This survey reviews the recent development of gradient domain mesh deformation method. Different to other deformation methods, the gradient domain deformation method is a surface-based, variational optimization method...This survey reviews the recent development of gradient domain mesh deformation method. Different to other deformation methods, the gradient domain deformation method is a surface-based, variational optimization method. It directly encodes the geometric details in differential coordinates, which are also called Laplacian coordinates in literature. By preserving the Laplacian coordinates, the mesh details can be well preserved during deformation. Due to the locality of the Laplacian coordinates, the variational optimization problem can be casted into a sparse linear system. Fast sparse linear solver can be adopted to generate deformation result interactively, or even in real-time. The nonlinear nature of gradient domain mesh deformation leads to the development of two categories of deformation methods： linearization methods and nonlinear optimization methods. Basically, the linearization methods only need to solve the linear least-squares system once. They are fast, easy to understand and control, while the deformation result might be suboptimal. Nonlinear optimization methods can reach optimal solution of deformation energy function by iterative updating. Since the computation of nonlinear methods is expensive, reduced deformable models should be adopted to achieve interactive performance. The nonlinear optimization methods avoid the user burden to input transformation at deformation handles, and they can be extended to incorporate various nonlinear constraints, like volume constraint, skeleton constraint, and so on. We review representative methods and related approaches of each category comparatively and hope to help the user understand the motivation behind the algorithms. Finally, we discuss the relation between physical simulation and gradient domain mesh deformation to reveal why it can achieve physically plausible deformation result. Kun Zhou is currently a Cheung Kong professor in the Department of Computer Science, Zhejiang Uni- versity, and a member of the State Key Laboratory of CAD＆CG. He received his B.S. degree and Ph.D. degree from Zhejiang University in 1997 and 2002, respectively. Af- ter graduation, he joined Microsoft Research Asia as an associate re-展开更多
Aeromagnetic gradients are often used to enhance details or add new insights for interpretation. The gradients may be measured or derived from the total field or from transformation between horizontal and vertical gra...Aeromagnetic gradients are often used to enhance details or add new insights for interpretation. The gradients may be measured or derived from the total field or from transformation between horizontal and vertical gradients. At present, vertical, horizontal, and triaxial aeromagnetic gradiometers are in operation throughout the world, while the first two are used more widely. Transformations between horizontal and vertical gradients are needed for acquiring three gradient components or for checking the validity of measured gradients. Transformation of potential field by fast Fourier transform technique in frequency domain is popularly used; however, when applied to transforming between gradients, there is a problem that needs resolving. Because those expressions of transform operators are undefined when u or v is equal to zero or u and v are simultaneously equal to zero （u is the frequency in x-direction, and v is the frequency in y-direction）, the operators cannot be sampled at these frequencies. Consequently, the transformation cannot be implemented by fast Fourier transform technique directly. In this article, shift sampling theory is employed for resolving this problem. Model test results show that the technique has good accuracy, and the real case of transformation indicates that the computed results agree better with the measured gradients; it demonstrates not only the effective- ness of method but also the reliability of the measured gradients.展开更多
Curvature-driven diffusion (CDD) principles were used to develop a novel gradient based image restora- tion algorithm. The algorithm fills in blocks of missing data in a wireless image after transmission through the n...Curvature-driven diffusion (CDD) principles were used to develop a novel gradient based image restora- tion algorithm. The algorithm fills in blocks of missing data in a wireless image after transmission through the network. When images are transmitted over fading channels, especially in the severe circum- stances of a coal mine, blocks of the image may be destroyed by the effects of noise. Instead of using com- mon retransmission query protocols the lost data is reconstructed by using the adaptive curvature-driven diffusion (ACDD) image restoration algorithm in the gradient domain of the destroyed image. Missing blocks are restored by the method in two steps: In step one, the missing blocks are filled in the gradient domain by the ACDD algorithm; in step two, and the image is reconstructed from the reformed gradients by solving a Poisson equation. The proposed method eliminates the staircase effect and accelerates the convergence rate. This is demonstrated by experimental results.展开更多
Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse ...Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse matrix factorization, combined with nine-point finite-difference for the linear system of equations. In the waveform inversion, we use preconditioned gradient method where the preconditioner is provided by the diagonal of the approximate Hessian matrix. We successfully applied waveform inversion method from low to high frequency in two sets of Marmousi data. One is the data set generated by frequencydomain finite-difference modeling, and the other is the original Marmousi shots data set. The former result is very close to the true velocity model. In the original shots data set inversion, we replace the prior source with estimated source; the result is also acceptable, and consistent with the true model.展开更多
Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy f...Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy for forward modeling. For arbitrarily distributed susceptibility data on an undulated surface, we propose a fast 3D forward modeling method in the wavenumber domain based on(1) the wavenumber-domain expression of the prism combination model and the Gauss–FFT algorithm and(2) cubic spline interpolation. We apply the proposed 3D forward modeling method to synthetic data and use weighting coefficients in the wavenumber domain to improve the modeling for multiple observation surfaces, and also demonstrate the accuracy and efficiency of the proposed method.展开更多
