软形态学算子在医学图像边缘检测中的应用研究

简要介绍了软数学形态学的基本原理及形态学在图像边缘检测中的应用.利用软数学形态学中基本算子构造了一种新的边缘检测器,并将其用于医学图像的边缘检测.仿真结果表明,该边缘检测器可以较好地去除噪声并同时进行边缘检测.     

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     

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。     

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     

On the Decomposition of Interval-Valued Fuzzy Morphological Operators

Interval-valued fuzzy mathematical morphology is an extension of classical fuzzy mathematical morphology, which is in turn one of the extensions of binary morphology to greyscale morphology. The uncertainty that may exist concerning the grey value of a pixel due to technical limitations or bad recording circumstances, is taken into account by mapping the pixels in the image domain onto an interval to which the pixel’s grey value is expected to belong instead of one specific value. Such image representation corresponds to the representation of an interval-valued fuzzy set and thus techniques from interval-valued fuzzy set theory can be applied to extend greyscale mathematical morphology. In this paper, we study the decomposition of the interval-valued fuzzy morphological operators. We investigate in which cases the [α ₁,α ₂]-cuts of these operators can be written or approximated in terms of the corresponding binary operators. Such conversion into binary operators results in a reduction of the computation time and is further also theoretically interesting since it provides us a link between interval-valued fuzzy and binary morphology.     

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.     

基于数学形态学的微阵列芯片荧光图像处理与分析

微阵列芯片技术由于其高通量分析的特点被广泛应用在生命科学领域,图像处理与分析是微阵列芯片技术中的一个重要环节.文中主要研究了基于数学形态学的微阵列芯片图像处理及数据提取方法,该方法采用形态学重构对图像投影产生的一维信号进行处理,进而完成对图像样点阵列的网格划分,运用自适应阈值分割算法对每个网格内的样点进行了图像分割,运用前景和背景校正的方法对样点的光密度值进行提取.结果显示,该算法具有简单、快速、易于实现,对样点形状没有限制而且精确度高等特点.     

The recognition of road network from high‐resolution satellite remotely sensed data using image morphological characteristics

With the development of remote sensors and satellite technologies, high‐resolution satellite data such as IKONOS images have been available recently. By these new high‐resolution satellite data, remote sensing technologies can be successfully applied to more application areas such as extracting road network from high‐resolution satellite images. This paper proposes a newly developed approach to extract a road network from high‐resolution satellite images. The approach is based on the binary and greyscale mathematical morphology and a line segment match method. First, the outline of road network is detected based on the grey morphological characteristics. Then, the basic road network is detected by the line segment match method. Next, the detected basic road network is processed based on the knowledge about the roads and binary mathematical morphological methods. Finally, visual analysis and three indicators are used to evaluate the accuracy of the extracted road networks. The results of the accuracy evaluation demonstrate that the developed road network extraction approach can provide both good visual effect and high positional accuracy.     

基于柔性形态学的梯度边缘检测算法

在深入研究柔性数学形态学边缘检测算法的基础上,提出比传统柔性形态学膨胀和腐蚀算子具有更强鲁棒性的柔性形态学膨胀和腐蚀算子,在此基础上提出柔性形态学梯度边缘检测算法,实验证明了该算法对噪声特别是脉冲噪声有很强的抑制作用,并能很好地检测出图像的边缘信息。     

Grey-Scale Morphology Based on Fuzzy Logic

There exist several methods to extend binary morphology to grey-scale images. One of these methods is based on fuzzy logic and fuzzy set theory. Another approach starts from the complete lattice framework for morphology and the theory of adjunctions. In this paper, both approaches are combined. The basic idea is to use (fuzzy) conjunctions and implications which are adjoint in the definition of dilations and erosions, respectively. This gives rise to a large class of morphological operators for grey-scale images. It turns out that this class includes the often used grey-scale Minkowski addition and subtraction.     

