一种混合曲率流图像除噪方法

基于几何曲线(曲面)演化的图像除噪和恢复是图像处理领域中的一个研究热点.本文利用几何和非线性扩散理论分析最大最小曲率流曲线演化方程,提出结合边缘信息的开关函数控制曲线(曲面)演化的混合曲率流图像除噪模型.实验证明,与其它除噪模型比较,该模型能更好解决曲线演化模型在对图像除噪时边缘保护和噪声去除的问题,提高曲线演化模型的图像除噪能力,并改善图像的可视性.     

Min/Max曲率流实现图像去噪和增强分析

分析Min/Max曲率流在图像去噪和增强方面的机理。针对Min/Max曲率流结合水平集方法通过曲线(曲面)演化对图像去噪和增强的特点,给出了Min/Max曲率流模型新的数值计算方法。新的方法主要是关于边缘保护和除噪的自适应算法,较好地解决了Min/Max曲率流在去噪和增强时对图像边缘尖点的扩散模糊问题。通过数值实验证明该方法能去除图像噪声,使图像的可视性得到显著提高。     

三次平面H-Bézier 螺线

基于光顺曲线设计需求,一条曲率单调且曲率正负不变的三次平面 H-Bézier 螺线段被构造。由于此螺线具有起点曲率为零的特性,它可以替代回旋曲线作为道 路设计中的缓和曲线。同时螺线还含有形状参数,故它具有曲线形状可调性的优点。最后, 利用此H-Bézier 螺线,构造了两直线间满足G2 连续的缓和曲线。     

用反调和平均曲率流实现网格保特征平滑

利用反调和平均曲率流，提出一种各向异性、快速的不规则三角网格去噪算法．模型中选择的各向异性演化权函数比较简单，同时保持了网格的几何特征．分别用显式格式和半隐式格式实现了此平滑算法．提供的数值例子显示了模型的有效性．     

基于高斯曲率的曲面光顺方法研究

在交互设计系统中曲率(包括高斯曲率和平均曲率)评价是分析曲线曲面质量的重要工具。对于B样条曲线的光顺算法已经比较成熟。但对于如何基于曲率（包括高斯曲率和平均曲率）的曲面光顺算法则还有许多工作要做。该文提出了一种基于最小二乘的曲面优化算法，可以得到比较好的结果。该光顺算法主要包括两个步骤：依据曲率光顺准则修改曲面的曲率和修改后的曲率基于原曲面优化反向求出新的控制顶点。     

基于B样条的Level-Set GPU演化算法

大部分Level-Set演化模型基于平均曲率或梯度,这对去除3D数据的噪声时保持线状特征是不利的;在解Level-Set演化方程时一般采用迎风格式,精度较低。设计了基于曲率差的高阶演化方程以及基于B样条和中心差分的混合GPU解法器。实验结果表明,基于曲率差的演化方程能够在光顺数据时保持线状特征。     

一种新型GVF-Snake模型

针对GVF-Snake模型对虚假边界敏感的缺陷,在原模型基础上提出一种有效梯度向量流外力场的概念,并引入自适应性气球力。有效梯度向量流外力场是对GVF模型外力场的优化,它将演化曲线过程中曲线和梯度向量之间的夹角作为模型的一个新因素,降低演化过程中噪声和虚假边界对演化曲线的干扰。自适应性气球力的引入加快了演化曲线收敛速度。实验结果表明,与原模型相比,新模型曲线在演化过程中对噪音和虚假边界的抗性得到提高。     

多支撑区域模式化融合角点检测算法仿真

传统的基于轮廓的角点检测算法常常会因为阈值选择不当,使检测准确率降低.针对上述问题,提出一种多支撑区域下模式化的角点融合方法.首先计算曲线上各点的曲率值,然后对曲线上的点进行初步筛选并分组,使曲线上相邻且曲率相近的点分为一组,在每组中选取局部曲率极大值点作为备选角点,再修改支撑区域,重复上述步骤,产生多组备选角点,最后对轮廓曲线进行模式划分,在不同模式下进行角点融合.实验分别在旋转变换和伸缩变换下评估平均重复率和准确率,通过与CSS、He&Yung角点检测器进行对比实验,所提算法提高了平均重复率和准确率,是一种可行的角点检测算法.     

基于演化曲线自适应的图像分割模型的研究

利用图像梯度和几何曲率等信息可以准确定位分割图像的边缘。基于此,在对图像分割典型变分模型有效性及所存在问题分析和讨论的基础上,提出了一种演化曲线自适应驱动的图像分割水平集模型。模型通过调整演化曲线长度项和面积项的权重函数,使演化曲线能够根据图像当前的状态自适应地调整演化幅度和方向,不仅提高了图像分割的准确度,还大大缩减了图像分割时间;模型在利用图像局部区域信息的同时,也利用全局化的正则函数来兼顾模型能量泛函的全局性,使模型有了对异质区域边界的捕捉能力。经试验验证,文章所提出的新模型有效可靠。     

高阶PDE模型中的松弛中值图像去噪方法

针对平均曲率极小化模型在去噪过程中产生斑点的问题,提出了一种平均曲率和松弛中值滤波结合的迭代算法。首先,使用平均曲率模型对噪声图像处理,根据局部方差信息,利用阈值确定斑点的位置。其次,利用具一定边界保持性质的松弛中值滤波器消除斑点噪声。最后,为更有效地消除斑点,在每一次随着时间的迭代后都使用松弛中值滤波。对曲线和图像进行去噪仿真实验,结果表明,相对于平均曲率模型,本文算法在客观指标和主观视觉效果上均有更好的去噪效果和更低的时间复杂度。     

