小波变换在图像处理中的应用
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摘要
小波分析是继Fourier分析之后的新的时频域分析工具。在图像处理领域，其应用包括从图像生成、图像预处理、图像压缩与传输、图像配准、图像分析、特征提取与图像分类等图像处理的几乎所有阶段。本文对小波分析在多尺度边缘检测、静止图像压缩和数字水印三个方面应用的方法进行了研究。
传统的边缘检测基于一阶导数极大值或二阶导数零交叉的定义。这种定义对噪声非常敏感，因此边缘检测需要通过图像平滑在大尺度下进行。但在大尺度下进行边缘检测的一个缺点是边缘位置容易发生偏移。这对于基于边缘特征的模式识别而言会造成误识别。小波分析具有多尺度特性，既有大尺度的基函数，又有小尺度的基函数，因而在运用于边缘检测时，正好解决了这个问题。本文证明了，基于对称小波基的小波变换，在用于多尺度边缘检测时，可以很好地保持边缘位置；本文的工作提出了一种基于双正交对称小波的多尺度边缘检测算法。该算法在获得良好边缘的情况下，边缘定位准确度高。
数字水印技术作为数字产品版权保护的一项新技术，已受到越来越多的关注。为保证水印的安全性，提出了一种基于小波变换的水印嵌入方法，即在嵌入之前先对水印做置乱处理，然后根据小波变换后高低频分量的特点，在高频部分嵌入较多的水印信息，而在低频部分嵌入较少的信息，亦即利用小波变换的层次结构，将同一水印反复嵌入到不同的位置。实验证明，该方法对剪裁、JPEG压缩和锐化等图象退化处理均具有一定的抵抗力，是一种行之有效的水印嵌入方法。
本文在对零树编码方法研究的基础上，针对零树编码方法没有充分利用HVS特性来有效消除视觉冗余的缺点，提出了一种基于小波系数的零树编码方案。其主要包括对最低频子带单独进行无损压缩编码，对最高频对角线方向子带舍去不编码。对其余各子带根据视觉特点的不同，分别分配不同的比特数并按其进行零树量化，最后再游程编码。实验表明，该方法是一种比较有效的方法。
Wavelet analysis is a tool of time-frequency analysis after Fourier analysis. In the field of image processing, its application covered imaging technique, image pre-processing, image compression and transferring, image registration, image analysis, feature extraction and pattern classification, etc. In this paper, it's researched on wavelets application in the fields of multi-scale edge detection, remote sensing image processing and medical imaging.
The traditional methods of edge detection are based on one-order derivative's maximum, or two-order derivative's zero-crossing. This kind of edge definition is very sensitive to noises. And thus, edge detection should be carried out in large scale, by which the image was smoothed. One of the shortcomings of edge detection in large scale is that it's difficult to locate edge precisely, which will make mistakes in pattern recognition based on edge features. With multi-scale characterization, wavelet analysis was widely used to multi-scale edge detection. In this paper, it was proved that, wavelet-based multi-scale edge detection would keep edge positions very well, if symmetric bases were used in wavelet transform. Furthermore, an algorithm of multi-scale edge detection based on bi-orthogonal symmetric wavelet was put forward, with which, "good edges" will be obtained while the edge positions will be kept well.
As a new technique applying to protecting the copyright of digital productions, the digital watermark technique has drawn extensive attention. A method of embedding the watermark in digital images based on the discrete wavelet transform is proposed. The watermark used here is not the conventional patterns such as a pseudo-random sequence or a bit stream but a text watermark. The information which the text watermark contains is abundant and intuitionistic, also the watermark is robust. To ensure the security of the watermark and make the watermark be hard to be extracted, the watermark is scrambled with Arnold scrambling transformation before embedded into the original image. According to the different characteristics of the high and the low frequency components of the wavelet coefficients of the original image, more watermark information is embedded in the high frequency components while less information in the low ones. That is to say, by using the hierarchical structure of the wavelet, the watermark is repeatedly embedded in various places. Moreover, experimental results have proved that the method is robust
enough to some image degradation process such as cropping, JPEG compression and sharpening etc.
