基于扩散的自适应超分辨率重建

从各向异性角度分析了P-M模型、L1范式(TV模型)、L2范式(调和模型)的不足,通过扩散模型建立超分辨率重建的偏微分方程,提出一种非线性各向异性和超分辨率重建组合的模型。该模型在图像平坦区域具有线性各向同性扩散,能够有效消除噪声,在图像边缘区域具有非线性各向异性扩散保留边缘,有效减少了滤波产生的阶梯效应和P-M模型过渡平滑忽略细节的现象。仿真结果表明,该模型能够有效地提高图像重建质量,能在消除噪声的同时保留边缘,具有很好的鲁棒性。     

基于PDE的自适应各向异性图像配准方法研究

针对传统光流场配准模型会造成图像模糊和细节丢失的问题,提出了一种基于偏微分方程的自适应各向异性配准模型。新模型将具有自适应性的扩散滤波方法引入图像配准,定义具有图像结构保持能力的各向异性扩散函数作为模型的正则项;数据项采用作用于亮度常量假设的非二次惩罚函数以增加模型的稳健性。实验结果表明,新模型能够有效保持图像特征,实现对大脑等复杂图像的有效配准。     

基于局部结构张量的红外图像背景抑制

文中将局部结构张量与双边滤波相结合,提出了一种基于局部结构张量的红外图像结构化背景抑制算法。该算法采用局部结构张量的标准差作为双边滤波的执行判定,并利用双边滤波加权系数实现背景估计,从而实现结构化背景抑制和目标信息增强。实验结果显示,与二维最小均方滤波和偏微分方程算法相比,该算法对含有弱小目标的复杂背景具有良好抑制效果。     

基于各向异性扩散的图像去噪并放大

本文从各向异性扩散图像去噪方法出发,在偏微分方程有限元方法的基础上,提出一种图像复原并放大的 算法,实验表明该算法比中值滤波后插值所得图像的主、客观质量要好。     

基于非线性结构张量自适应滤波图像去噪算法研究

针对Wiener滤波对具不同局部的图像去噪效果不佳的不足,研究了由非线性扩散方程导出结构张量的非线性形式,结合空间域自适应wiener滤波,优化滤波窗而达到更好去噪的一种图像去噪算法。通过基于扩散张量成像方法的改进不仅提高图像处理过程的计算效率,而且更好地保持了图像边缘等细微结构特征。实验结果进一步验证了该算法的有效性。     

基于GPU加速的各向异性双边滤波图像抽象化绘制算法

本文提出基于GPU加速的图像及视频的实时抽象化绘制算法。首先通过运用Kuwahara滤波实现图像的颜色特征快速聚类,其次采用各向异性双边滤波算法对图像沿结构张量场进行平滑,从而获得连续的、局部区域色彩一致的结果图像,实验表明该算法简单、易于实现。     

各向异性扩散图像去噪现状研究

介绍了基于偏微分方程(Partial Differential Equations,PDE)各向异性扩散图像去噪的P&M数学模型及各种改进方法,以及引入结构张量的PDE去噪模型和冲击滤波PDE去噪模型,分析各种模型的优缺点,为扩散模型的设计提供了参考。揭示了各向异性扩散去噪与贝叶斯最大后验估计(MAP)去噪的内在联系,通过扩散系数的计算分析几类常用去噪模型的保边性能。阐述了一类特殊PDE去噪模型(总变分去噪模型)与小波阈值去噪之间的相关性,从而可以通过小波系数的范数近似求解一些特殊的变分问题,避免复杂的非线性求解过程。最后对各向异性扩散图像去噪的未来发展进行了展望。     

一种简单有效的自动多阈值分割算3法

本文提出了一种自动多阔值分割算法,通过直接对图像的灰度直方图曲线进行分析,判断极小值所在的灰度级,再对所有极小值点进行相应的分类合并来最终确定阈值的位置,避免出现过分割的现象。在预处理阶段本文采用了基于各向异性扩散的平滑方法对图像进行滤波,以消除噪声,同时还可以使图像的灰度直方图曲线更为连续,从而加速算法的执行效率。     

一种简单有效的自动多阈值分割算法

本文提出了一种自动多阈值分割算法,通过直接对图像的灰度直方图曲线进行分析,判断极小值所在的灰度级,再对所有极小值点进行相应的分类合并来最终确定阈值的位置,避免出现过分割的现象.在预处理阶段本文采用了基于各向异性扩散的平滑方法对图像进行滤波,以消除噪声,同时还可以使图像的灰度直方图曲线更为连续,从而加速算法的执行效率.     

基于结构张量图像建模方法的滤波性能研究

主要研究结构张量驱动的变分偏微分方程(variational Partial Differential Equation; variati0nal PDE)图像建模方法的滤波性能.基于角形强度度量和水平线演化理论,设计了一种具有角点增强性能的角形冲击滤波器,以克服边缘冲击滤波器增强图像的不足.基于边缘和角形冲击滤波器,...     

Noise-Driven Anisotropic Diffusion Filtering of MRI

A new filtering method to remove Rician noise from magnetic resonance images is presented. This filter relies on a robust estimation of the standard deviation of the noise and combines local linear minimum mean square error filters and partial differential equations for MRI, as the speckle reducing anisotropic diffusion did for ultrasound images. The parameters of the filter are automatically chosen from the estimated noise. This property improves the convergence rate of the diffusion while preserving contours, leading to more robust and intuitive filtering. The partial derivative equation of the filter is extended to a new matrix diffusion filter which allows a coherent diffusion based on the local structure of the image and on the corresponding oriented local standard deviations. This new filter combines volumetric, planar, and linear components of the local image structure. The numerical scheme is explained and visual and quantitative results on simulated and real data sets are presented. In the experiments, the new filter leads to the best results.     

