基于数学形态学和分形的金相图像处理关键技术研究
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摘要
随着生产的快速发展和科学技术的日趋进步,对制造机械设备的各种金属材料的可靠性和安全性要求越来越高,进而对金属材料质量检验和控制的手段、方法的要求也越来越高。迄今为止,金相技术一直是材料科学与工程领域应用最广泛、最易行有效的研究和检验方法,计算机辅助定量金相分析,具有精度高、速度快等优点,现正逐渐成为金相技术的核心,而金相图像处理又是定量金相分析的关键环节,因此开展对金相图像处理中关键技术的研究对金相技术的应用和发展有着巨大的工程价值。
金相图像处理的关键技术包括金相图像的边缘检测、图像分割(包括晶界恢复与重建)算法和分形维数计算。数学形态学是一种非常实用的金相图像处理方法,其关键是膨胀和腐蚀两种基本运算以及结构元素的构造。但传统的数学形态学膨胀运算影响金相图像灰度的连续性和均匀性,并且其形态变换的结构元素不变,是对整个图像的一种均衡的处理过程,这就会导致图像的“过处理”或“欠处理”,影响定量金相分析的准确性。为此,本文首先依据数学形态学理论,对金相图像的边缘检测和图像分割(包括晶界恢复与重建)进行深入研究,提出相关的理论和方法,并通过实验加以验证。分形理论是现代数学与非线性科学研究中十分活跃的一个分支,分形维数则是分形理论应用中最重要的一个方面,广泛应用于图像处理和分析领域。数学上有关分形维数的定义有好几种,但采用什么方法来计算金相图像的分形维数则是一个急待研究的问题。为此,本文深入分析金相图像和分形维数各种算法的特点,结合二者的特点提出相关的理论和方法,并通过实验加以验证。
本文的主要研究工作和创新性成果包括:
(1)针对现有金相图像边缘检测导致伪检测、漏检测以及多像素宽度边缘等“错误处理”问题,结合考虑金相图像复杂、含杂质和噪声较多等特点,提出了基于多尺度多结构元素的数学形态学边缘检测方法。经实验证明该算法是行之有效的,与传统的边缘检测方法相比,它提取的边缘更准确,连续性和光滑性更好,为金相图像晶粒参数的准确测定及分形维数的准确计算提供了技术支撑。
(2)从理论上系统论证了传统的膨胀运算对金相图像灰度连续性、均匀性的不良影响以及这种影响的程度与相应的结构元素之间的关系,对传统的灰度膨胀运算的定义作了合理的改进,为本文提出的金相图像晶界恢复与重建技术——多尺度测地膨胀奠定了理论基础。此外,还从理论上系统论证了传统的腐蚀运算保持金相图像灰度的连续性和均匀性,为结构元素尺度的选取提供了理论依据。
(3)依据已经证明的关于灰度膨胀、腐蚀运算对图像灰度连续性影响的结论,针对传统的金相图像分割算法的不足,结合金相图像的特点,提出了基于改进的膨胀运算的金相图像晶界恢复与重建技术——多尺度测地膨胀。用改进的膨胀运算取代传统的膨胀运算,提高了金相图像晶粒的边界恢复和重建的准确度、清晰度,减少了金相图像“过分割”、“欠分割”或“错误分割”的现象;用多尺度迭代腐蚀取代了传统的(单一尺度)重复腐蚀,用多尺度测地膨胀取代了传统的(单一尺度)重复测地膨胀,缩短了程序运行时间,提高了金相图像晶粒的边界恢复和重建的效率。
(4)结合金相图像的特点,利用本文构建的多尺度多结构元素边缘检测算子,提出基于形态膨胀体覆盖的金相图像分形维数算法。通过实验验证该算法是行之有效的,具有较高的理论和工程应用价值。
With the rapid development of production and the great progress of science and technology, the reqirements for reliability and safety of all kinds of metal materials applied in machinery and equipment have become more sophisticated, which requires more sophisticated methods to inspect and control the quality of the metal materials. So far, the metallographical technology has been the most easy and effective method of research and testing that widely applied in materials science and engineering. The computer-aided quantitative metallographical analysis, with a high accuracy, speed, etc., now is becoming the core of the metallographical technology, while the technology of the metallographical image processing is the key to the computer-aided quantitative metallographical analysis. Therefore, the research of the key technologies in the metallographical image processing has a great practical value in the developments and applications of the metallographical technology.
