一种灰度形态算子的构造方法

提出了采用灰度结构元图像的灰度形态算子的构造方法。所构造的形态算子采用了适合灰度结构元图像与灰度图像间操作的结构，其相应的操作具有较明确的物理解释，从而适合招待灰度图像处理任务。     

Soft Morphological Filtering Using a Fuzzy Model and its Application to Colour Image Processing

Abstract Soft morphological filters form a class of filters with many desirable properties. They were introduced to improve the behaviour of standard morphological filters in detail preservation and noise elimination. In this paper, a framework for soft morphological colour image processing using a fuzzy model is introduced. This extends the standard colour morphological operators in the same way that soft greyscale morphology extends the standard greyscale morphology theory. The primary and secondary operations of the new soft morphological approach are defined. The proposed operators are less sensitive to image distortion and to small variations in the shape of the objects, and perform significantly better in impulse noise removal problems, compared to standard morphological operators. Experimental results of the application to real colour images demonstrate these advantageous characteristics of the new operators. Additionally, illustrative examples that exhibit the applicability of the proposed methodology to edge detection problems are also included.An erratum to this article can be found at     

矢量自对偶形态学滤波算子

自对偶形态学算子不依赖形态学腐蚀、膨胀算子的先后次序, 是一种等同处理图像背景和前景的形态学算子. 而将自对偶形态学算子拓展到多通道图像处理是一个难题. 为了解决该问题, 提出了基于极值约束的矢量自对偶形态学滤波算子(EC-VSDMF). 首先根据对称矢量排序算法构建满足对偶性的矢量形态学算子, 然后依据形态学算子中的极值原理优化矢量集合, 从而有效抑制矢量集合中包含单通道极值的矢量作为输出结果, 最终实现了具有约束功能的矢量自对偶形态学滤波算子(VSDMF). 实验结果表明, EC-VSDMF继承了传统自对偶形态学滤波算子的性质, 将其应用于彩色图像滤波可以改善现有矢量形态学滤波算子导致滤波后图像亮度和色度发生偏移的问题. 滤波后的图像在有效抑制噪声的同时较好地保留了图像细节, 滤波性能甚至超过了多种现有的矢量中值滤波算子.     

Probabilistic pseudo-morphology for grayscale and color images

Mathematical morphology offers popular image processing tools, successfully used for binary and grayscale images. Recently, its extension to color images has become of interest and several approaches were proposed. Due to various issues arising from the vectorial nature of the data, none of them imposed as a generally valid solution. We propose a probabilistic pseudo-morphological approach, by estimating two pseudo-extrema based on Chebyshev inequality. The framework embeds a parameter which allows controlling the linear versus non-linear behavior of the probabilistic pseudo-morphological operators. We compare our approach for grayscale images with the classical morphology and we emphasize the impact of this parameter on the results. Then, we extend the approach to color images, using principal component analysis. As validation criteria, we use the estimation of the color fractal dimension, color textured image segmentation and color texture classification. Furthermore, we compare our proposed method against two widely used approaches, one morphological and one pseudo-morphological.     

基于HSV彩色空间的矢量形态学算子

在HSV彩色空间中,现有的矢量形态学算子对彩色像素的排序依据V、S、H顺序分层进行,从而违背了彩色图像中三个分量的平等原则,导致矢量形态学滤波算子难以去除彩色图像中由色调和饱和度分量引起的噪声,因此滤波算子性能较差.文中提出了一种基于HSV三分量混合运算的矢量形态学排序规则,并根据该规则定义了新的矢量形态学腐蚀、膨胀算子以及常用的矢量形态学滤波算子.实验结果表明,新的矢量形态学滤波算子较现有的矢量形态学滤波算子具有更强的噪声抑制性能,在保证图像不增加新的彩色像素的同时,去除了噪声并保留了图像细节,滤波后的图像具有较高的峰值信噪比和较小的均方根误差.     

Fast Algorithms for Area Morphology

Acton, S. T., Fast Algorithms for Area Morphology, Digital Signal Processing11 (2001) 187–203Efficient algorithms are developed for area morphology. As opposed to traditional morphological operations that alter grayscale images via a concatenation of order statistic filters, the area morphological operators manipulate connected components within the image level sets. Essentially, the area morphology filters are capable of removing objects based on the object area solely. These operators can then be effectively used in important multiscale and scale space tasks such as object-based coding and hierarchical image searches. Unfortunately, the traditional implementation of these filters based on level set theory precludes real-time implementation. This paper reviews previous fast algorithms and introduces a pyramidal approach. The full pyramidal algorithm is over 1000 times faster than the standard algorithm for typical image sizes. The paper provides supporting simulation results in terms of computational complexity and solution quality.     