Bilateral filtering of diffusion tensor magnetic resonance images.

We extend the well-known scalar image bilateral filtering technique to diffusion tensor magnetic resonance images (DTMRI). The scalar version of bilateral image filtering is extended to perform edge-preserving smoothing of DT field data. The bilateral DT filtering is performed in the Log-Euclidean framework which guarantees valid output tensors. Smoothing is achieved by weighted averaging of neighboring tensors. Analogous to bilateral filtering of scalar images, the weights are chosen to be inversely proportional to two distance measures: The geometrical Euclidean distance between the spatial locations of tensors and the dissimilarity of tensors. We describe the noniterative DT smoothing equation in closed form and show how interpolation of DT data is treated as a special case of bilateral filtering where only spatial distance is used. We evaluate different recent DT tensor dissimilarity metrics including the Log-Euclidean, the similarity-invariant Log-Euclidean, the square root of the J-divergence, and the distance scaled mutual diffusion coefficient. We present qualitative and quantitative smoothing and interpolation results and show their effect on segmentation, for both synthetic DT field data, as well as real cardiac and brain DTMRI data.     

Scale-Space Properties of Nonstationary Iterative Regularization Methods

Most scale-space concepts have been expressed as parabolic or hyperbolic partial differential equations (PDEs). In this paper we extend our work on scale-space properties of elliptic PDEs arising from regularization methods: we study linear and nonlinear regularization methods that are applied iteratively and with different regularization parameters. For these so-called nonstationary iterative regularization techniques we clarify their relations to both isotropic diffusion filters with a scalar-valued diffusivity and anisotropic diffusion filters with a diffusion tensor. We establish scale-space properties for iterative regularization methods that are in complete accordance with those for diffusion filtering. In particular, we show that nonstationary iterative regularization satisfies a causality property in terms of a maximum–minimum principle, possesses a large class of Lyapunov functionals, and converges to a constant image as the regularization parameters tend to infinity. We also establish continuous dependence of the result with respect to the sequence of regularization parameters. Numerical experiments in two and three space dimensions are presented that illustrate the scale-space behavior of regularization methods.     

Color image enhancement via chromaticity diffusion

A novel approach for color image denoising is proposed in this paper. The algorithm is based on separating the color data into chromaticity and brightness, and then processing each one of these components with partial differential equations or diffusion flows. In the proposed algorithm, each color pixel is considered as an n-dimensional vector. The vectors' direction, a unit vector, gives the chromaticity, while the magnitude represents the pixel brightness. The chromaticity is processed with a system of coupled diffusion equations adapted from the theory of harmonic maps in liquid crystals. This theory deals with the regularization of vectorial data, while satisfying the intrinsic unit norm constraint of directional data such as chromaticity. Both isotropic and anisotropic diffusion flows are presented for this n-dimensional chromaticity diffusion flow. The brightness is processed by a scalar median filter or any of the popular and well established anisotropic diffusion flows for scalar image enhancement. We present the underlying theory, a number of examples, and briefly compare with the current literature.     

一种基于偏微分方程的图像分割算法

针对几何活动轮廓模型（GAC模型）在基于偏微分方程的图像分割领域中,算法复杂,计算量大导致演化时间长,演化速度在边界上通常不为零,引起演化曲线进入到目标的内部;或是当图像的对象有较深的凹陷边界时,曲线停在某一局部极小值状态,并不与对象的边界相一致等问题。本文提出了一种基于偏微分方程的图像分割算法,通过对停止速度场进行多尺度张量扩散,然后运用GACA模型进行分割。实验证明：本算法在不降低射线图像分割质量的前提下,可使演化时间比传统的GAC模型演化时间减少65%左右,还在一定程度上减少了边界泄露问题。     

A Diffusion Tensor Imaging Tractography Algorithm Based on Navier–Stokes Fluid Mechanics

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier–Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.      

一种改进的二阶偏微分去噪模型

分析了基于二阶偏微分的扩散方程模型的基本原理,针对该模型在去噪的同时会产生阶梯效应的缺点,提出了一种基于图像结构信息的二阶偏微分去噪模型。在该模型中,在二阶偏微分的全变分模型的正则化项加入图像的切矢量和法矢量信息,并由此推导出相应的扩散方程,再对扩散方程的扩散强度因子进行修改。在实验中,将模型分别与基于二阶偏微分、四阶偏微分的全变分模型进行对比分析表明,实验结果证明该模型能有效地去除图像噪声,克服阶梯效应的产生,主观性能最优。     

基于结构张量特征值的纹理图像分割模型

通过对结构张量的研究和对纹理图像的分析,提出了一种基于结构张量特征值的标量型纹理特征描述,将其和原图像分别嵌入到两相模糊区域竞争模型和CV模型中,给出了一种纹理和灰度相结合的无监督纹理图像分割模型.为获得新模型的全局最优解,采用了Chambolle对偶法加以实现.针对自然和合成纹理图像进行了相关实验,结果表明该模型特征数据维数少,具有较快的收敛速度和更准确的分割效果.     

基于PDE的非线性图像去噪与增强

应用偏微分理论,提出一种改进的基于偏微分方程的非线性图像去噪与增强方法,对传统的P-M非线性扩散模型进行改进。首先将图像变换到梯度域,然后通过改变梯度域扩散函数来达到去噪和增强的目的。与以往的时域和频域图像去噪方法相比,本文方法不仅能有效去除噪声,还能很好地保留图像的纹理细节。文章采用有限差分法将偏微分方程离散化,并结合热方程简化计算复杂度,从而实现简单快速的计算过程,为实时的图像去噪与增强处理提供保证。