The key technology in the metallographical image processing includes edge detection, segmentation (including the restoration and reconstruction of grain edges) and fractal dimension calculation of the metallographical image. Mathematical morphology is a very practical method of metallographical image processing. The key of the method is the construction of two basic operations namely dilation and erosion, and the construction of structural elements in the mathematical morphology. However, the traditional morphological dilation affects the continuity and uniformity of gray of the metallographical image. In addition, the form and size of the structural elements in the traditional operations do not change, which means that the traditional operations are uniformily balanced processings to the whole morphological image and would cause the image to over-processing (over-segmentation) or less-processing (less-segmentation) that reduces the accuracy of the computer-aided quantitative metallographical analysis. Therefore, in this paper, the key processes in the metallographical image processing——edge detection and image segmentation (including the restoration and reconstruction of grain edges) are researched first based on mathematical morphology theory. Some theories and methods relevant to the edge detection and image segmentation are suggested and verified theoretically and experimentally. Fractal theory is a very active branch of modern mathematics and nonlinear science.
Fractal dimension, now widely applied in image processing and analysis, is the most important aspect of the application of fractal theory. There are several kinds of mathematical definition of fractal dimension, but how to calculate the fractal dimension of the metallographical image is a pressing issue for further study. Therefore, in this paper, the characteristics of the metallographical image and the algorithm of the fractal dimension are analyzed thoroughly. Some theories and methods are put forward combined with the characteristics and verified by experiments.
The main results of research and innovation in this paper include:
(1) For the false detection, leak detection, and multi-pixel width edge in the existing metallographical image edge detection, the "error processing" problem, and for the complexity of metallographical images that contains a large number of impurities and noise, edge detection algorithms based on multi-scale and muti-form of morphological structureal elements are proposed in this paper. A large number of experiments show that this algorithm is more effective and the edges detected by it are more accurate, continous and smooth in comparison to the traditional edge detection methods. This provides a technical support for the accurate measurements of the grain parameters and calculation of the fractal dimension in the metallographical images.
(2) The adverse effects of traditional operation of dilation on the gray continuity in the metallographical image is researched theoretically, which is related to the size of structural element. The traditional definition of dilation is modified reasonablly which lays the theoretical foundation for the multi-scale geodesic deliltion, the technology of restoration and reconstruction of the grain edges in the metallographical image. In addition, demonstrate theoretically that the traditional operation of erosion maintain the continuity and uniformity of gray in the metallographical image, which provides the theory basis for the selection of scale of structure elements.
(3) Based on the conclusions proved in (2) and related to the effects of traditional operation of dilation and erosion on the gray continuity in the metallographical image, aimed at the shortage of the traditional watershed segmentation algorithm, and combined with the features of the metallographical image, a new algorithm based on the modified delition, called multi-scale geodesic deliltion, the technology of restoration and reconstruction of the grain edges in the metallographical image, is proposed in this paper. In this algorithm, the traditional delition is replaced by the modified delition, which improves the accuracy and clarity of the grain edges restored and reconstructed and reduces greatly the phenomenon of“over-segmentation”,“less-segmentation”or“wrong- segmentation”in the metallographical image. In addition, the traditional iterative erosion with single-scale is replaced by the multi-scale iterative erosion, and the traditional repeat geodesic delition with single-scale is replaced by the multi-scale geodesic delition, which reduces the program run time greatly and improves the efficiency of the restoration and reconstruction of grain edges in the metallographical image.