均匀空间色差度量的矢量形态学图像处理

彩色图像矢量形态学处理中,针对矢量排序准则存在模糊性和片面性等缺点,提出一种新的矢量排序方法。首先根据在均匀的Lab空间中,颜色之间视觉上的差距与颜色坐标上的欧几里得距离成正比的特点,将量化后的色差大小作矢量排序准则;然后利用四元数法建立彩色图像模型和形态学结构元素模型,在此基础上定义新的彩色形态学基本运算子;最后研究了矢量形态学图像处理算法,对比了本文方法和HSV矢量排序法的应用效果。实验结果表明,本文方法能较好地用于提取图像边缘和去除椒盐噪声。     

基于模糊相似性的彩色形态学图像处理方法

为了将传统灰度图像数学形态学扩展到彩色图像,提出一种结合矢量空间模糊相似性的彩色形态学图像处理方法。首先,在RGB彩色空间中利用彩色矢量间的距离和角度定义模糊相似性测度,以刻画与人类视觉感知相一致的彩色相似程度;以上述相似性测度为准则定义彩色空间中任意一组彩色的上确界和下确界;利用中心像素及其结构单元内像素的上确界和下确界构建彩色形态学的基本操作,包括膨胀、腐蚀、开、闭等操作;进一步将提出的彩色形态学操作应用于高分辨率遥感图像,通过实验对比验证其对地物目标的形变和平滑能力,说明其实用性和有效性。     

鲁棒的形态学彩色图像边缘检测算法

针对传统边缘检测算子对噪声敏感的缺点,提出一种新的基于数学形态学的彩色图像边缘检测算法。该算法在传统形态学边缘检测算子的基础上,通过综合形态膨胀和形态腐蚀,设计出一种多尺度、多结构元素的抗噪型边缘检测算子,利用新算子对R、G、B三个分量分别检测出图像的边缘分量,对三个边缘分量进行融合得到最终的彩色边缘信息。仿真实验表明,该方法得到的边缘轮廓清晰,边缘定位精度较高,比传统的边缘检测方法具有更好的噪声鲁棒性和边缘细节保护能力。     

灰阶边缘的细化

本文提出了一种改进了的灰阶图象Sobel边缘细化新方法,通过对灰阶边缘图多次Sobel边缘细化结果的叠加使边缘点的数值拔高、变陡,再通过灰阶边缘图中各3x3邻域内取数值最大的三个点作边缘,得到单点宽的边缘-其中后者也适用于其它边缘检测算子.此方法处理简单、效果明显,为从图象中提取模糊边缘和微弱边缘、提高定位精度,提供了一种有效的手段.     

A comparative study on multivariate mathematical morphology

The successful application of univariate morphological operators on several domains, along with the increasing need for processing the plethora of available multivalued images, have been the main motives behind the efforts concentrated on extending the mathematical morphology framework to multivariate data. The few theoretical requirements of this extension, consisting primarily of a ranking scheme as well as extrema operators for vectorial data, have led to numerous suggestions with diverse properties. However, none of them has yet been widely accepted. Furthermore, the comparison research work in the current literature, evaluating the results obtained from these approaches, is either outdated or limited to a particular application domain. In this paper, a comprehensive review of the proposed multivariate morphological frameworks is provided. In particular, they are examined mainly with respect to their data ordering methodologies. Additionally, the results of a brief series of illustrative application oriented tests of selected vector orderings on colour and multispectral remote sensing data are also discussed.     

基于HSL空间彩色图像多结构元形态边缘检测

构建了一类在HSL颜色空间基于多结构元彩色形态边缘梯度检测算法实现彩色图像边缘检测新算法,多结构元形态边缘检测有着比单一结构元素形态边缘检测更优越的性能。该方法是把RGB空间的彩色图像转换到HSL空间,并且定义了在HSL空间的彩色形态学基本算子,提出了改进的多结构元彩色形态边缘检测算法。经过大量实验证明,该算法在有噪声的干扰下,比传统的方法能够更好地抑制噪声并提取有用的图像边缘信息,能满足不同的应用需要。     

Theoretical foundations of spatially-variant mathematical morphology part I: binary images

