are shaped to meet aerodynamic requirements can increase range and speed for the host platform. Because these domes typically deviate greatly from spherical surface descriptions, a variety of aberrations are induced which vary with the field-of-regard （FOR） angle. A system for correcting optical aberrations created by a conformal dome has an outer surface and an inner surface. Optimizing the inner surface is regard as static aberration correction. A deformable mirror is placed at the position of the secondary mirror in the two-mirror all reflective imaging system, which is the dynamic aberration correction. An ellipsoidal MgF2 conformal dome with a fineness ratio of 1.0 is designed as an example. The FOR angle is 0°-30°, and the design wavelength is 4μm. After the optimization at 7 zoom positions by using the design tools Code V, the root-mean-square （RMS） spot size is reduced to approximately 0.99 to 1.48 times the diffraction limit. The design results show that the performances of the conformal optical systems can be greatly improved by the combination of the static correction and the dynamic correction.展开更多
Vibration mode shape description of an aero-engine casing structure using Zernike moment descriptor(ZMD) was introduced in this paper.The mode shapes of the aero-engine casing structure can be decomposed as a linear c...Vibration mode shape description of an aero-engine casing structure using Zernike moment descriptor(ZMD) was introduced in this paper.The mode shapes of the aero-engine casing structure can be decomposed as a linear combination of a series of Zernike polynomials,with the feature of each Zernike polynomial reflecting a part of characteristic of mode shapes,based on Zernike moment transformation.Meanwhile,the reconstruction of mode shapes with ZMD was explored and its ability to filtering the noise contaminated in the mode shapes was studied.Simulation of the aero-engine casing structure indicated the advantage of this method to depict the mode shapes of a symmetric structure.Results demonstrate that the Zernike moment description of the mode shapes can effectively describe the double modes in the symmetric structure and also has the ability to remove or significantly reduce the influence of noise in the mode shapes.Such feature shows great practical value for further research on the correlation,model updating and model validation of the symmetric structure's finite element model.展开更多
We propose a new algorithm for wavefront sensing based on binary intensity modulation. The algorithm is based on the fact that a wavefront can be expended with a series of orthogonal and binary functions, the Walsh se...We propose a new algorithm for wavefront sensing based on binary intensity modulation. The algorithm is based on the fact that a wavefront can be expended with a series of orthogonal and binary functions, the Walsh series. We use a spatial light modulator（SLM） to produce different binary-intensity-modulation patterns which are the simple linear transformation of the Walsh series. The optical fields under different binary-intensity-modulation patterns are detected with a photodiode.The relationships between the incident wavefront modulated with the patterns and their optical fields are built to determinate the coefficients of the Walsh series. More detailed and strict relationship equations are established with the algorithm by adding new modulation patterns according to the properties of the Walsh functions. An exact value can be acquired by solving the equations. Finally, with the help of phase unwrapping and smoothing, the wavefront can be reconstructed. The advantage of the algorithm is providing an analytical solution for the coefficients of the Walsh series to reconstruct the wavefront. The simulation experiments are presented and the effectiveness of the algorithm is demonstrated.展开更多
The image shape feature can be described by the image Zernike moments. In this paper, we points out the problem that the high dimension image Zernike moments shape feature vector can describe more detail of the origin...The image shape feature can be described by the image Zernike moments. In this paper, we points out the problem that the high dimension image Zernike moments shape feature vector can describe more detail of the original image but has too many elements making trouble for the next image analysis phases. Then the low dimension image Zernike moments shape feature vector should be improved and optimized to describe more detail of the original image. So the optimization algorithm based on evolutionary computation is designed and implemented in this paper to solve this problem. The experimental results demonstrate the feasibility of the optimization algorithm.展开更多