法曲率驱动曲面演化图像去噪模型研究

曲面演化图像去噪模型将图像看作嵌入高维空间中的曲面,并利用曲面局部几何特征来区分图像边缘和噪声信息,以此控制图像曲面演化速率,取得了良好的处理效果。通过分析现有基于主曲率的曲面演化图像去噪模型的优缺点,提出利用能够更好地刻画图像曲面几何结构的法曲率来控制曲面的演化过程。该模型将现有主曲率驱动的模型推广到了更一般的法曲率驱动的曲面演化模型。同时,由于法曲率在描述图像边缘、纹理、噪声等方面优于已有方法采用的主曲率,该模型在保持图像边缘、纹理等细节信息方面能够取得更好的性能。     

Anisotropic Filtering of Non-Linear Surface Features

A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non‐linear geometric features such as curved surface regions and feature lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operator and principal curvature properties on simplicial surfaces that is fully consistent with the well‐known discrete mean curvature formula, 2. an anisotropic discrete mean curvature vector that combines the advantages of the mean curvature normal with the special anisotropic behaviour along feature lines of a surface, and 3. an anisotropic prescribed mean curvature flow which converges to surfaces with an estimated mean curvature distribution and with preserved non‐linear features. Additionally, the PMC flow prevents boundary shrinkage at constrained and free boundary segments.     

Shape Restoration via a Regularized Curvature Flow

Any image filtering operator designed for automatic shape restoration should satisfy robustness (whatever the nature and degree of noise is) as well as non-trivial smooth asymptotic behavior. Moreover, a stopping criterion should be determined by characteristics of the evolved image rather than dependent on the number of iterations. Among the several PDE based techniques, curvature flows appear to be highly reliable for strongly noisy images compared to image diffusion processes.In the present paper, we introduce a regularized curvature flow (RCF) that admits non-trivial steady states. It is based on a measure of the local curve smoothness that takes into account regularity of the curve curvature and serves as stopping term in the mean curvature flow. We prove that this measure decreases over the orbits of RCF, which endows the method with a natural stop criterion in terms of the magnitude of this measure. Further, in its discrete version it produces steady states consisting of piece-wise regular curves. Numerical experiments made on synthetic shapes corrupted with different kinds of noise show the abilities and limitations of each of the current geometric flows and the benefits of RCF. Finally, we present results on real images that illustrate the usefulness of the present approach in practical applications.     

A curvature-based approach to terrain recognition

The authors describe an algorithm which uses a Gaussian and mean curvature profile for extracting special points on terrain and then use these points for recognition of particular regions of the terrain. The Gaussian and mean curvatures are chosen because they are invariant under rotation and translation. In the Gaussian and mean curvature image, the points of maximum and minimum curvature are extracted and used for matching. The stability of the position of those points in the presence of noise and with resampling is investigated. The input for this algorithm consists of 3-D digital terrain data. Curvature values are calculated from the data by fitting a quadratic surface over a square window and calculating directional derivatives of this surface. A method of surface fitting which is invariant to coordinate system transformation is suggested and implemented. The algorithm is tested with and without the presence of noise, and its performance is described     

梯度与曲率变形力相结合的图像配准方法——大形变非刚性图像配准

Active Demons算法是Demons算法的改进形式,其将形变配准视作扩散问题,利用牛顿作用力与反作用力思想,仅依靠梯度信息确定浮动图像的位移,在处理大形变配准问题时存在配准精度不高的弊病。将等照度线曲率作为一个控制形变的驱动力因素引入Active Demons扩散方程,建立了一个具有梯度与曲率双重驱动力相结合的非线性扩散模型（Active G&C model）,并在Active G&C模型应用于大形变图像配准的算法实现过程中加入多分辨率策略,以提高大形变图像的配准精度。实验结果表明,这一模型较经典的Active Demons算法具有更好的配准性能。     

Numerical solution of parabolic equations related to level set formulation of mean curvature flow

Numerical approximation of a nonlinear diffusion equation of mean curvature flow type is discussed. Computational results related to image processing are presented. Received: 22 April 1997 / Accepted: 27 February 1998     

非线性扩散图像去噪中的耦合自适应保真项研究

讨论了一种基于非线性扩散方程的图像去噪方法.在讨论了图像去噪的3个基本要求的基础上,总结了平均曲率运动去噪模型和总变差去噪模型中利用保真项的不足.将利用图像的局部信息构造的自适应保真项引入到方向扩散去噪模型中,克服了原有方法在耦合保真项上的不足,使新的非线性扩散去噪模型能够在有效地去除噪声的同时很好地保持目标尖角、边缘等重要的几何结构.实验结果表明,耦合自适应保真项的扩散方程能够很好地保持图像中目标的几何结构,同时具有良好的去噪能力.     

Shape‐simplifying Image Abstraction

This paper presents a simple algorithm for producing stylistic abstraction of a photograph. Based on mean curvature flow in conjunction with shock filter, our method simplifies both shapes and colors simultaneously while preserving important features. In particular, we develop a constrained mean curvature flow, which outperforms the original mean curvature flow in conveying the directionality of features and shape boundaries. The proposed algorithm is iterative and incremental, and therefore the level of abstraction is intuitively controlled. Optionally, simple user masking can be incorporated into the algorithm to selectively control the abstraction speed and to protect particular regions. Experimental results show that our method effectively produces highly abstract yet feature‐preserving illustrations from photographs.