基于鞍点搜索的粘连对象图像分割方法

针对图像中不规则形状物体接触的分割问题,提出一种采用Hessian矩阵来判断分割点（即鞍点）进行粘连对象分割的方法。根据对图像进行腐蚀操作得到的三维地貌图,结合鞍点的数学特性,运用Hessian矩阵的特征值对鞍点进行搜索定位,沿经过鞍点的最大梯度路径分割粘连对象。与目前已有的几种分割算法相比,该方法具有算法简捷、分割效果好以及易于实现的特点。     

基于自适应多重欧氏距离变换的分水岭粘连颗粒分割方法

颗粒形状以及颗粒粘连程度是影响粘连颗粒分割效果的主要因素,现有粘连颗粒分割方法主要存在两方面不足:一些方法只能应对某一特定形状颗粒的分割问题;大多数方法不能根据颗粒粘连程度自适应地调整分割算法,当粘连程度较大时容易出现欠分割。针对上述问题,该文提出了一种不限定颗粒形状的自适应粘连颗粒图像分割方法,该方法根据颗粒粘连程度对图像进行自适应多重欧氏距离变换,得出分水岭脊线对粘连颗粒图像进行分割。实验表明,本算法对不同形状、不同粘连程度的颗粒均具有较好的分割效果。     

粘连颗粒分割方法研究

颗粒图像的分割中,经常遇到颗粒粘连、重叠在一起的现象,需要将它们分离为单个颗粒目标。本文提出了一种基于灰度形态学重建的图像分割新算法,实验结果表明,该算法既能更有效地分割粘连颗粒,其应用于图像处理也有着较好的应用前景。     

基于模糊距离变换的岩心图像颗粒分割算法

岩心CT图像中相邻颗粒之间存在相互粘连,粒度参数分析等需要对粘连颗粒进行分割。结合岩心粘连颗粒的特性,提出一种基于模糊距离变换的改进颗粒分割算法。首先,对预处理后的岩心图像进行模糊距离变换并提取出距离信息的灰度图像,然后利用形态学膨胀重构方法提取标记作为后续分水岭算法的种子点,根据种子点采用一种基于测地重建的改进分水岭算法得到相邻种子点之间的分割线,最后完成粘连颗粒的分割。实验结果表明本文算法可以提高粘连颗粒分割的准确度并减轻分水岭算法的过分割现象。     

基于流域算法的粘连颗粒图像分割

在分割颗粒图像中,经常会有颗粒重叠粘连,这给图像的后续分析处理带来了很大的麻烦。针对这一问题,提出了一种有效的基于流域分割算法的颗粒图像分析方法。该算法提出一种新的种子点选取方法,使得种子区域最大化,然后以种子区域为核心通过流域膨胀变换重建原图,当图像中所有像素点都重建完时,粘连颗粒图像的分割就完成了。文中主要叙述了算法的设计思想及实现,并给出了实验结果。实验表明该算法能有效改善因多种子点而引起的过分割现象,对形状不规则的颗粒也同样适用,能取得比较满意的分割效果。     

基于流域算法的粘连颗粒图像分割

在分割颗粒图像中,经常会有颗粒重叠粘连,这给图像的后续分析处理带来了很大的麻烦。针对这一问题,提出了一种有效的基于流域分割算法的颗粒图像分析方法。该算法提出一种新的种子点选取方法,使得种子区域最大化,然后以种子区域为核心通过流域膨胀变换重建原图,当图像中所有像素点都重建完时,粘连颗粒图像的分割就完成了。文中主要叙述了算法的设计思想及实现,并给出了实验结果。实验表明该算法能有效改善因多种子点而引起的过分割现象,对形状不规则的颗粒也同样适用,能取得比较满意的分割效果。     

一种基于纹理方向场的图像分割方法

提出了一种基于纹理方向场的图像分割方法。根据图像平滑滤波原理构造了高斯滤波器与分块滤波器相结合的平滑方法,利用纹理梯度方向场特征形成纹理梯度图像,以此为基础用分水岭算法对图像进行分割。结果表明,将该方法应用于粘连大米颗粒图像,能有效分割粘连大米图像,较好地解决了分水岭算法的过分割问题,具有较强的边缘稳定性。     

基于图像处理的微小电子元器件自动计数算法

根据微小电子元器件的形状和正反两面的纹理特征,提出一种基于图像处理的微小电子元器件自动计数算法.该算法采用层次特征提取及数学形态学的图像分割算法,对图像中的元器件正面和反面,分别进行图像处理.根据元器件反面亮度高及纹理简单的特点,采用阈值化方法对其进行完全分割.将正面朝上的元器件从图像中分割出来,并采用数学形态学方法分离粘连的正面元器件.从而对粘连在一起的微小电子元器件实现了完全分割.对元器件进行精确分割后,即可采用连通区域标记的方法对所有分离的元器件进行计数.该算法实现了微小电子元器件实时自动计数,计数精度达到百分之百.     