In this paper, illumination-affine invariant methods are presented based onaffine moment normalization techniques, Zernike moments, and multiband correlation functions. Themethods are suitable for the illumination inv...In this paper, illumination-affine invariant methods are presented based onaffine moment normalization techniques, Zernike moments, and multiband correlation functions. Themethods are suitable for the illumination invariant recognition of 3D color texture. Complex valuedmoments (i.e., Zernike moments) and affine moment normalization are used in the derivation ofillumination affine invariants where the real valued affine moment invariants fail to provide affineinvariants that are independent of illumination changes. Three different moment normalizationmethods have been used, two of which are based on affine moment normalization technique and thethird is based on reducing the affine transformation to a Euclidian transform. It is shown that fora change of illumination and orientation, the affinely normalized Zernike moment matrices arerelated by a linear transform. Experimental results are obtained in two tests: the first is usedwith textures of outdoor scenes while the second is performed on the well-known CUReT texturedatabase. Both tests show high recognition efficiency of the proposed recognition methods.展开更多
An effective algorithm is proposed to detect copy-move forgery.In this algorithm,first,the PatchMatch algorithm is improved by using a reliable order-statistics-based approximate nearest neighbor search algorithm(ROSA...An effective algorithm is proposed to detect copy-move forgery.In this algorithm,first,the PatchMatch algorithm is improved by using a reliable order-statistics-based approximate nearest neighbor search algorithm(ROSANNA)to modify the propagation process.Then,fractional quaternion Zernike moments(FrQZMs)are considered to be features extracted from color forged images.Finally,the extracted FrQZMs features are matched by the improved PatchMatch algorithm.The experimental results on two publicly available datasets(FAU and GRIP datasets)show that the proposed algorithm performs better than the state-of-the-art algorithms not only in objective criteria F-measure value but also in visual.Moreover,the proposed algorithm is robust to some attacks,such as additive white Gaussian noise,JPEG compression,rotation,and scaling.展开更多
Cryo-electron microscopy (cryo-EM) plays an important role in determining the structure of proteins, viruses, and even the whole cell. It can capture dynamic structural changes of large protein complexes, which other ...Cryo-electron microscopy (cryo-EM) plays an important role in determining the structure of proteins, viruses, and even the whole cell. It can capture dynamic structural changes of large protein complexes, which other methods such as X-ray crystallography and nuclear magnetic resonance analysis find difficult. The signal-to-noise ratio of cryo-EM images is low and the contrast is very weak, and therefore, the images are very noisy and require filtering. In this paper, a filtering method based on non-local means and Zernike moments is proposed. The method takes into account the rotational symmetry of some biological molecules to enhance the signal-to-noise ratio of cryo-EM images. The method may be useful in cryo-EM image processing such as the automatic selection of particles, orientation determination, and the building of initial models.展开更多
With the increasing necessities for reliable printed circuit board(PCB) product, there has been a considerable demand for high speed and high precision vision positioning system. To locate a rectangular lead component...With the increasing necessities for reliable printed circuit board(PCB) product, there has been a considerable demand for high speed and high precision vision positioning system. To locate a rectangular lead component with high accuracy and reliability, a new visual positioning method was introduced. Considering the limitations of Ghosal sub-pixel edge detection algorithm, an improved algorithm was proposed, in which Harris corner features were used to coarsely detect the edge points and Zernike moments were adopted to accurately detect the edge points. Besides, two formulas were developed to determine the edge intersections whose sub-pixel coordinates were calculated with bilinear interpolation and conjugate gradient method. The last experimental results show that the proposed method can detect the deflection and offset, and the detection errors are less than 0.04° and 0.02 pixels.展开更多
基金supported by the Scientific and Technological Program of Wenzhou[Y20160438,G20160033]National Natural Science Foundation of China[61775171]+1 种基金Natural Science Foundation of Zhejiang Province[LY14F050009,LY16H120007]National Key Research and Development Program of China[2016YFC0100200].
