二值图像边缘检测的动态数学形态运算方法

应用基本形态运算,定义了动态形态学运算,并将动态膨胀运算应用到图像对象的边缘检测,运算方法只对图像中的对象进行运算,在每一步运算中,动态地选择结构元素的下一个原点位置。运算方法减少了运算量,执行速度快、效率高,在MATLAB6.5上得到了满意的仿真效果。     

A system for fast erosion and dilation of Bi-level images

Computer image-processing techniques are often used in, for example, the analysis of thin sections of reservoir rock because of the large amounts of data contained in a single digitized section image. Erosion and dilation are operations frequently used in this type of work to iteratively smooth the pore perimeters and in estimating pore radii, volume, and roughness. Because of the size of each image, erosion and dilation of pore complex images is a time-consuming process. A recent method calledglobal erosion is much faster whether used on small, in-memory images or large images residing on a file. Use of this method should allow processing of larger images, or a greater number of small images, than do the standard methods.     

Mutational equations for shapes and vision-based control

Basic idea of vision-based control in robotics is to include the vision system directly in the control servo loop of the robot. When images are binary, this problem corresponds to the control of the evolution of a geometric domain. The present paper proposes mathematical tools derived from shape analysis and optimization to study this problem in a quite general way, i.e., without any regularity assumptions or modelsa priori on the domains that we deal with. Indeed, despite the lackness of a vectorial structure, one can develop a differential calculus in the metric space of all non-empty compact subsets of a given domain ofR ⁿ , and adapt ideas and results of classical differential systems to study and control the evolution of geometric domains. For instance, a shape Lyapunov characterization allows to investigate the asymptotic behavior of these geometric domains using the notion of directional shape derivative. We apply this inR ² to the visual servoing problem using the optical flow equations and some experimental simulations illustrate this approach.     

数学形态学在图象处理中的应用进展

数学形态学是一种非线性滤波方法,形态和差运算,即膨胀与腐蚀是数学形态学的基础,数学形态学已由二值形态学、灰度形态软数学形态学、模糊形态学发展到模糊软形态学,可用于抑制噪声、特征提取、边缘检测、图象分割、形状识别,纹理分析、图象恢复与重建等图象处理问题,在图象处理领域得到了越来越广泛的应用,本文结合目前的研究进展,对数学形态学的理论研究及其应用进展进行综述性阐述。     

Vector-space solution for a morphological shape-decomposition problem

We define a restricted domain as the discrete set of points representing any convex, four-connected, filled polygon whose (i) vertices lie on the lattice points, (ii) interior angles are multiples of 45°, and (iii) number of sides are at most eight. We describe the boundary code and discrete half-plane representation and use them for representing restricted domains. Morphological operations of dilation and n-fold dilation on the restricted domains with structuring elements that are also restricted domains are expressed in terms of the above representations. We give algorithms for these operations and prove that they are of O(1) complexity and hence are independent of the size of the objects.We prove that there is a set of 13 restricted domains {K ₁, K ₂, ..., K ₁₃} such that any given restricted domain K is expressible as % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiabg2% da9iaadUeadaWgaaWcbaGaaGimaaqabaGccqGHvksXdaqadeqaamaa% xababaGaeyyLIumaleaacaWGRbWaaSbaaWqaaiaaigdaaeqaaaWcbe% aakiaadUeadaWgaaWcbaGaaGymaaqabaaakiaawIcacaGLPaaacqGH% vksXdaqadeqaamaaxababaGaeyyLIumaleaacaWGRbWaaSbaaWqaai% aaikdaaeqaaaWcbeaakiaadUeadaWgaaWcbaGaaGymaaqabaaakiaa% wIcacaGLPaaacqGHvksXcaGGUaGaaiOlaiaac6cacqGHvksXdaqade% qaamaaxababaGaeyyLIumaleaacaWGRbWaaSbaaWqaaiaaigdacaaI% ZaaabeaaaSqabaGccaWGlbWaaSbaaSqaaiaaigdacaaIZaaabeaaaO% GaayjkaiaawMcaaaaa!5B9E!\[K = K_0 \oplus \left( {\mathop \oplus \limits_{k_1 } K_1 } \right) \oplus \left( {\mathop \oplus \limits_{k_2 } K_1 } \right) \oplus ... \oplus \left( {\mathop \oplus \limits_{k_{13} } K_{13} } \right)\] where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWabeaada% WfqaqaaiabgwPifdWcbaGaam4AamaaBaaameaacaWGPbaabeaaaSqa% baGccaWGlbWaaSbaaSqaaiaadMgaaeqaaaGccaGLOaGaayzkaaaaaa!3DCB!\[\left( {\mathop \oplus \limits_{k_i } K_i } \right)\] represents the k _i -fold dilation of K _i and K ₀ is a translation. We show that this entails a linear transformation from a 13-dimensional space in which restricted domains are represented in terms of n-fold dilations of the 13 basis structuring elements, to an eight-dimensional space in which restricted domains are represented in terms of their eight side lengths. Furthermore, we show that any particular decomposition forms a particular solution of this transformation and that finding all possible dilation decompositions of a restricted domain is equivalent to finding the general solution of this transformation. Finally, we derive a finite-step algorithm for finding a particular decomposition and then give an algorithm for finding all possible decompositions.     