基于模糊距离变换的颗粒图像分割方法

在颗粒图像中,经常存在颗粒重叠或者粘连现象。本文提出了一种新的图像分割方法。该方法首先对颗粒图像进行二值化,然后对图像作模糊距离变换得到模糊距离图,再利用分水岭算法将粘连或者部分重叠颗粒分离。实验证明,此法能够将粘连颗粒物图像有效分离。     

能克服鞍点的并行计算寻优算法

为有效解决在求解具有鞍点的无约束最优化问题时寻优算法提前终止的问题,提出了一种能克服鞍点的计算机并行计算寻优算法。该算法以共轭梯度法为基础,对该算法寻优终止的条件进一步改进,提出当算法迭代到鞍点时,选择雅克比矩阵的所有正特征值对应的特征向量所对应的方向作为新的搜寻方向,重新搜索且并行计算取最优。最后通过实例验证了该算法能成功克服鞍点,并成功收敛到函数的极小值。     

求解马鞍点的两种算法及性能分析

求解矩阵中的马鞍点是计算机程序设计中的常见问题。结合矩阵中马鞍点的特点,给出了求解矩阵中的马鞍点的依次搜索法和多马鞍点相等法,详细叙述了它们的算法思想,特别对多马鞍点相等法的理论基础做了证明,分别给出了对应的算法。最后针对这两种算法进行了时间性能和空间性能的分析和比较,总结了两种算法各自的优缺点。     

An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games

In this paper, a new iterative adaptive dynamic programming (ADP) method is proposed to solve a class of continuous-time nonlinear two-person zero-sum differential games. The idea is to use the ADP technique to obtain the optimal control pair iteratively which makes the performance index function reach the saddle point of the zero-sum differential games. If the saddle point does not exist, the mixed optimal control pair is obtained to make the performance index function reach the mixed optimum. Stability analysis of the nonlinear systems is presented and the convergence property of the performance index function is also proved. Two simulation examples are given to illustrate the performance of the proposed method.     

Research on 3D medial axis transform via the saddle point programming method

The present paper investigates the 3D medial axis transform of objects bounded by freeform surfaces via the saddle point programming method, a mathematical programming approach used to identify the saddle points of a function. After exploring the local geometry and saddle point property of 3D medial axis transform, the mathematical programming method is employed to construct the saddle point programming models. Based on the optimality conditions that the optimal solutions should satisfy, a generic algorithm for computing various medial axis points is developed. In order to identify the junction points and localize the problem, the boundary and the skeletal curves are divided into skeletal segments, and it is proved to be efficient and accurate by numerical examples.     

基于迭代式动态规划的影像密集匹配

针对动态规划影像密集匹配中因匹配的整体相关性导致的误匹配点连带扩散效应问题,提出了一种基于迭代式动态规划的影像密集匹配算法。该算法在影像密集匹配过程中引入了视差方向一致性、视差突变性作为迭代判定准则,通过对动态规划匹配结果中不满足迭代条件的候选匹配点子集进行分析,在候选匹配点子集中识别出误匹配点并去除之,反复迭代直至满足迭代准则,从而解决了误匹配点的连带扩散效应问题。该算法已成功应用于嫦娥三号遥操作项目,经在轨应用的检验表明,提出的基于迭代式动态规划的影像密集匹配算法能够极大地降低立体影像匹配中密集同名点的误匹配率。     

Computation of the medial axis of planar domains based on saddle point programming

This paper presents a saddle point programming approach to compute the medial axis (MA). After exploring the saddle point properties of the medial axis transform (MAT), the mathematical programming method is employed to establish the saddle point programming model of the MAT. By using the optimal conditions, i.e., the number and distribution of the tangent points between the boundary and medial axis disk, the one- and two-dimensional saddle point algorithms are developed. In order to determine the branch point, it is better to consider its generating mechanism. Here, we identify the branch point according to the sudden changes of the solutions to the one-dimensional saddle point algorithm. Hence, all the regular and irregular points of MA can be computed by a general algorithm, and it is proved to be efficient and accurate by the numerical examples.     