We develop a general theory of spatially-variant (SV) mathematical morphology for binary images in the Euclidean space. The basic SV morphological operators (i.e., SV erosion, SV dilation, SV opening and SV closing) are defined. We demonstrate the ubiquity of SV morphological operators by providing a SV kernel representation of increasing operators. The latter representation is a generalization of Matheron's representation theorem of increasing and translation-invariant operators. The SV kernel representation is redundant, in the sense that a smaller subset of the SV kernel is sufficient for the representation of increasing operators. We provide sufficient conditions for the existence of the minimal basis representation in terms of upper-semi-continuity in the hit-or-miss topology. The latter minimal basis representation is a generalization of Maragos' minimal basis representation for increasing and translation-invariant operators. Moreover, we investigate the upper-semi-continuity property of the basic SV morphological operators. Several examples are used to demonstrate that the theory of spatially-variant mathematical morphology provides a general framework for the unification of various morphological schemes based on spatiallyvariant geometrical structuring elements (e.g., circular, affine and motion morphology). Simulation results illustrate the theory of the proposed spatially-variant morphological framework and show its potential power in various image processing applications.     

关于彩色图象处理的形态学算子研究

彩色形态变换是数学形态学从灰度图象到彩色图象的推广,基于ＲＧＢ（ｒｅｄ－ｇｒｅｅｎ－ｂｌｕｅ）彩色坐标系统,提出了彩色形态变换的理论,并讨论了它们的性质,进而建立了彩色形态变换与灰度形态学的联系,彩色形态变换作为一种数学形态学方法在彩色空间的延拓,可有效地应用于彩色图象处理、图象编码和目标形状特征提取等。     

On the role of complete lattices in mathematical morphology: From tool to uncertainty model

Mathematical morphology has a rich history. Originally introduced for binary images, it was quite soon extended to grayscale images, leading to grayscale morphology with the threshold approach and the umbra approach. Later on, different models based on fuzzy set theory were introduced. These models were based on the observation that, from a formal point of view, grayscale images and fuzzy sets are modeled in the same way. Consequently, techniques from fuzzy set theory could be applied in the context of mathematical morphology, and fuzzy mathematical morphology was born. In that framework, fuzzy set theory was only a tool to construct morphological models, and was not employed to model any fuzziness or uncertainty. Quite recently however, new extensions have led to the construction of fuzzy interval-valued and fuzzy intuitionistic mathematical morphologies. Here, extensions of fuzzy set theory actually take into account the uncertainty that comes along with image capture, specifically regarding the grayscale values, which in some cases is also related to the uncertainty regarding the spatial position of an object in an image. In this framework, (extended) fuzzy set theory not only serves as a tool to deal with grayscale images, but also as a model for uncertainty. This paper sketches this evolution of fuzzy set theory in the field of mathematical morphology, and also points out some directions for future research.     

卷积形态滤波与图像去噪

本文提出的卷积形态变换是一种新的形态变换形式,具有线性卷积的结构和形态变换的性质。这种新的形态变换以乘性结构元素为特征,它不同于具有加性结构元素的普通形态变换,对于它们的性质和结构的研究也是本文的主要工作之一。另一方面的工作是针对卷积形态核提出了一种结构化的自动生成算法。研究表明,卷积形态滤波与卷积积分变换一样,对于图像具有去噪和平滑作用,且在实验效果上具有较通常的形态滤波和线性卷积变换更优的去噪和平滑功能。     

柔性(soft)形态学在图象边缘检测中的应用

根据柔性形态学单调性、扩展性、和反扩展性等基本理论,讨论了柔性形态学在边缘检测中的应用,柔性形态变换是在经典形态变换基础提出了提出的一些非线性算子,它放宽了经典形态变换的定义,以获得一定程度的鲁棒性,但是,还保留了经典形态算子的优良特性,进而从理论上和几何意义上讨论了其进行边缘检测的原理,及算子的选择,另外,还与标准形态算子及Ｒｏｂｅｒｔ算子的处理结果进行了比较。通过计算机模拟实验表明：基于柔性形     

Comparative evaluation of linear edge detection methods

A comparative evaluation of the most commonly used linear methods for edge detection in grayscale images are presented. Detectors based on the first and second derivatives of image brightness are considered. The method for automatic edge tracking in grayscale images is proposed. The model for assessing errors and artifacts caused by sampling during digitization of real input images is proposed. Investigation of edge detectors isotropy and errors caused by input images sampling is conducted. The advantage of the Isotropic operator for edge tracking is shown. The noise immunity of linear edge detection methods is assessed and the superiority of 3 × 3 gradient operators for noisy images is shown. Isotropic and Sobel operators are identified to be optimal on a basis of sampling errors, output noise level, and computational complexity.     

一种新颖的灰度形态学算子

数学形态学方法是非线性图像处理中的一种重要方法,在二值图像处理中已获得了广泛的应用,但在灰度图像处理中的应用却相对有限,文中从形态学算子构造的角度出发,提出了一种具有较强实用能力的灰度形态学算子的构造方法。