文摘Background:This retrospective study was designed to investigate the sole influence of orthokeratology(OK)lens fitting decentration on the Zernike coefficients of the reshaped anterior corneal surface.Methods:This study comprised a review of 106 right eyes and measurements of corneal topography both before OK and at 1-month follow-up visit.A routine was designed to calculate local corneal surface astigmatism and assist the determination of OK lens fitting decentration from pupil center.The pupil-centered corneal Zernike coefficients of baseline(PCCB)and post-treatment(PCCP)were calculated.Meanwhile,the OK-lens-centered corneal Zernike coefficients of post-treatment(OCCP)were also calculated and considered as the presumptive ideal fitting group without decentration.Relationships between lens fitting decentration and the change of Zernike coefficients including(PCCP−PCCB)and(PCCP−OCCP)were analyzed.Results:Patients with a mean age of 11±2.36 years old had an average spherical equivalent refractive error of−3.52±1.06 D before OK.One month after treatment,OK lens fitting decentration from pupil center was 0.68±0.35 mm.RMS of 3rd-order(P<0.05),RMS of 4th-order(P<0.001)and RMS of total high order(P<0.001)corneal Zernike coefficients were increased in PCCP by comparing with OCCP,which was solely caused by lens fitting decentration.Nevertheless,no significant difference was observed in C^(0)_(2)(P>0.05).For the high order corneal Zernike coefficients in(PCCP–OCCP),radial distance of decentration was correlated with C^(−1)_(3)(r=−0.296,P<0.05),C^(1)_(3)(r=−0.396,P<0.001),and C^(0)_(4)(r=0.449,P<0.001),horizontal decentration was significantly correlated with C^(1)_(3)(r=0.901,P<0.001)and C^(1)_(5)(r=0.340,P<0.001),and vertical decentration was significantly correlated with C^(−1)_(3)(r=0.904,P<0.001).Conclusions:OK lens fitting decentration within 1.5 mm hardly influenced the change of corneal spherical power for myopia correction,but significantly induced additional corneal high order Zernike coefficien
基金supported by the National High Technology Research and Development Program of China (Grant No 2006AA012339)
文摘Conformal domes that are shaped to meet aerodynamic requirements can increase range and speed for the host platform. Because these domes typically deviate greatly from spherical surface descriptions, a variety of aberrations are induced which vary with the field-of-regard （FOR） angle. A system for correcting optical aberrations created by a conformal dome has an outer surface and an inner surface. Optimizing the inner surface is regard as static aberration correction. A deformable mirror is placed at the position of the secondary mirror in the two-mirror all reflective imaging system, which is the dynamic aberration correction. An ellipsoidal MgF2 conformal dome with a fineness ratio of 1.0 is designed as an example. The FOR angle is 0°-30°, and the design wavelength is 4μm. After the optimization at 7 zoom positions by using the design tools Code V, the root-mean-square （RMS） spot size is reduced to approximately 0.99 to 1.48 times the diffraction limit. The design results show that the performances of the conformal optical systems can be greatly improved by the combination of the static correction and the dynamic correction.
基金Supported by Research Fund for the Doctoral Program of Higher Education of China(20093218110008)The SRF for ROCS,SPM(No.R0861-21)+1 种基金Jiangsu Research Foundation of Talented Scholars in Six Fields(No.P0951-021)The Nanjing University of Aeronautics and Astronautics Postgraduate Innovation Fund
文摘Vibration mode shape description of an aero-engine casing structure using Zernike moment descriptor(ZMD) was introduced in this paper.The mode shapes of the aero-engine casing structure can be decomposed as a linear combination of a series of Zernike polynomials,with the feature of each Zernike polynomial reflecting a part of characteristic of mode shapes,based on Zernike moment transformation.Meanwhile,the reconstruction of mode shapes with ZMD was explored and its ability to filtering the noise contaminated in the mode shapes was studied.Simulation of the aero-engine casing structure indicated the advantage of this method to depict the mode shapes of a symmetric structure.Results demonstrate that the Zernike moment description of the mode shapes can effectively describe the double modes in the symmetric structure and also has the ability to remove or significantly reduce the influence of noise in the mode shapes.Such feature shows great practical value for further research on the correlation,model updating and model validation of the symmetric structure's finite element model.
基金Project supported by the National Innovation Fund of Chinese Academy of Sciences(Grant No.CXJJ-16M208)the Preeminent Youth Fund of Sichuan Province,China(Grant No.2012JQ0012)the Outstanding Youth Science Fund of Chinese Academy of Sciences
文摘We propose a new algorithm for wavefront sensing based on binary intensity modulation. The algorithm is based on the fact that a wavefront can be expended with a series of orthogonal and binary functions, the Walsh series. We use a spatial light modulator（SLM） to produce different binary-intensity-modulation patterns which are the simple linear transformation of the Walsh series. The optical fields under different binary-intensity-modulation patterns are detected with a photodiode.The relationships between the incident wavefront modulated with the patterns and their optical fields are built to determinate the coefficients of the Walsh series. More detailed and strict relationship equations are established with the algorithm by adding new modulation patterns according to the properties of the Walsh functions. An exact value can be acquired by solving the equations. Finally, with the help of phase unwrapping and smoothing, the wavefront can be reconstructed. The advantage of the algorithm is providing an analytical solution for the coefficients of the Walsh series to reconstruct the wavefront. The simulation experiments are presented and the effectiveness of the algorithm is demonstrated.