(4) Combined with the characteristics of the metallographical image, using the edge detection algorithms based on multi-scale and muti-form of morphological structureal elements, an algorithm of fractal dimension in the metallographical image based on the morphological dilation body coverage is suggested in this paper. It is proved by a large number of experiments that the algorithm is more effective compared with the current algorithm and has certain advantages over the current algorithm.
金相图像处理的关键技术包括金相图像的边缘检测、图像分割(包括晶界恢复与重建)算法和分形维数计算。数学形态学是一种非常实用的金相图像处理方法,其关键是膨胀和腐蚀两种基本运算以及结构元素的构造。但传统的数学形态学膨胀运算影响金相图像灰度的连续性和均匀性,并且其形态变换的结构元素不变,是对整个图像的一种均衡的处理过程,这就会导致图像的“过处理”或“欠处理”,影响定量金相分析的准确性。为此,本文首先依据数学形态学理论,对金相图像的边缘检测和图像分割(包括晶界恢复与重建)进行深入研究,提出相关的理论和方法,并通过实验加以验证。分形理论是现代数学与非线性科学研究中十分活跃的一个分支,分形维数则是分形理论应用中最重要的一个方面,广泛应用于图像处理和分析领域。数学上有关分形维数的定义有好几种,但采用什么方法来计算金相图像的分形维数则是一个急待研究的问题。为此,本文深入分析金相图像和分形维数各种算法的特点,结合二者的特点提出相关的理论和方法,并通过实验加以验证。
本文的主要研究工作和创新性成果包括:
(1)针对现有金相图像边缘检测导致伪检测、漏检测以及多像素宽度边缘等“错误处理”问题,结合考虑金相图像复杂、含杂质和噪声较多等特点,提出了基于多尺度多结构元素的数学形态学边缘检测方法。经实验证明该算法是行之有效的,与传统的边缘检测方法相比,它提取的边缘更准确,连续性和光滑性更好,为金相图像晶粒参数的准确测定及分形维数的准确计算提供了技术支撑。
(2)从理论上系统论证了传统的膨胀运算对金相图像灰度连续性、均匀性的不良影响以及这种影响的程度与相应的结构元素之间的关系,对传统的灰度膨胀运算的定义作了合理的改进,为本文提出的金相图像晶界恢复与重建技术——多尺度测地膨胀奠定了理论基础。此外,还从理论上系统论证了传统的腐蚀运算保持金相图像灰度的连续性和均匀性,为结构元素尺度的选取提供了理论依据。
(3)依据已经证明的关于灰度膨胀、腐蚀运算对图像灰度连续性影响的结论,针对传统的金相图像分割算法的不足,结合金相图像的特点,提出了基于改进的膨胀运算的金相图像晶界恢复与重建技术——多尺度测地膨胀。用改进的膨胀运算取代传统的膨胀运算,提高了金相图像晶粒的边界恢复和重建的准确度、清晰度,减少了金相图像“过分割”、“欠分割”或“错误分割”的现象;用多尺度迭代腐蚀取代了传统的(单一尺度)重复腐蚀,用多尺度测地膨胀取代了传统的(单一尺度)重复测地膨胀,缩短了程序运行时间,提高了金相图像晶粒的边界恢复和重建的效率。
(4)结合金相图像的特点,利用本文构建的多尺度多结构元素边缘检测算子,提出基于形态膨胀体覆盖的金相图像分形维数算法。通过实验验证该算法是行之有效的,具有较高的理论和工程应用价值。
With the rapid development of production and the great progress of science and technology, the reqirements for reliability and safety of all kinds of metal materials applied in machinery and equipment have become more sophisticated, which requires more sophisticated methods to inspect and control the quality of the metal materials. So far, the metallographical technology has been the most easy and effective method of research and testing that widely applied in materials science and engineering. The computer-aided quantitative metallographical analysis, with a high accuracy, speed, etc., now is becoming the core of the metallographical technology, while the technology of the metallographical image processing is the key to the computer-aided quantitative metallographical analysis. Therefore, the research of the key technologies in the metallographical image processing has a great practical value in the developments and applications of the metallographical technology.