Saddle Point Optimality Criteria of Interval Valued Non-Linear Programming Problem

The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem. To achieve the study objective, we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem. Also, we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems. After that, we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem. Next, we have shown that both the saddle point conditions (Fritz-John and Kuhn-Tucker) are sufficient without any convexity requirements. Then with the convexity requirements, we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints. Here, all the results are derived with the help of interval order relations. Finally, we illustrate all the results with the help of a numerical example.     

非线性零和微分对策的事件触发自适应动态规划算法

针对一类非线性零和微分对策问题,本文提出了一种事件触发自适应动态规划(event-triggered adaptive dynamic programming,ET--ADP)算法在线求解其鞍点.首先,提出一个新的自适应事件触发条件.然后,利用一个输入为采样数据的神经网络(评价网络)近似最优值函数,并设计了新型的神经网络权值更新律使得值函数、控制策略及扰动策略仅在事件触发时刻同步更新.进一步地,利用Lyapunov稳定性理论证明了所提出的算法能够在线获得非线性零和微分对策的鞍点且不会引起Zeno行为.所提出的ET--ADP算法仅在事件触发条件满足时才更新值函数、控制策略和扰动策略,因而可有效减少计算量和降低网络负荷.最后,两个仿真例子验证了所提出的ET--ADP算法的有效性.     

Local shading analysis

Local analysis of image shading, in the absence of prior knowledge about the viewed scene, may be used to provide information about the scene. The following has been proved. Every image point has the same image intensity and first and second derivatives as the image of some point on a Lambertian surface with principal curvatures of equal magnitude. Further, if the principal curvatures are assumed to be equal there is a unique combination of image formation parameters (up to a mirror reversal) that will produce a particular set of image intensity and first and second derivatives. A solution for the unique combination of surface orientation, etc., is presented. This solution has been extended to natural imagery by using general position and regional constraints to obtain estimates of the following: ? surface orientation at each image point; ? the qualitative type of the surface, i.e., whether the surface is planar, cylindrical, convex, concave, or saddle; ? the illuminant direction within a region. Algorithms to recover illuminant direction and estimate surface orientation have been evaluated on both natural and synthesized images, and have been found to produce useful information about the scene.     

On the classification of toppoints in scale space

An algebraic classification scheme for toppoints in scale space is proposed. A critical point is a point whose spatial derivatives are zero, and a toppoint is a critical point in which the Hessian does not have full rank. A critical curve is a curve consisting of critical points. It is proposed that toppoints be classified according to the number of critical curves that intersect at the toppoint.Toppoints are analyzed further when one or two critical curves pass through the toppoint. If the Hessian is of rank one, a single critical curve passes through the toppoint; an extremum and a saddle point meet along a curve with a horizontal tangent at the toppoint. Two possibilities exist in the generic case. Either an extremum and a saddle point approach each other with increasing scale and disappear at the toppoint, or an extremum and a saddle are created at the toppoint and diverge from each other at increasing scale.If two critical curves intersect at a toppoint, there are again two different cases when Gaussian blurring is used. In the first case the Hessian has rank zero and the two curves intersect with horizontal perpendicular tangents. Two subcases occur, depending on the root structure of the cubic form of the Taylor expansion of the image at the toppoint. If this cubic form has a single real root, two extrema and two saddles approach the toppoint from below and disappear at the toppoint. The two extrema approach each other along a tangent from opposite directions. Similarly, the two saddles approach each other along the perpendicular tangent. If the cubic form has three distinct real roots, two saddles approach each other from below along a tangent from opposite directions. Above the toppoint the two saddles separate from each other in the perpendicular direction.In the second case the Hessian has rank one and there also exists another algebraic constraint on the coefficients of the cubic form of the Taylor expansion of the image of the toppoint. Two critical curves intersect at the toppoint. Again, two subcases occur, depending on whether the curves are real or complex. If the curves are real, there are two tangents at the intersection point but they are not horizontal, as in the previous subcase. An extremum and a saddle approach each other from below. Above the toppoint an extremum and a saddle separate from each other. The saddle above the toppoint moves in the same direction as the extremum below the toppoint, and the extremum above the toppoint moves in the same direction as the saddle below the toppoint. If the curves are complex, the toppoint is an isolated point in scale space.     

用单幅图像重建三维凸面和两类鞍面的方法

利用Eikonal方程的粘性解给出了基于单幅图像的凸面三维重建算法；定义了2类鞍面——加性鞍面和乘性鞍面．利用凸面法和凹面法从鞍面单幅图像重建2个抛物柱面，然后根据鞍面的结构特点将2个抛物柱面重新合成鞍面．文中算法从临界点开始计算，不要求边界条件，具有较高的精确度．最后通过实验分析了该算法对噪声的敏感性．