摘 要

随着图像获取与数据存储等技术的进步，图像数据急剧增加，人类对能从图像数据中自动抽取有意义的语义信息或知识的图像挖掘系统或工具的需求日益迫切。图像基本视觉特征包括颜色、纹理、形状和物体间方位关系等。在图像挖掘中，图像的形状特征是最重要的目标特征。通常形状的描述可以分为基于轮廓和基于区域2类。其中，基于轮廓的形状描述技术已相当成熟，但不足之处在于没有考虑形状区域内的像素。但基于矩的描述方法更适合图像的形状特征，因为它们不仅仅计算轮廓上的像素点，而且还计算构成形状的所有像素点。目前常用的矩主要有几何矩、中心矩、正交不变矩等，而Zernike矩就是正交不变矩中比较成熟并被广泛使用的一种。在图像挖掘领域，Zernike矩是否能精确描述图像的形状特征需要作进一步评价与验证，而使用提取出的矩形状特征重构原图像就成了一个必要的途径。这种基于图像重构的对Zernike 矩描述能力的评价方法同样适合于Legendre、伪Zernike、Fourier-Mellin 等正交不变矩。在图像挖掘中，最关键的步骤是提取图像特征并对之进行描述和评价。Zernike矩的基是正交径向多项式，可以保证所提取的特征相关性小，冗余性小，抗噪声能力强；Zernike 矩具有平移不变性，经过相关改进后可以具备旋转不变性以及更好的比例不变性。一幅图像的形状特征可以用一组Zernike 矩集合很好地表示，低阶矩描述的是一个图像目标的整体形状，高阶矩描述的是图像目标的细节。

关键词：图像挖掘；Zernike 矩；形状特征集；描述图像

Abstract

With the image acquisition and data storage technology, the rapid increase in image data, human data are automatically extracted from the image meaningful semantic information or knowledge of image mining system or tool needs more urgent. Basic visual features of images, including color, texture, shape and orientation relationships between objects. In image mining, image of the shape feature is the most important target feature. Usually the description of the shape can be divided into regions based on contour and Class 2. Which, based on contour shape description technique is quite mature, but is not considered the inadequacies of the shape of the pixels within the region. However, the description based on moment method is more suitable for the shape of the image features, because they not only outline the calculation of the pixel, but also calculate all the pixels form shapes. There are moments of the most commonly used geometric moments, central moments, orthogonal invariant moments, etc., and Zernike moments are orthogonal moment invariants of the more mature and widely used one. Mining areas in the image, Zernike moments are accurately describe the image of the shape of the need for further evaluation and validation, and use the extracted features rectangular shape reconstruction of the original image has become a necessary way. This image reconstruction based on Zernike Moments capacity evaluation method is also suitable for Legendre, pseudo-Zernike, Fourier-Mellin invariant moments such as orthogonal. In image mining, the most critical step is to extract the image features and described and evaluated. Zernike moments are orthogonal radial polynomial basis can ensure that the extracted features associated small, redundancy is small, anti-noise capability; Zernike moments has the translation invariance, could have been related to improved rotation invariance, and more good proportion of invariance. The shape feature of an image can be a good representative collection of Zernike moments, order moment describes the overall shape of an image target, higher moments describe the details of the image target.
Keywords: image mining; Zernike moments; shape feature set; description of image

目 录

1 绪论 1

1.1 课题的背景和意义 1

1.1.1 研究的目的及意义 1

1.1.2 国内外同类研究概况 2

1.2 研究内容 3

1.3 特色与创新 5

1.4 研究计划 5

1.4.1 研究计划概述 5

2图像的区域匹配方法 7

2.1 引言 7

2.2 基于Zernike矩的区域匹配方法 8

2.2.1 Zernike矩的定义以及区域匹配 9

2.2.2　Zernike矩的不变性与实现 11

3图像重构和Zernike矩的归一化 13

3.1 图像重构 13

3.2 特征描述与评价 13

3.3 基于Zernike矩的图像归一化 15

4实验分析 18

5 小结与展望 23

致 谢 25

参考文献 26

1 绪论

1.1 课题的背景和意义

1.1.1 研究的目的及意义

Zernike矩是一种特殊的复数矩,它是基于称为Zernike多项式的正交函数^{[1 ,2]}。尽管,与几何矩和Legendre矩相比其计算更加复杂,但Zernike矩在其特征表达能力和噪声敏感度方面是有其较大的优越性^{[3 - 5 ]}。

模式识别是指计算机系统对目标的自动识别,字符识别则是模式识别的重要方式之一。如何提取图像的不变性特征,构造一个高效率的分类识别系统一直是计算机视觉研究领域的一项热门课题。图像的不变性特征包含三层含义,即旋转不变性、平移不变性和尺度变化不变性。平移不变性和尺度变化不变性可简单地通过图像规格化获得,而旋转不变性的获得方法较多,如付氏描绘子、圆谐波展开以及由Hu.M. K.提出的普通矩方法等^[6]。目前,人工神经网络技术已泛应用于各种研究领域,同时也为模式识别提供了一种新的技术方法。