图像特征提取与识别的迹空间投影方法研究
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摘要
图像的特征提取是图像内容识别领域中的研究重点，它涉及到图像处理、模式识别、信号处理、机器学习等多个学科的研究内容。在图像特征提取研究中，具有几何不变性，对图像内容具有强描述性和具有低信息冗余度的特征受到人们的广泛关注。Radon域分析和Trace变换是近年来兴起的图像特征提取方法，前者通过将图像进行Radon变换，然后在变换域进行特征提取得到具有几何不变性的图像特征；后者为Radon变换在二维的推广，通过定义不变泛函和敏感泛函，将图像内容的平移、旋转和缩放变化转化为泛函参数的变化，然后通过计算参数，构造出图像的几何不变特征。
上述工作均获得许多成果，但尚未有一个模型能对这些方法进行统一的分析。本文在Radon域分析和Trace变换的基础上，进一步提出一种“迹空间投影”的图像特征提取方法。本文的主要研究工作包括以下几个方面：
1.在深入研究Radon域分析和Trace变换理论的基础上，提出一种迹空间投影的数学方法。这个方法通过定义图像上的迹线，将二维图像映射到一个三维数据空间，通过对三维数据空间的不同方向做积分或者变换，得到图像特征。这个方法既可以检测图像的线特征，也可以用以提取图像的几何不变性特征，具有广泛的应用价值。在理论上，这个方法可以将Radon变换、Trace变换、Ridgelet变换和二维傅里叶变换统一到一个数学框架内，与极坐标图像矩分析方法也有深刻的内在联系。本文提出了迹空间投影的变换公式，特征提取方法并给出了迹空间投影的实现方法并通过实验进行了验证，随后讨论了迹空间投影的一般形式。
2.针对平面内具有随机角度旋转的人脸图像难以识别的问题，提出一种融合二维近邻保持投影（2DNPP）和迹空间投影方法的人脸图像旋转不变特征提取和识别的方法。首先对图像做迹空间投影，并提取一重和二重积分特征，然后使用高阶谱方法对二重曲线进行匹配计算，得到既对平面内旋转变化具有鲁棒性，又能保存丰富图像信息的特征，最后通过2DNPP进行降维并对降维后数据进行分类。与SIFT、pseudo-Zernike等方法比较，实验说明本文提出的方法更高的识别率，同时对白噪声具有较强的鲁棒性。
3.深入研究迹空间投影在图像线特征中的应用。提出一种新的T泛函对SAR图像的迹空间投影数据进行积分，可以有效提取出其中的船舶轨迹特征和车辆方向角特征。通过对棋盘格图像做两次迹空间投影分析，提出一种双重迹空间投影的方法，可得到棋盘格图像的平行线位置信息，然后通过几何关系计算，可以有效定位棋盘格图像上的角点，同时避免噪声干扰。在图像数字水印的嵌入研究中，用迹空间投影方法对图像进行分析，得到其中线特征的位置，在特定位置嵌入水印，可得到具有透明性和鲁棒性的数字水印。
4.提出一种融合正交多项式矩和迹空间投影的图像特征提取方法，通过对图像做迹空间投影，得到图像正弦图，然后在正交多项式基函数空间对图像正弦图进行分解，得到具有旋转和缩放不变性的低冗余度正交特征。和Zernike矩， Tchebichef矩和orthogonal Fourier-Mellin矩方法相比，这种特征具有更好的图像形状和纹理信息的描述能力，在满足一定条件下，还可以使用这种特征对原图像进行还原。
本文提出的迹空间投影的图像特征提取算法可以提取图像的线性和几何不变性特征，同时能将Radon域分析，极坐标图像矩分析等多种方法统一到一个框架下进行研究，具备一定的理论价值。迹空间投影特征可以应用在图像特征提取和模式识别中，因此也具备较广泛的实用价值。
Image feature extraction is a key point in the study of the image content recognition,which involves research content of many disciplines such as image processing, patternrecognition, signal processing and machine learning. In study of image feature extraction,such features as geometrical invariability,the strong descriptive of image content and the lowinformation redundancy always draw people’s attention. In recent years, Radon domainanalysis and Trace transformation have become the latest extraction methods of imagefeatures. The former can achieve geometrical invariability of image features by Radontransformation and then by image features extraction in the transformation domain; the latter,which is a promotion of Radon transformation in two dimensional space, can transform thetranslation of image content, rotation and scale change into functional parameters change bydefining Invariant and Sensitive functionals. Then the image invariant features can beconstructed through the calculation of the parameters.
