In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution o...In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution obtained using the Gaver-Stehfest algorithm, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. The numerical direct Laplace transform is implemented with a composite Simpson’s rule. Challenging numerical examples involving periodic and oscillatory functions, are investigated. The numerical examples illustrate the computational accuracy and efficiency of the direct Laplace transform and its inverse due to increasing the precision level and the number of terms included in the expansion. It is found that the number of expansion terms and the precision level selected must be in a harmonious balance in order for correct and stable results to be obtained.展开更多
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （...Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.展开更多
弥散张量成像(Diffusion Tensor Magnetic Resonance Imaging,DT-MRI)是近年来新兴的一种核磁共振成像技术,作为一种无创伤的描述大脑结构的新方法,弥散张量成像在临床诊断中发挥着重要的作用。由于不同个体或者同一个体不同状态下获取...弥散张量成像(Diffusion Tensor Magnetic Resonance Imaging,DT-MRI)是近年来新兴的一种核磁共振成像技术,作为一种无创伤的描述大脑结构的新方法,弥散张量成像在临床诊断中发挥着重要的作用。由于不同个体或者同一个体不同状态下获取的张量数据展开的多幅图像之间存在一定偏差,需要将这些图像对齐,即配准。逆向组合算法是一种很好的配准方法,但是当模板图像和目标图像之间存在多种几何变化时,算法的收敛速度往往很慢。提出了一种可变步长的逆向组合算法,通过自适应改变原始算法的步长达到加快算法收敛速度的目的。实验表明,该算法在保持原始算法精度的基础上能够加快收敛速度,并且对图像的几何变换有很好的鲁棒性。展开更多
文摘In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution obtained using the Gaver-Stehfest algorithm, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. The numerical direct Laplace transform is implemented with a composite Simpson’s rule. Challenging numerical examples involving periodic and oscillatory functions, are investigated. The numerical examples illustrate the computational accuracy and efficiency of the direct Laplace transform and its inverse due to increasing the precision level and the number of terms included in the expansion. It is found that the number of expansion terms and the precision level selected must be in a harmonious balance in order for correct and stable results to be obtained.
基金financially supported by the National Natural Science Foundation of China(11202081,11272124,and 11472109)the State Key Lab of Subtropical Building Science,South China University of Technology(2014ZC17)
文摘Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
文摘弥散张量成像(Diffusion Tensor Magnetic Resonance Imaging,DT-MRI)是近年来新兴的一种核磁共振成像技术,作为一种无创伤的描述大脑结构的新方法,弥散张量成像在临床诊断中发挥着重要的作用。由于不同个体或者同一个体不同状态下获取的张量数据展开的多幅图像之间存在一定偏差,需要将这些图像对齐,即配准。逆向组合算法是一种很好的配准方法,但是当模板图像和目标图像之间存在多种几何变化时,算法的收敛速度往往很慢。提出了一种可变步长的逆向组合算法,通过自适应改变原始算法的步长达到加快算法收敛速度的目的。实验表明,该算法在保持原始算法精度的基础上能够加快收敛速度,并且对图像的几何变换有很好的鲁棒性。