脉冲噪声污染图象中的数学形态边缘检测器

深入地研究了数学形态学在边缘检测领域中的应用，系统地给出了形态差分算子的定义。同时，还研究了在受脉冲噪声污染的情况下，如何用形态差分算子准确地提取图象的边缘，并提出了几种具有抗噪能力的数学形态边缘检测算子。计算机模拟实验表明，正确使用数学形态的４种基本运算，将使数学形态边缘检测算子能较好地消除脉冲噪声对边缘的影响，效果优于其它边缘检测算子     

General-purpose curvilinear object detection with fuzzy mathematical morphology

Curvilinear object detection is the common denominator of several applications. Some illustrative examples are road detection from aerial or satellite images, human airways from volumetric 3D scans or vascular structures in eye-fundus images. In this work, we propose two general-purpose curvilinear object detectors that may serve as building blocks for application-specific systems. To do so, we employ fuzzy mathematical morphology operators due to their robustness with respect to uncertainty and noise, and the trade-off they offer between expressive power and computational requirements. The extraction of linear features is based on, respectively, the fuzzy hit-or-miss transform and the fuzzy top-hat transform. They can be customized depending on the width of the objects of interest. We compare these two approaches with other state-of-the-art, general-purpose curvilinear object detectors to highlight their strengths and shortcomings. Both detectors succeed at localizing the objects of interest in different greyscale images.     

Variable structuring element based fuzzy morphological operations for single viewpoint omnidirectional images

Morphological tools can provide transformations suitable for real projective images, but the camera and objects to be analyzed have to be positioned in such a manner that a regular mesh on the objects projects a regular mesh on the image. A morphological modification of the image is thus the projection of an equivalent operation on the object. Otherwise, due to perspective effects, a morphological operation on the image is not the projection of an equivalent operation on the objects to be analyzed. With catadioptric omnidirectional images, it is almost impossible to place the sensor such that a regular mesh on the scene projects a regular mesh on the image. Nevertheless, with proper calibration of a central catadioptric system, the projection of a regular structuring element in a scene can be determined for each point on the image.

The aim of this paper is to present new morphological operators that use this projective property. These operators make use of a structuring element of varying shape. Since this varying shape cannot be represented as a binary union of pixels, we propose to use a fuzzy extension of the classical gray-level morphology to account for this phenomenon. This fuzzy extension is performed via fuzzy integrals.     

基于柔性数学形态学的医学图像边缘提取

医学图像边缘提取,尤其是病灶部位的边缘提取,是医学图像处理中非常重要的预处理步骤,边缘提取的质量决定了图像的最终处理结果。人们一般习惯于用微分算子和梯度形态学算子提取边缘,但这类算子都不能很好地滤除噪声,也不能提取边缘细节。文章在阐述了数学形态学一般原理与方法及柔性数学形态学原理与性质的基础上,将柔性数学形态学用于左肺上叶周围型肺癌CT图像边缘提取。实验结果表明,这一方法比微分算子和形态学边缘梯度算子更能有效地滤除噪声并将肺部轮廓和肿瘤的大小与边缘准确地提取出来。     

一种计算图象形态梯度的多尺度算法

分水岭变换是一种非常适用于图象分割的形态算子,然而,基于分水岭变换的图象分割方法,其性能在很大程度上依赖于用来计算待分割图象梯度的算法。为了高效地进行分水岭变换,提出了一种计算图象形态梯度的多尺度算法,从而对阶跃边缘和“模糊”边缘进行了有效的处理,此外,还提出了一种去除因噪声或量化误差造成的局部“谷底”的算法,实验结果表明,图象采用本文算法处理后,再进行分水岭变换,即使不进行区域合并,也能产生有意义的分割,因而极大地减轻了计算负担。     

An Application of Fuzzy Mathematical Morphology to Interval-Valued Knowledge Representation: A Remark

Mathematical morphology is known by its useful tools for processing binary (black-and-white) and gray-tone images. Due to the success of mathematical morphology in processing binary images, there have been many successful attempts to generalize its methods to more general, i.e. gray-tone images. One of these attempts—the most intuitive one is based on replacing sets by fuzzy sets, thus defining so called fuzzy morphological operations. In this paper we show that these operations can be used successfully in nonimage applications. We can use methods developed in fuzzy mathematical morphology to compute the membership functions of different "approximate" statements. Also, an application to interval-valued knowledge representation is given.     