The key technology in the metallographical image processing includes edge detection, segmentation (including the restoration and reconstruction of grain edges) and fractal dimension calculation of the metallographical image. Mathematical morphology is a very practical method of metallographical image processing. The key of the method is the construction of two basic operations namely dilation and erosion, and the construction of structural elements in the mathematical morphology. However, the traditional morphological dilation affects the continuity and uniformity of gray of the metallographical image. In addition, the form and size of the structural elements in the traditional operations do not change, which means that the traditional operations are uniformily balanced processings to the whole morphological image and would cause the image to over-processing (over-segmentation) or less-processing (less-segmentation) that reduces the accuracy of the computer-aided quantitative metallographical analysis. Therefore, in this paper, the key processes in the metallographical image processing——edge detection and image segmentation (including the restoration and reconstruction of grain edges) are researched first based on mathematical morphology theory. Some theories and methods relevant to the edge detection and image segmentation are suggested and verified theoretically and experimentally. Fractal theory is a very active branch of modern mathematics and nonlinear science.
Fractal dimension, now widely applied in image processing and analysis, is the most important aspect of the application of fractal theory. There are several kinds of mathematical definition of fractal dimension, but how to calculate the fractal dimension of the metallographical image is a pressing issue for further study. Therefore, in this paper, the characteristics of the metallographical image and the algorithm of the fractal dimension are analyzed thoroughly. Some theories and methods are put forward combined with the characteristics and verified by experiments.
The main results of research and innovation in this paper include:
(1) For the false detection, leak detection, and multi-pixel width edge in the existing metallographical image edge detection, the "error processing" problem, and for the complexity of metallographical images that contains a large number of impurities and noise, edge detection algorithms based on multi-scale and muti-form of morphological structureal elements are proposed in this paper. A large number of experiments show that this algorithm is more effective and the edges detected by it are more accurate, continous and smooth in comparison to the traditional edge detection methods. This provides a technical support for the accurate measurements of the grain parameters and calculation of the fractal dimension in the metallographical images.
(2) The adverse effects of traditional operation of dilation on the gray continuity in the metallographical image is researched theoretically, which is related to the size of structural element. The traditional definition of dilation is modified reasonablly which lays the theoretical foundation for the multi-scale geodesic deliltion, the technology of restoration and reconstruction of the grain edges in the metallographical image. In addition, demonstrate theoretically that the traditional operation of erosion maintain the continuity and uniformity of gray in the metallographical image, which provides the theory basis for the selection of scale of structure elements.
(3) Based on the conclusions proved in (2) and related to the effects of traditional operation of dilation and erosion on the gray continuity in the metallographical image, aimed at the shortage of the traditional watershed segmentation algorithm, and combined with the features of the metallographical image, a new algorithm based on the modified delition, called multi-scale geodesic deliltion, the technology of restoration and reconstruction of the grain edges in the metallographical image, is proposed in this paper. In this algorithm, the traditional delition is replaced by the modified delition, which improves the accuracy and clarity of the grain edges restored and reconstructed and reduces greatly the phenomenon of“over-segmentation”,“less-segmentation”or“wrong- segmentation”in the metallographical image. In addition, the traditional iterative erosion with single-scale is replaced by the multi-scale iterative erosion, and the traditional repeat geodesic delition with single-scale is replaced by the multi-scale geodesic delition, which reduces the program run time greatly and improves the efficiency of the restoration and reconstruction of grain edges in the metallographical image.
(4) Combined with the characteristics of the metallographical image, using the edge detection algorithms based on multi-scale and muti-form of morphological structureal elements, an algorithm of fractal dimension in the metallographical image based on the morphological dilation body coverage is suggested in this paper. It is proved by a large number of experiments that the algorithm is more effective compared with the current algorithm and has certain advantages over the current algorithm.
引文
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