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1、成都理工大学 硕士学位论文 数学形态学与变换域图像去噪算法及其并行化研究 姓名：曹海燕 申请学位级别：硕士 专业：信号与信息处理 指导教师：罗省贤 20090501 摘 要 I 数学形态学与变换域图像去噪算法及其并行化研究 作者简介：曹海燕，女，1979 年 12 月生，师从成都理工大学罗省贤教授， 2009 年 7 月毕业于成都理工大学信号与信息系统专业，获得工学硕士学位。 摘摘 要要 图像去噪是图像处理中一种基本而重要的技术。图像在数字化的过程中不 可避免地会引入一些噪声，这些噪声会妨碍人们对图像的理解，影响图像的质 量。利用去噪技术可以从复杂的信号中提取出所需要的信号，并抑制干扰信号，
2、使图像更加清晰，反映出的信息更准确。图像的清晰度主要决定于图像边缘、 细线和小特征是否清晰，特征之间的区域变化是否平滑。传统的图像去噪方式， 在去除噪声污染的同时会造成图像边缘的模糊，不能很好地保持轮廓信息。为 了解决图像滤波时的轮廓保持问题，研究者们提出了一类新的非线性方法，即 基于数学形态学的图像去噪方法。这种方法对图像形态特征进行分析，利用预 先定义的结构元对信号进行匹配，以达到提取信号、抑制噪声的目的，具有并 行性和快速性的特点，因而在国内外受到普遍关注。 本论文以数学形态学理论为基础，分别研究了二值图像、灰度图像、彩色 图像的去噪算法，在传统的形态学去噪算法的基础上，进行改进和创新，
3、进一 步提高了图像的质量。 在二值图像去噪算法中，设计与实现了一种多结构元素的串行广义复合形 态滤波器。由于传统的形态滤波只采用单一结构元素，致使滤波结果无法顾及 图像在不同方向上的特征，不能完全滤除噪声，模糊了图像的细节特征。本文 在二值图像去噪算法中采用了多尺度多方向的结构元素，不仅有效地抑制了图 像中的噪声，而且较好地保持了图像的几何特征。同时利用广义复合形态滤波 具有平移不变性、递增性、等幂性等重要特征进行图像降噪。在灰度图像去噪 算法的设计上，采用了一种 Contourlet 变换结合 Cycle Spinning 技术、形态学 HMT 变换的去噪方法。Contourlet 变换是一
4、种真正的图像二维表示方法，具有 多分辨性、局域性、方向性的优点，而 Cycle Spinning 技术能够有效抑制由于 Contourlet 变换缺乏平移不变性而引起的伪 Gibbs 现象， 在以上两者结合的基础 上，对于 Contourlet 分解后高频子带中的噪声，运用数学形态学中的 HMT 变换 进行有针对性的提取和去除。与传统的小波变换阈值去噪方法相比，这种方法 更好的平滑了噪声，保持了更多的图像边缘和纹理细节，视觉效果也更好。 成都理工大学硕士学位论文 II 对于彩色图像去噪，采用了一种基于 RGB 彩色空间的改进的中值滤波， 结合多结构元素的标量形态滤波算法。传统的中值滤波对所有的
5、数据采用统一 的处理方法，对每个像素都进行排序取中值，计算量巨大，时间复杂度高。而 改进的中值滤波采用信噪分别处理的算法，排序时充分利用更新后的数据，克 服了传统中值的不足，降低了时间复杂度，滤波效果也明显得到改善。同时根 据人眼对三基色不同的敏感程度，选用不同大小的结构元素对三基色分别进行 处理，与采用同样的结构元素对整个图像处理相比，在滤除噪声的同时，保留 了更多的色彩信息，且不影响人眼对图像的视觉效果。本文在彩色图像去噪算 法中，深入研究了改进的中值滤波算法并行化的可行性，实现了基于 MPI 的改 进中值滤波的并行化算法，显著提高了改进的中值滤波算法的计算效率。 通过对各种改进算法的仿真
6、实验效果和去噪算法性能指标(MAE、MSE、 NMSE、PSNR)分析，表明本文各种改进算法比传统算法具有更大的灵活性， 滤除噪声的能力显著增强，证实了算法的可行性和有效性。 关键词：数学形态学 去噪算法 结构元素 Contourlet 变换 并行化 Abstract III Reserch of the Image Denosing Algorithm and Its Parallelization Based on Mathematics Morphology and Transformation Domain Introduction of the author: Cao Haiyan,
7、 female, was born in December, 1979, whose tutor was Professor LuoShengxian. She graduated from Chengdu University of Technology in Image and Signal non-linear Processing major and was granted the Master Degree in July, 2009. ABSTRACT Image denoising is a fundamental and significant technique in ima
8、ge processing. During the procedure of image digitalization, it is inevitable to bring in some noise, which will have side effect on peoples understanding about the image and become the main factor of affecting the quality of the image. Using the technique of denosing, we can extract required signal
9、 from complex signal, control the interfering signal and make the image clear and precise. The clarity of the image mainly depends on the clarity of the curve of image, tiny line and tiny features, it also depends on whether the areas change between features is smooth enough. As for the traditional
10、ways for image denosing, in the process of Image denoising, the edge of the will becomes vague so as to the information of these areas can not be keep anymore. In order to solve this problem, the researchers proposed a new kind of nonlinear method which is based on mathematics morphology. This metho
11、d firstly analyze the character of the image, then matching signals with the pre-defined structured cell, using this method, we can extract the signal we need, and depress the noise, this method also has the feature about parallelism and speediness. This thesis is based on the theory of mathematics
12、morphology, research denosing algorithm on binary image, gray scale image, color image. Based these traditional algorithms, according to some innovation and improvement, we further enhance the quality of the image. Designing and implementing the serial generalized composite types filter for binary i
13、mage denosing algorithm. Due to the traditional morphological filter just use single cell structure, the result can not contain feature of 成都理工大学硕士学位论文 IV different dimensions, and this method can not filter completely, so as to the detail of the image is vague. In this paper, we adopt the multi-sca
14、le and multi-dimension cell structure for the binary image denosing algorithm, not only the noise in the image can be controlled efficiently but also the geometrical characteristics of the image can be kept quite well. Meanwhile this thesis uses several important features of generalized composite ty
15、pes filter such as translation invariance, increase by degrees and idempotence to decrease the image noise. Based on the denosing algorithm of gray scale image, this thesis adopt a kind of Contourlet transformation which combine the denosing method of Cycle Spinning technique and HMT transformation
16、of morphology. Contourlet transformation is a very kind of denoting method for two dimension imageit has several good qualities such as ， multi-distinguishability, local property and directivity. Besides, the Cycle Spinning technique can depress the fake Gibbs phenomenon which is caused by lacking of translation invariance for Contourlet transformation. On the basis of combining these two method, this thesis use the