基金the National Natural Science Foundation of China (60303029)
文摘The image shape feature can be described by the image Zernike moments. In this paper, we points out the problem that the high dimension image Zernike moments shape feature vector can describe more detail of the original image but has too many elements making trouble for the next image analysis phases. Then the low dimension image Zernike moments shape feature vector should be improved and optimized to describe more detail of the original image. So the optimization algorithm based on evolutionary computation is designed and implemented in this paper to solve this problem. The experimental results demonstrate the feasibility of the optimization algorithm.
基金Sino-French Program of Advanced Research under，上海市科委资助项目
文摘In this paper, illumination-affine invariant methods are presented based onaffine moment normalization techniques, Zernike moments, and multiband correlation functions. Themethods are suitable for the illumination invariant recognition of 3D color texture. Complex valuedmoments (i.e., Zernike moments) and affine moment normalization are used in the derivation ofillumination affine invariants where the real valued affine moment invariants fail to provide affineinvariants that are independent of illumination changes. Three different moment normalizationmethods have been used, two of which are based on affine moment normalization technique and thethird is based on reducing the affine transformation to a Euclidian transform. It is shown that fora change of illumination and orientation, the affinely normalized Zernike moment matrices arerelated by a linear transform. Experimental results are obtained in two tests: the first is usedwith textures of outdoor scenes while the second is performed on the well-known CUReT texturedatabase. Both tests show high recognition efficiency of the proposed recognition methods.
基金The National Natural Science of China(No.61572258,61771231,61772281,61672294)the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe Qing Lan Project of Jiangsu Higher Education Institutions
文摘An effective algorithm is proposed to detect copy-move forgery.In this algorithm,first,the PatchMatch algorithm is improved by using a reliable order-statistics-based approximate nearest neighbor search algorithm(ROSANNA)to modify the propagation process.Then,fractional quaternion Zernike moments(FrQZMs)are considered to be features extracted from color forged images.Finally,the extracted FrQZMs features are matched by the improved PatchMatch algorithm.The experimental results on two publicly available datasets(FAU and GRIP datasets)show that the proposed algorithm performs better than the state-of-the-art algorithms not only in objective criteria F-measure value but also in visual.Moreover,the proposed algorithm is robust to some attacks,such as additive white Gaussian noise,JPEG compression,rotation,and scaling.
基金supported by the National Basic Research Program of China (2010CB912400)
文摘Cryo-electron microscopy (cryo-EM) plays an important role in determining the structure of proteins, viruses, and even the whole cell. It can capture dynamic structural changes of large protein complexes, which other methods such as X-ray crystallography and nuclear magnetic resonance analysis find difficult. The signal-to-noise ratio of cryo-EM images is low and the contrast is very weak, and therefore, the images are very noisy and require filtering. In this paper, a filtering method based on non-local means and Zernike moments is proposed. The method takes into account the rotational symmetry of some biological molecules to enhance the signal-to-noise ratio of cryo-EM images. The method may be useful in cryo-EM image processing such as the automatic selection of particles, orientation determination, and the building of initial models.
基金Project(51175242)supported by the National Natural Science Foundation of ChinaProject(BA2012031)supported by the Jiangsu Province Science and Technology Foundation of China
文摘With the increasing necessities for reliable printed circuit board(PCB) product, there has been a considerable demand for high speed and high precision vision positioning system. To locate a rectangular lead component with high accuracy and reliability, a new visual positioning method was introduced. Considering the limitations of Ghosal sub-pixel edge detection algorithm, an improved algorithm was proposed, in which Harris corner features were used to coarsely detect the edge points and Zernike moments were adopted to accurately detect the edge points. Besides, two formulas were developed to determine the edge intersections whose sub-pixel coordinates were calculated with bilinear interpolation and conjugate gradient method. The last experimental results show that the proposed method can detect the deflection and offset, and the detection errors are less than 0.04° and 0.02 pixels.