二值图像膨胀腐蚀的快速算法

传统二值图像膨胀腐蚀算法存在大量冗余操作,运算效率低,制约了大结构元素在实际工程上的应用。提出了一种快速膨胀腐蚀算法。首先针对结构元素建立方向-位置偏移表,然后提取图像的边界,对每一条边界用一个起始点和一条方向链表示。对边界进行膨胀处理,根据方向链查询方向-位置偏移表,对表中记录的像素进行填充。将边界的膨胀结果与原图像的并集作为对原图膨胀的结果。快速腐蚀运算可根据膨胀与腐蚀的对偶性在此基础上实现。实验结果表明,相对于传统算法及其他优化算法,该算法速度更快,实用性更强。     

调节形态学运算及其神经网络实现

数学形态学是一门建立在集合论基础上的学科,为数字图像处理和分析提供了一种有效的工具.在分析传统的数学形态学基本运算的基础上,引入调节数学形态学运算的概念,然后讨论了调节形态学运算的神经网络实现,并给出了用于图像滤波的计算机仿真结果.该方法较之传统的数学形态学基本运算更为灵活.     

Mathematical morphological operations of boundary-represented geometric objects

The resemblance between the integer number system with multiplication and division and the system of convex objects with Minkowski addition and decomposition is really striking. The resemblance also indicates a computational technique which unifies the two Minkowski operations as a single operation. To view multiplication and division as a single operation, it became necessary to extend the integer number system to the rational number system. The unification of the two Minkowski operations also requires that the ordinary convex object domain must be appended by a notion of inverse objects or negative objects. More interestingly, the concept of negative objects permits further unification. A nonconvex object may be viewed as a mixture of ordinary convex object and negative object, and thereby, makes it possible to adopt exactly the same computational technique for convex as well as nonconvex objects. The unified technique, we show, can be easily understood and implemented if the input polygons and polyhedra are represented by their slope diagram representations.     

腐蚀/膨胀算法在足球机器人视觉系统中的应用

在FIRA MiroSot机器人足球比赛中;视觉系统是获得比赛场上机器人与球位置信息的唯一途径。视觉系统的识别速度、精度直接影响到比赛的胜负。针对传统视觉系统在机器人足球比赛中获取各实体的位置不够准确的问题;提出了一种结合数学形态学中腐蚀/膨胀算法来处理视觉系统中的实时图像;增加足球机器人视觉系统识别的精度的设计方案。实验结果表明;该方案在没有降低比赛中识别速度的前提下;大大地提高了识别精度。     

彩色图像形态学的研究及其应用

基于对彩色图像形态学的研究,提出一种面向RGB颜色空间的距离和字典序相结合的颜色向量序,给出基于所定义像素序实现的彩色图像形态学膨胀、腐蚀、开和闭算子。把灰度图像形态学重构及一种边缘增强和噪声清除的算法推广到彩色图像。实验结果表明,基于向量序实现的彩色图像形态学的基本算子性能良好,边缘增强和过滤的效果较好。     

数学形态学在作物病害图像处理中的应用研究

作为一种2维卷积运算的非线性图像处理方法,数学形态学的内容包括二值形态学、灰度形态学和彩色形态学。膨胀、腐蚀、开运算、闭运算是数学形态学的基础。数学形态学可用于噪声去除、边缘检测、图像分割、特征提取等图像处理问题,在图像处理领域得到了越来越广泛的应用。结合目前的研究进展,对数学形态学的分类及其在作物病害图像处理中的应用进行综合性阐述,并对数学形态学目前存在的问题以及未来的发展方向进行了讨论。     

基于改进的彩色图像形态学膨胀和腐蚀算子设计

分析了RGB、LSH、L^*a^*b^*颜色空间的优缺点,提出了一种面向RGB颜色空间的、基于改进的距离序和字典序相结合的颜色向量序并分析了其性能;定义了彩色图像形态学的基本算子,实现了彩色图像形态学重构开算法。实验结果表明提出的颜色向量序性能良好,建立在该向量序上的彩色图像形态学算法能够较好的保持图像的边缘信息和色调,并且亮度均匀,与原图像相比对比度均匀增强,重构开算法的实验结果比原文献中方法有了较大的改进;具有不需要在不同的颜色空间之间转换的优点。     

Boundary detection using mathematical morphology

Object boundaries contain important shape information in an image. Mathematical morphology is shape sensitive and can be used in boundary detection. In this paper, we propose dynamic mathematical morphology which only operates on the parts of interest in an image and reacts to certain characteristics of the region. The next position of the structuring element is dynamically selected at each step of the operation. The technique is used to detect object boundaries and has produced encouraging results.     