The research mentioned above has obtained many achievements, but not yet has anydefinite model to analyze all these methods. Based on Radon domain analysis and Tracetransformation, a kind of “Trace space projection” image feature extraction method isproposed in this dissertation. The main research includes the following several aspects:
1. Based on the further study of Radon domain analysis and Trace transformation theory,a kind of mathematical method called Trace space projection is proposed in this dissertation.By defining image trace line, a two dimensional image is projected into a three dimensionalspace. By intrgrating and transforming the three dimensional data space in different directions,this method can be used not only to detect image linear features, but also to extract thecharacteristics of image with geometrical invariability, which is of great application value.Theoretically,this method can unit Radon transform, Trace transform, Ridgelet transform andthe two dimensional Fourier transform into a same mathematical framework of Trace spaceprojection, and by which polar coordinate image moment method can be analysed. The Tracespace projection transformation formula, the extraction method of image features and theTrace space projection realization method is proposed in this dissertation, and general type ofTracespace projection is also discussed.
2. Concerning the fact that the face image with in-plane rotation by stochastic angle isdifficult to identify,a method by fusion of2DNPP and Trace space projection is proposed toextract and identify invariant features of face images rotation. First Trace space projection isdone to the image to extract a sinogram and double trace feature, then higher order spectralmethod is used to match and calculate the double curve, the characteristics obtained arediscovered of robustness for the in-plane rotation changes and the maintenance of the imageinformation by the bispectrum function. Finally2DNPP is used to reduce dimension andclassification to obtain the invariant feature. Compared with SIFT, Pseudo-Zernike momentmethods, the proposed method has better performance with higher recognition rate, and is ofstronger robustness to the white noise.
3. The application of the Trace space projection in the image linear features extraction isfurther explored. A new T functional for SAR image Trace space projection data is proposedto extract the ship orbit characteristics and vehicle direction angle characteristics. Simulationresult shows that the method is effectively used in SAR image recognition. By doing twiceanalysis of Trace space projection of the checkerboard image, a kind of double trace spaceprojection method is proposed to obtain the checkerboard image parallel line positioninformation, and then through the geometrical relationship computation, the checkerboardimages Corner`s positions are got, This method can avoid noise interference outside thecheckerboard. In the image digital watermark embedding study, the linear feature position isobtained by Trace space projection for image analysing, and at the given place digitalwatermark embing, the watermark with transparency and robustness can be obtained.
4. A novel image feature extraction method of fusing orthogonal polynomial moment andTrace space projection is proposed. In this method, the sinogram is obtained by calculatingTrace space projection. And the image sinogram is is decomposed in the orthogonal basisfunction space to obtain the low redundancy orthogonal characteristics of rotation and scalinginvariance. Compared with Zernike moment, Tchebichef moment and OrthogonalFourier-Mellin moment algorithm, this method is of better image shape and textureinformation description ability.At a given condition, the feature obtained by this method canalso be used to reconstruct the original image.
The proposed Trace space projection image feature extraction algorithm can be used toextract the linear or the geometrical invariability characteristics of the image and unite Radondomain analysis, polar image moment analysis and many other methods into the sameframework for research, which is of great theoretical value. The Trace space projectionfeatures can also be applied in image feature extraction and pattern recognition, which is of certain practical value.
上述工作均获得许多成果，但尚未有一个模型能对这些方法进行统一的分析。本文在Radon域分析和Trace变换的基础上，进一步提出一种“迹空间投影”的图像特征提取方法。本文的主要研究工作包括以下几个方面：
1.在深入研究Radon域分析和Trace变换理论的基础上，提出一种迹空间投影的数学方法。这个方法通过定义图像上的迹线，将二维图像映射到一个三维数据空间，通过对三维数据空间的不同方向做积分或者变换，得到图像特征。这个方法既可以检测图像的线特征，也可以用以提取图像的几何不变性特征，具有广泛的应用价值。在理论上，这个方法可以将Radon变换、Trace变换、Ridgelet变换和二维傅里叶变换统一到一个数学框架内，与极坐标图像矩分析方法也有深刻的内在联系。本文提出了迹空间投影的变换公式，特征提取方法并给出了迹空间投影的实现方法并通过实验进行了验证，随后讨论了迹空间投影的一般形式。
2.针对平面内具有随机角度旋转的人脸图像难以识别的问题，提出一种融合二维近邻保持投影（2DNPP）和迹空间投影方法的人脸图像旋转不变特征提取和识别的方法。首先对图像做迹空间投影，并提取一重和二重积分特征，然后使用高阶谱方法对二重曲线进行匹配计算，得到既对平面内旋转变化具有鲁棒性，又能保存丰富图像信息的特征，最后通过2DNPP进行降维并对降维后数据进行分类。与SIFT、pseudo-Zernike等方法比较，实验说明本文提出的方法更高的识别率，同时对白噪声具有较强的鲁棒性。
3.深入研究迹空间投影在图像线特征中的应用。提出一种新的T泛函对SAR图像的迹空间投影数据进行积分，可以有效提取出其中的船舶轨迹特征和车辆方向角特征。通过对棋盘格图像做两次迹空间投影分析，提出一种双重迹空间投影的方法，可得到棋盘格图像的平行线位置信息，然后通过几何关系计算，可以有效定位棋盘格图像上的角点，同时避免噪声干扰。在图像数字水印的嵌入研究中，用迹空间投影方法对图像进行分析，得到其中线特征的位置，在特定位置嵌入水印，可得到具有透明性和鲁棒性的数字水印。
4.提出一种融合正交多项式矩和迹空间投影的图像特征提取方法，通过对图像做迹空间投影，得到图像正弦图，然后在正交多项式基函数空间对图像正弦图进行分解，得到具有旋转和缩放不变性的低冗余度正交特征。和Zernike矩， Tchebichef矩和orthogonal Fourier-Mellin矩方法相比，这种特征具有更好的图像形状和纹理信息的描述能力，在满足一定条件下，还可以使用这种特征对原图像进行还原。
本文提出的迹空间投影的图像特征提取算法可以提取图像的线性和几何不变性特征，同时能将Radon域分析，极坐标图像矩分析等多种方法统一到一个框架下进行研究，具备一定的理论价值。迹空间投影特征可以应用在图像特征提取和模式识别中，因此也具备较广泛的实用价值。