Hypercomplex Mathematical Morphology

The natural ordering of grey levels is used in classical mathematical morphology for scalar images to define the erosion/dilation and the evolved operators. Various operators can be sequentially applied to the resulting images always using the same ordering. In this paper we propose to consider the result of a prior transformation to define the imaginary part of a complex image, where the real part is the initial image. Then, total orderings between complex numbers allow defining subsequent morphological operations between complex pixels. More precisely, the total orderings are lexicographic cascades with the local modulus and phase values of these complex images. In this case, the operators take into account simultaneously the information of the initial image and the processed image. In addition, the approach can be generalized to the hypercomplex representation (i.e., real quaternion) by associating to each image three different operations, for instance directional filters. Total orderings initially introduced for colour quaternions are used to define the evolved morphological transformations. Effects of these new operators are illustrated with different examples of filtering.     

基于局部连接度和差异度算子的水平集纹理图像分割

目的 复杂纹理的图像分割一直是图像分割的难题,现有的一些纹理图像分割方法主要通过提取图像确定方向的灰度变化特征或者提取图像的局部灰度相似性特征得到特征图像,从而进行纹理图像的分割,然而,自然纹理中普遍存在局部形态相似和方向不确定的现象,导致现有方法不能准确地分割纹理图像。方法 本文提出局部连接算子和局部差异算子来描述局部纹理的形态相似性和局部纹理的差异度。一方面,通过设定一定阈值,将局部区域的灰度差异分为两类,分析两类差异的分布特征,从而提取图像的形态特性及局部连接度算子;另一方面,设置一种无方向性的灰度差异分析算子,提取图像局部的灰度差异值从而得到局部差异度算子。两个算子结合以更好地提取纹理图像的局部特征,然后通过融合局部相似度特征、局部差异度特征和灰度信息,构造水平集能量泛函,进而通过最小化能量泛函实现纹理图像分割。结果 相比基于Gabor变换、结构张量、局部相似度因子的纹理分割方法,提出的局部算子能够更好地区分自然图像的不同纹理区域,且对实验图像的平均分割准确率高达97%,远高于其他方法。因此,提出的模型对于自然纹理图像具有更好的分割效果。结论 本文提出了两种新颖的纹理特征局部描述子：局部连接度算子和局部差异度算子,能够有效地提取纹理特征,且有一定的互补性。实验表明,提出的方法对于复杂自然纹理图像具有良好的分割效果。     

基于模糊细胞神经网络的彩色图像形态学重构

利用彩色图像的ＲＧＢ空间分解,在模糊细胞神经网络上实现了彩色图像数学形态学的基本算子,并讨论了该实现相对于常规串行计算机算法的优越性和局阴,进一步地利用按分量的灰度重构,实现了彩色重构算法,最后讨论了该重构算法在抑帛镐频噪声中的应用,给出的仿真结果对对于推广模糊细胞神经网络在彩色图像实时处理和硅眼等模拟逻辑中的应用有着重要的意义。     

自适应多方向模糊形态学边缘检测算法*

提出了一种新的基于模糊增强的自适应多方向模糊形态学边缘检测算法。该算法可以适应多峰直方图分布图像的模糊边缘检测,结合了模糊增强方法和模糊形态学边缘检测方法,先使用隶属函数将图像转换为等效的图像模糊特征平面,在此基础上进行模糊增强,降低边缘模糊度,然后再转换到统一模糊区域中;最后进行多方向模糊形态学边缘提取。仿真实验证明该方法能够较好地去除椒盐噪声,并且能够检测出图像中模糊的边缘。