Local decomposition of gray-scale morphological templates

Template decomposition techniques can be useful for improving the efficiency of imageprocessing algorithms. The improved efficiency can be realized either by reorganizing a computation to fit a specialized structure, such as an image-processing pipeline, or by reducing the number of operations used. In this paper two techniques are described for decomposing templates into sequences of 3×3 templates with respect to gray-scale morphological operations. Both techniques use linear programming and are guaranteed to find a decomposition of one exists.This work was supported in part by the U.S. Air Force Armament Laboratory of Eglin Air Force Base under contract F08635-89-C-0134.     

基于数学形态学与Hough变换的乐谱谱线探测算法研究

数学形态学是综合了多学科知识的交叉学科,是一种非线性的图像分析理论,己成为图像处理的重要工具之一。文章简单介绍了数学形态学和二值形态学的基本运算—腐蚀和膨胀,并提出了基于数学形态学的乐谱谱线探测算法。实验结果证明,与Hough变换探测直线算法相比,该乐谱谱线探测算法具有运算速度快、效率高、抗噪声能力强等优点。     

Optimal mean-absolute-error filtering of gray-scale signals by the morphological hit-or-miss transform

The binary hit-or-miss transform is applied to filter digital gray-scale signals. This is accomplished by applying a union of hit-or-miss transforms to an observed signal's umbra and then taking the surface of the filtered umbra as the estimate of the ideal signal. The hit-or-miss union is constructed to provide the optimal mean-absolute-error filter for both the ideal signal and its umbra. The method is developed in detail for thinning hit-or-miss filters and applies at once to the dual thickening filters. It requires the output of the umbra filter to be an umbra, which in general is not true. A key aspect of the paper is the complete characterization of umbra-preserving union-of-hit-or-miss thinning and thickening filters. Taken together, the mean-absolute-error theory and the umbra-preservation characterization provide a full characterization of binary hit-or-miss filtering as applied to digital gray-scale signals. The theory is at once applicable to hit-or-miss filtering of digital gray-scale images through the three-dimensional (3-D) binary hit-or-miss transform.     

基于数学形态学的文档图像倾斜校正算法

随着信息采集技术的不断发展,文档图像在信息的数字化管理中越来越重要.对文档图像的倾斜校正进行了研究,给出了基于数学形态学和Hough变换相结合的算法,进行文档图像的倾斜校正,同时将算法应用于印刷体和手写体的文档图像.实验表明该算法可以有效应用于两种文档图像的倾斜校正.     

基于粗糙集模型的形态学算子

本文从数学形态学算子与粗糙集中上下近似算子的关系入手,指出了形态学运算膨胀与腐蚀、开与闭分别可视为相似关系下的两对上下近似算子,并构造出新的形态学算子。实现该算子,发现该算子具有良好的性质。     

数学形态学梯度算子检测铸铁金相图像边缘

金相图像处理是进行定量分析的前提,将金相图像中的目标物正确的提取出来对定量分析起着重要的作用.利用同态滤波器对亮度不均匀的铸铁金相图像进行滤波,校正因反射光强引起的亮度不均匀现象.基于数学形态学梯度算子提出新算法,利用预先定义的结构元素对图像中石墨边缘进行提取,之后经过后处理再进行填充.实验结果表明,该方法在保证石墨边缘的同时可以抑制噪声,能够有效提取出石墨的边界.     

Hole-spectrum representation and model-based optimal morphological restoration of binary images degraded by subtractive noise

A shape-based image representation grounded on the distribution of holes within an image is developed, and the manner in which this representation can be used to design optimal morphological filters to restore images suffering from subtractive-noise degradation is investigated. The image and noise models are predicated on the existence of some class of shape primitives into which both image and noise can be decomposed (relative to union), and this decomposition is developed within the framework of a general algebraic paradigm for component-based filtering that does not depend on the linear-space structure typically used in spectral representations. Both deterministic and nondeterministic models are considered, and in each case the necessary model constraints are fully explored. Moreover, the type of filters that are naturally compatible with the image-noise models are analyzed. Specifically, optimal morphological filter design is studied in terms of the shape-based hole spectrum (as linear filter design is studied in terms of the frequency spectrum). Various forms of a design algorithm are discussed, the particulars depending on a symmetric-difference error analysis yielding approximate error expressions in terms of the spectral decomposition and the geometry of the underlying shape primitives. Finally, the statistical estimation procedures required for practical implementation of the entire spectrum-filter paradigm are explained.