Image feature extraction is a key point in the study of the image content recognition,which involves research content of many disciplines such as image processing, patternrecognition, signal processing and machine learning. In study of image feature extraction,such features as geometrical invariability,the strong descriptive of image content and the lowinformation redundancy always draw people’s attention. In recent years, Radon domainanalysis and Trace transformation have become the latest extraction methods of imagefeatures. The former can achieve geometrical invariability of image features by Radontransformation and then by image features extraction in the transformation domain; the latter,which is a promotion of Radon transformation in two dimensional space, can transform thetranslation of image content, rotation and scale change into functional parameters change bydefining Invariant and Sensitive functionals. Then the image invariant features can beconstructed through the calculation of the parameters.
The research mentioned above has obtained many achievements, but not yet has anydefinite model to analyze all these methods. Based on Radon domain analysis and Tracetransformation, a kind of “Trace space projection” image feature extraction method isproposed in this dissertation. The main research includes the following several aspects:
1. Based on the further study of Radon domain analysis and Trace transformation theory,a kind of mathematical method called Trace space projection is proposed in this dissertation.By defining image trace line, a two dimensional image is projected into a three dimensionalspace. By intrgrating and transforming the three dimensional data space in different directions,this method can be used not only to detect image linear features, but also to extract thecharacteristics of image with geometrical invariability, which is of great application value.Theoretically,this method can unit Radon transform, Trace transform, Ridgelet transform andthe two dimensional Fourier transform into a same mathematical framework of Trace spaceprojection, and by which polar coordinate image moment method can be analysed. The Tracespace projection transformation formula, the extraction method of image features and theTrace space projection realization method is proposed in this dissertation, and general type ofTracespace projection is also discussed.
2. Concerning the fact that the face image with in-plane rotation by stochastic angle isdifficult to identify,a method by fusion of2DNPP and Trace space projection is proposed toextract and identify invariant features of face images rotation. First Trace space projection isdone to the image to extract a sinogram and double trace feature, then higher order spectralmethod is used to match and calculate the double curve, the characteristics obtained arediscovered of robustness for the in-plane rotation changes and the maintenance of the imageinformation by the bispectrum function. Finally2DNPP is used to reduce dimension andclassification to obtain the invariant feature. Compared with SIFT, Pseudo-Zernike momentmethods, the proposed method has better performance with higher recognition rate, and is ofstronger robustness to the white noise.
3. The application of the Trace space projection in the image linear features extraction isfurther explored. A new T functional for SAR image Trace space projection data is proposedto extract the ship orbit characteristics and vehicle direction angle characteristics. Simulationresult shows that the method is effectively used in SAR image recognition. By doing twiceanalysis of Trace space projection of the checkerboard image, a kind of double trace spaceprojection method is proposed to obtain the checkerboard image parallel line positioninformation, and then through the geometrical relationship computation, the checkerboardimages Corner`s positions are got, This method can avoid noise interference outside thecheckerboard. In the image digital watermark embedding study, the linear feature position isobtained by Trace space projection for image analysing, and at the given place digitalwatermark embing, the watermark with transparency and robustness can be obtained.
4. A novel image feature extraction method of fusing orthogonal polynomial moment andTrace space projection is proposed. In this method, the sinogram is obtained by calculatingTrace space projection. And the image sinogram is is decomposed in the orthogonal basisfunction space to obtain the low redundancy orthogonal characteristics of rotation and scalinginvariance. Compared with Zernike moment, Tchebichef moment and OrthogonalFourier-Mellin moment algorithm, this method is of better image shape and textureinformation description ability.At a given condition, the feature obtained by this method canalso be used to reconstruct the original image.
The proposed Trace space projection image feature extraction algorithm can be used toextract the linear or the geometrical invariability characteristics of the image and unite Radondomain analysis, polar image moment analysis and many other methods into the sameframework for research, which is of great theoretical value. The Trace space projectionfeatures can also be applied in image feature extraction and pattern recognition, which is of certain practical value.
引文
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