文摘This survey reviews the recent development of gradient domain mesh deformation method. Different to other deformation methods, the gradient domain deformation method is a surface-based, variational optimization method. It directly encodes the geometric details in differential coordinates, which are also called Laplacian coordinates in literature. By preserving the Laplacian coordinates, the mesh details can be well preserved during deformation. Due to the locality of the Laplacian coordinates, the variational optimization problem can be casted into a sparse linear system. Fast sparse linear solver can be adopted to generate deformation result interactively, or even in real-time. The nonlinear nature of gradient domain mesh deformation leads to the development of two categories of deformation methods： linearization methods and nonlinear optimization methods. Basically, the linearization methods only need to solve the linear least-squares system once. They are fast, easy to understand and control, while the deformation result might be suboptimal. Nonlinear optimization methods can reach optimal solution of deformation energy function by iterative updating. Since the computation of nonlinear methods is expensive, reduced deformable models should be adopted to achieve interactive performance. The nonlinear optimization methods avoid the user burden to input transformation at deformation handles, and they can be extended to incorporate various nonlinear constraints, like volume constraint, skeleton constraint, and so on. We review representative methods and related approaches of each category comparatively and hope to help the user understand the motivation behind the algorithms. Finally, we discuss the relation between physical simulation and gradient domain mesh deformation to reveal why it can achieve physically plausible deformation result. Kun Zhou is currently a Cheung Kong professor in the Department of Computer Science, Zhejiang Uni- versity, and a member of the State Key Laboratory of CAD＆CG. He received his B.S. degree and Ph.D. degree from Zhejiang University in 1997 and 2002, respectively. Af- ter graduation, he joined Microsoft Research Asia as an associate re-
基金supported by China Aero Geophysical Survey & Remote Sensing Center for Land & Resources (863 Program, No. 2006AA06A201)
文摘Aeromagnetic gradients are often used to enhance details or add new insights for interpretation. The gradients may be measured or derived from the total field or from transformation between horizontal and vertical gradients. At present, vertical, horizontal, and triaxial aeromagnetic gradiometers are in operation throughout the world, while the first two are used more widely. Transformations between horizontal and vertical gradients are needed for acquiring three gradient components or for checking the validity of measured gradients. Transformation of potential field by fast Fourier transform technique in frequency domain is popularly used; however, when applied to transforming between gradients, there is a problem that needs resolving. Because those expressions of transform operators are undefined when u or v is equal to zero or u and v are simultaneously equal to zero （u is the frequency in x-direction, and v is the frequency in y-direction）, the operators cannot be sampled at these frequencies. Consequently, the transformation cannot be implemented by fast Fourier transform technique directly. In this article, shift sampling theory is employed for resolving this problem. Model test results show that the technique has good accuracy, and the real case of transformation indicates that the computed results agree better with the measured gradients; it demonstrates not only the effective- ness of method but also the reliability of the measured gradients.
基金supported by the National High-Tech Research and Development Program of China (No. 2008AA062200)the National Natural Science Foundation of China (No.60802077)the Fundamental Research Funds for the Central Universities (No. 2010QNA43)
文摘Curvature-driven diffusion (CDD) principles were used to develop a novel gradient based image restora- tion algorithm. The algorithm fills in blocks of missing data in a wireless image after transmission through the network. When images are transmitted over fading channels, especially in the severe circum- stances of a coal mine, blocks of the image may be destroyed by the effects of noise. Instead of using com- mon retransmission query protocols the lost data is reconstructed by using the adaptive curvature-driven diffusion (ACDD) image restoration algorithm in the gradient domain of the destroyed image. Missing blocks are restored by the method in two steps: In step one, the missing blocks are filled in the gradient domain by the ACDD algorithm; in step two, and the image is reconstructed from the reformed gradients by solving a Poisson equation. The proposed method eliminates the staircase effect and accelerates the convergence rate. This is demonstrated by experimental results.
基金Supported by the National Natural Science Foundation of China (69983005)
文摘Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse matrix factorization, combined with nine-point finite-difference for the linear system of equations. In the waveform inversion, we use preconditioned gradient method where the preconditioner is provided by the diagonal of the approximate Hessian matrix. We successfully applied waveform inversion method from low to high frequency in two sets of Marmousi data. One is the data set generated by frequencydomain finite-difference modeling, and the other is the original Marmousi shots data set. The former result is very close to the true velocity model. In the original shots data set inversion, we replace the prior source with estimated source; the result is also acceptable, and consistent with the true model.
基金supported by the National Special Plan for the 13th Five-Year Plan of China(No.2017YFC0602204-10)Independent Exploration of the Innovation Project for Graduate Students at Central South University(No.2017zzts176)+3 种基金National Natural Science Foundation of China(Nos.41574127,41404106,and 41674075)Postdoctoral Fund Projects of China(No.2017M622608)National Key R&D Program of China(No.2018YFC0603602)Natural Science Youth Fund Project of the Hunan Province,China(No.2018JJ3642)
文摘Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy for forward modeling. For arbitrarily distributed susceptibility data on an undulated surface, we propose a fast 3D forward modeling method in the wavenumber domain based on(1) the wavenumber-domain expression of the prism combination model and the Gauss–FFT algorithm and(2) cubic spline interpolation. We apply the proposed 3D forward modeling method to synthetic data and use weighting coefficients in the wavenumber domain to improve the modeling for multiple observation surfaces, and also demonstrate the accuracy and efficiency of the proposed method.
