【作者】 迟健男；

【导师】 徐心和；

【作者基本信息】 东北大学 ， 模式识别与智能系统， 2005， 博士

【摘要】 图像工程根据抽象程度和研究方法的不同可分为三个层次：图像处理、图像分析和图像理解，图像工程是三者有机结合及它们工程应用的总称。图像增强和边缘检测是图像处理中的重要内容，图像目标检测属于图像分析及其工程应用范畴。 数学形态学以集合理论为基础，是几何形状描述与分析和非线性滤波的有力工具。小波分析技术是泛函分析、数值分析等理论和方法长期发展的结果，是信号处理、图像处理、模式识别、机器视觉等领域在工具和方法上的重大突破。 因此本文的研究内容涉及图像处理、图像分析及其工程应用，是数学形态学和小波分析理论在图像工程中的应用研究，研究的重点包括染噪图像的增强和边缘检测等内容。 (1)根据并行复合顺序形态变换的相关概念，构造非线性滤波器抑制图像中的脉冲噪声和高斯噪声以及均匀分布噪声，进而提出了一种新的图像增强算法。该算法通过对图像做局部加权均值滤波，得到图像增强的基值分量；采用多方位结构元素与图像边缘匹配，计算图像关于各个方位结构元素的加权均值并选取其中的最大值来确定边缘；将此最大值与基值分量之差作为增强分量来扩大图像灰度梯度的动态范围；针对图像中的高灰度区和灰度剧变区，应用图像局部均值和方差自适应调节增强系数。因此，算法在抑制图像中的高频噪声的同时，能有效提升图像中的边缘和目标。增强前后图像均值、标准差、图像熵比较表明，图像对比度也得到了增强。 (2)在深入理解百分位形态变换基本概念及相关性质的基础上；阐述了应用百分位形态变换进行边缘检测的原理；讨论了结构元素和百分位值对边缘检测的影响；从采用平面型结构元素和立体型结构元素两方面，根据图像形态学多刻度形态滤波的思想，以抑制噪声为目的对基本边缘检测算子进行推广和扩展，构造了三种边缘检测算子，从理论上分析了算子的特性；在此基础上采用多结构元与图像边缘进行匹配，提出了三种广义形态边缘检测算子并给出了一般表达形式；着重探讨了多结构元素及百分位值选取原则。 (3)推导了反对称双正交小波所具有的卷积运算性质，分析了反对称双正交小波所具有的微分算子功能。在此基础上，根据给出的针对图像边缘检测的小波分解算法，提出了基于反对称双正交小波的多尺度边缘提取方法。根据给出的针更多还原

【Abstract】 Image engineering can be arranged into three catalogs according to class in term of research approach and nonfigurative degree, namely image engineering is combination of image processing, image analysis and image understanding and their engineering application. Image enhancement and edge detection is attached importance to image processing reaearch. Image target detection belongs to image analysis and its engineering application.Mathematics morphology is based on set theory, which is a powerful approach in geometrical description and nonlinear filtering. Wavelet analysis is result of development of functional analysis and numerical analysis and so on, which is a main implement or tool applied in computer vision, pattern recognition, signal and image processing.The research in this paper including noise image enhancement and edge detection relates to image processing, image analysis and their engineering application, which is application of image morphology and wavelet in image engineering.(1) According to correlative conception of parallel multiplex order morphology transformation, non-linear filter is constructed to remove high frequence noise of image such as noise of Gaussian and impulse. Within this algorithm, the local weighted mean value filtering is performed to obtain basic value of image enhancement; Structuring elements of different direction are used to match edge of image. Weighted average values about structuring elements of different direction are calculated to distinguish edge and reject noise; The difference between the maximum among these weighted average values and basic value above is served as enhancement value for enlarging dynamic scope of image gradient; For the regions in image where gray value is high or change intensely, local mean value and variance is adopted to control enhancement coefficients. So through the algorithm, the target and edge of image are elevated while high frequence noise of image is restrained. comparison of average value, standard deviation and entropy of image between original images and their enhancement show that contrast of images is improved.(2) Based on conception and correlative properties of percentile morphology transformation, the principle of edge detection using percentile morphological filtering is illustrated. The effect of structuring elements and percentile on edge detection is discussed. Based on the idea of multi-scale morophological filtering, Three order morphological operators of edge detection are constructed by extending the basic morphological operators of edge detection to restrain noise. The specialities of the operators which were monotony about percentile (p、q) in the area of image edge is analyzed in theory. Based on above, three general order morphological edge operators are constructed and their formats are given, in which multi-structuring elements are selected to match image edge according to geometrical feature of image. The rules of how to select structuring elements and percentile are studied.(3) Specialty of convolution operation and differential operation of anti- symmetrical biorthogonal wavelet transformation are deduced and analyzed. Based on above, In term of arithmetic of wavelet decomposition presented, an new approach of multi-scale image edge更多还原