Embedded ZeroTree Wavelet Coding(EZW) algorithm, it is found that this algorithm does not make full use of the properties of Human Visual System(HVS) to eliminate visual redundancy. An improved image compression algorithm based on bi-orthogonal wavelet coefficients is thus presented, maily including: 1. The subimage of the lowest frequency(LL4) is carried out lossless compressed coding;2 The subimages on diagonal direction of the highest frequency(HHl) is abandoned and is not carried out coding, because it is of great probability for zero, and it little affects visual. 3 The rest of the subimages are given different bit numbers according to their different characteristics. Then they are carried out quantization of zerotree and run-length coding. Experimental results show that this algorithm is more effective.
传统的边缘检测基于一阶导数极大值或二阶导数零交叉的定义。这种定义对噪声非常敏感，因此边缘检测需要通过图像平滑在大尺度下进行。但在大尺度下进行边缘检测的一个缺点是边缘位置容易发生偏移。这对于基于边缘特征的模式识别而言会造成误识别。小波分析具有多尺度特性，既有大尺度的基函数，又有小尺度的基函数，因而在运用于边缘检测时，正好解决了这个问题。本文证明了，基于对称小波基的小波变换，在用于多尺度边缘检测时，可以很好地保持边缘位置；本文的工作提出了一种基于双正交对称小波的多尺度边缘检测算法。该算法在获得良好边缘的情况下，边缘定位准确度高。
数字水印技术作为数字产品版权保护的一项新技术，已受到越来越多的关注。为保证水印的安全性，提出了一种基于小波变换的水印嵌入方法，即在嵌入之前先对水印做置乱处理，然后根据小波变换后高低频分量的特点，在高频部分嵌入较多的水印信息，而在低频部分嵌入较少的信息，亦即利用小波变换的层次结构，将同一水印反复嵌入到不同的位置。实验证明，该方法对剪裁、JPEG压缩和锐化等图象退化处理均具有一定的抵抗力，是一种行之有效的水印嵌入方法。
本文在对零树编码方法研究的基础上，针对零树编码方法没有充分利用HVS特性来有效消除视觉冗余的缺点，提出了一种基于小波系数的零树编码方案。其主要包括对最低频子带单独进行无损压缩编码，对最高频对角线方向子带舍去不编码。对其余各子带根据视觉特点的不同，分别分配不同的比特数并按其进行零树量化，最后再游程编码。实验表明，该方法是一种比较有效的方法。
Wavelet analysis is a tool of time-frequency analysis after Fourier analysis. In the field of image processing, its application covered imaging technique, image pre-processing, image compression and transferring, image registration, image analysis, feature extraction and pattern classification, etc. In this paper, it's researched on wavelets application in the fields of multi-scale edge detection, remote sensing image processing and medical imaging.
The traditional methods of edge detection are based on one-order derivative's maximum, or two-order derivative's zero-crossing. This kind of edge definition is very sensitive to noises. And thus, edge detection should be carried out in large scale, by which the image was smoothed. One of the shortcomings of edge detection in large scale is that it's difficult to locate edge precisely, which will make mistakes in pattern recognition based on edge features. With multi-scale characterization, wavelet analysis was widely used to multi-scale edge detection. In this paper, it was proved that, wavelet-based multi-scale edge detection would keep edge positions very well, if symmetric bases were used in wavelet transform. Furthermore, an algorithm of multi-scale edge detection based on bi-orthogonal symmetric wavelet was put forward, with which, "good edges" will be obtained while the edge positions will be kept well.
As a new technique applying to protecting the copyright of digital productions, the digital watermark technique has drawn extensive attention. A method of embedding the watermark in digital images based on the discrete wavelet transform is proposed. The watermark used here is not the conventional patterns such as a pseudo-random sequence or a bit stream but a text watermark. The information which the text watermark contains is abundant and intuitionistic, also the watermark is robust. To ensure the security of the watermark and make the watermark be hard to be extracted, the watermark is scrambled with Arnold scrambling transformation before embedded into the original image. According to the different characteristics of the high and the low frequency components of the wavelet coefficients of the original image, more watermark information is embedded in the high frequency components while less information in the low ones. That is to say, by using the hierarchical structure of the wavelet, the watermark is repeatedly embedded in various places. Moreover, experimental results have proved that the method is robust
enough to some image degradation process such as cropping, JPEG compression and sharpening etc.
