运动模糊图像的盲复原在现有的方法中多数针对灰度图像,而彩色图像是由多个图层耦合而成,将彩色图像转化为灰度图像过程中必然会造成信息丢失。针对彩色图像的去模糊问题,提出多尺度框架下,将曲率项对彩色图像的边缘保护特性和归一化的...运动模糊图像的盲复原在现有的方法中多数针对灰度图像,而彩色图像是由多个图层耦合而成,将彩色图像转化为灰度图像过程中必然会造成信息丢失。针对彩色图像的去模糊问题,提出多尺度框架下,将曲率项对彩色图像的边缘保护特性和归一化的曲率项的正则化约束相结合,在彩色图像各个通道上由粗尺度到细尺度估计模糊核,采用多通道全变分模型(Multi-channel total variation,MTV)进行图像复原。为降低去模糊方程的求解复杂度,求解时引入快速分裂(Split Bregman)算法。实验结果表明,尽管曲率项会加大算法的计算量,但是复原后的图像细节效果更明显,质量更好。展开更多
A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample ...A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.展开更多
We study special functions related to Lotka-Volterra equations and negative Volterra equation intro-duced from zero curvature representations . At first we show the relationships between Lotka-Volterra equations intro...We study special functions related to Lotka-Volterra equations and negative Volterra equation intro-duced from zero curvature representations . At first we show the relationships between Lotka-Volterra equations introduced from zero curvature representations and symmetric orthogonal polynomials. Sec-ondarily, we describe the relationships between negative Volterra equations with a special solutions and cylinder functions.展开更多
In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smoo...In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.展开更多
The authors prove the space of harmonic functions with polynomial growth of a fixed rate on a complete noncompact Riemannian manifold with asymptotically nonnegative curvature is finite dimensional.
文摘运动模糊图像的盲复原在现有的方法中多数针对灰度图像,而彩色图像是由多个图层耦合而成,将彩色图像转化为灰度图像过程中必然会造成信息丢失。针对彩色图像的去模糊问题,提出多尺度框架下,将曲率项对彩色图像的边缘保护特性和归一化的曲率项的正则化约束相结合,在彩色图像各个通道上由粗尺度到细尺度估计模糊核,采用多通道全变分模型(Multi-channel total variation,MTV)进行图像复原。为降低去模糊方程的求解复杂度,求解时引入快速分裂(Split Bregman)算法。实验结果表明,尽管曲率项会加大算法的计算量,但是复原后的图像细节效果更明显,质量更好。
文摘A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.
文摘We study special functions related to Lotka-Volterra equations and negative Volterra equation intro-duced from zero curvature representations . At first we show the relationships between Lotka-Volterra equations introduced from zero curvature representations and symmetric orthogonal polynomials. Sec-ondarily, we describe the relationships between negative Volterra equations with a special solutions and cylinder functions.
文摘In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.
基金Project supported by the National Natural Science Foundation of China (No.10271089).
文摘The authors prove the space of harmonic functions with polynomial growth of a fixed rate on a complete noncompact Riemannian manifold with asymptotically nonnegative curvature is finite dimensional.