Embedded ZeroTree Wavelet Coding(EZW) algorithm, it is found that this algorithm does not make full use of the properties of Human Visual System(HVS) to eliminate visual redundancy. An improved image compression algorithm based on bi-orthogonal wavelet coefficients is thus presented, maily including: 1. The subimage of the lowest frequency(LL4) is carried out lossless compressed coding;2 The subimages on diagonal direction of the highest frequency(HHl) is abandoned and is not carried out coding, because it is of great probability for zero, and it little affects visual. 3 The rest of the subimages are given different bit numbers according to their different characteristics. Then they are carried out quantization of zerotree and run-length coding. Experimental results show that this algorithm is more effective.
引文
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[17] 牛夏牧，陆哲明，孙圣和 “彩色数字水印嵌入技术“，电子学报2000．9 vol28，第9期
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[2] 魏海，沈兰荪 “反对称双正交小波应用于多尺度边缘提取的研究“，电子学报 2002年3月，vol130，No．3
[3] 王博，潘泉，张洪才，戴冠中“小波变换边缘检测特性分析“，电子科学学刊 1998年3月，vol20，No．2
[4] 丁艳，刘榴娣，郭宏，“小波变换在图象边缘检测中的应用“，北京理工大学学报 1998年10月，vol18，No．5
[5] Keita Alpha，彭嘉雄，“小波多尺度方法用于边缘检测“，华中科技大学学报 2001年5月，vol19，No．5
[6] 皮明红，李德仁，“一种多尺度边缘检测的方法“，信号处理2000年3月，vol16 No．1
[7] 徐琼，“一种基于小波变换的边缘检测方法”，四川轻工学院学报，200年6月，vol13，No．2
[8] 尹平，王郧生，“自适应多尺度边缘检测”，软件学报 2000年，11(8) 990-994
[9] 黄贤武，李家袆，陈东华“一种改进的基于人眼视觉特性的零树图像编码算法“，计算机研究与发展，2001年8月，vol38，No．8
[10] 张素文，杭小庆，王天珍 “一种改进的零树编码方法“，武汉理工大学学报，2001年9月，vol23，No．3
[11] 许娟，徐长发 “EZW编码中一种改进的小波零树系数分类算法设计“，计算机与数字工程，2002年，vol30，第三期
[12] 张海翔，陈纯，庄越挺“基于单队列递归扫描的嵌入式零树图像编码方法”，中国图像图形学报 2002．7 A版第7期
[13] 张宗念，马义德 “基于方向性零树小波的分形图像编码”，电子科学学刊2000．9 vol55 第5期
[14] 陈加忠，周敬利 “图像编码中的重要区域相关性研究及应用“，计算机学报，2001．3 vol24 第3期
[15] 杨云峰，苏志勋 “一种改进的基于小波零树的图像编码算法“，中国图像图形学报2001．6 vol6(A) 第6期
[16] 毛琼，陈明奇，夏光升“安全数字水印体系的研究”，电子与信息学报2001．9 vol23 第9期
[17] 牛夏牧，陆哲明，孙圣和 “彩色数字水印嵌入技术“，电子学报2000．9 vol28，第9期
[18] 潘蓉，高有行“基于小波变换的图像水印嵌入方法”，中国图像图形学报2002．7 Vol．7(A),No．7
[19] 华先胜，石青云 “局部化数字水印算法“，中国图像图形学报2001．7第6卷(A版)，No．7
[20] 陈明奇，杨义先 “数字水印的攻击方法“，电子与信息学报2001．7第23卷，第7期
[21] 陈明奇，杨义先 “数字水印的研究进展和应用“，通信学报
2001．5第22卷，第5期
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