统计流形框架下视觉特征的嵌入与目标识别
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摘要
颜色、纹理和形状是最基本的视觉特征,人们常用其来描述图像的属性,并广泛应用于目标识别任务。多尺度高斯导数滤波器和Gabor滤波器是构造图像局部形状和多谱纹理描述子的常用工具。在分析和应用时,通常将输入图像与一组高斯导数滤波器或Gabor滤波器的卷积输出作为多通道或多谱图像。这种多通道滤波图像与常见的彩色图像类似,具有局部多维和全局高维特性。全局方法习惯将所有通道逐像素点的滤波响应串联成一个高维向量。然而,在识别或学习等应用中,特征向量高维属性容易导致“维数灾难”,使得算法失效或输出次优结果。尽管下采样或其它压缩技术可以在一定程度上克服这些问题,但都是以丧失大量信息为代价。共生矩阵本质上是一种离散的概率分布,它利用像素特征空间上的共生信息描述图像纹理。传统方法常采用从共生矩阵中进一步提取Haralick特征,这时出现的问题是无法使用共生矩阵的全部统计信息。直方图是一种广泛使用的图像描述子,不过,目标图像与高斯导数或Gabor滤波器卷积生成的逐像素响应集大多呈现复杂的分布。在识别任务中如何从这些特征集中抽取判别直方图并赋予恰当的信息度量就显得十分重要。另外,直方图的非欧几何结构使得经典学习算法对其学习时难以得到令人满意的结果。针对上面提及的图像/滤波图像视觉特征用于识别和学习过程中所出现的问题,在统计流形框架下,本文考虑逐像素特征/共生特征的概率生成模型。通过使用模型离散化(仅针对非参数的概率模型)和紧致化嵌入技术,在(积)多项流形上借助(因子流形的)费舍尔-黎曼(Fisher-Riemannian)几何导出了生成模型间相似性度量。在此基础上,提出了基于特征/共生特征概率生成模型匹配的目标识别方法和基于随机直方图嵌入的统计流形学习方法。本篇论文的工作、主要成果和创新包括：
(1)提出了基于特征/共生特征概率生成模型的目标表示。即利用目标图像/滤波图像上逐像素点的特征集的联合(或边际)生成模型,将目标表示成为某个(积)非参数统计流形上的点。利用图像/滤波图像上共生特征的生成模型,将目标表示成一个(积)多项流形上的点。这些目标表示方法是本文算法设计的基础。
(2)理论上,证明了用多项流形的费舍尔几何来研究无限维非参数统计流形的某个子流形的合理性。应用上,给出了由非监督学习的分位点确定的模型离散化方法。为了获得与模型几何相适应的信息度量,采用了离散化模型的极大似然嵌入和嵌入的紧化技术。并对嵌入的(积)子流形赋予了由(因子)多项流形上测地距离导出的信息度量。由此,提出了基于特征概率生成模型匹配的目标识别方法。实验结果表明：当应用多通道Gabor特征或高斯微分特征进行目标识别时,该方法能在不同类型的目标库上获得较好的识别性能。
(3)通过引入紧化的(积)共生矩阵嵌入,提出了在嵌入(积)子流形上匹配灰度/颜色共生矩阵的目标识别方法。为了将这种方法加以推广,本文设计了一种新颖的图像描述子—Gabor幅值共生矩阵。通过对多项流形上的测地距离度量的延拓,提出了匹配Gabor幅值共生矩阵的目标识别方法。实验结果验证：本文提出的识别方法在性能上明显优于经典(核)子空间方法和Haralick特征匹配的方法。
(4)提出了基于随机直方图嵌入的统计流形学习方法。该方法不刻意追求从数据或特征集中抽取最优直方图,而是强调通过抽取多个低分辨率的随机直方图和紧致化嵌入,在积多项流形上对其判别信息加以整合。在嵌入积子流形上将经典流形学习算法和本征维数估计算法调整成与导出度量相适应的形式,由此实现积子流形的低维欧氏嵌入。实验结果证实,该方法在特征提取以及目标或数据集的可视化方面均有很好的表现。
As the basic visual features, color, texture and shape are usually adopted to describe image properities and applied to object recognition tasks. Gabor filter and Gaussian derivative filter are two kinds of tools to construct multispectral texture and local shape descriptors of image. For any input image, the collection of filtered images outputted from a bank of Gabor filters or Gaussian derivative filters used to be viewed as a multichannel or multispectral image for alanysis and application. This sort of multichannel image owns the global high-dimensional and local multi-dimensional natures similar to common color image. Global approaches are accustomed to concatenating all channels of pixel-by-pixel filtered responses to form a high-dimensional vector. But, the high-dimensional nature of feature vectors tends to cause "the curse of dimensionality" in a learning or recognition task, which makes algorithm invalid or only output suboptimal result. Although sampling and other compression techniques can solve the problem to certain extent, it is often at the cost of multitudinous information loss. A co-occurrence matrix is essentially a discrete probability distribution that describes image texture with spatial co-occurrence information of pixel features. The classical methods use Haralick features, but then the complete information of the co-occurrence matrix can not be summarized into these features. Histograms are a kind of widely used image descriptors, but the response sets obtained by convoluting an image with a bank of Gabor or Gaussian derivative filters have complex distributions in most cases. Then it is necessary to extract discriminative histograms and endow them with appropriate information metric. In addition, the non-Euclidean structured histograms determine that it is hard to get satisfactory results as applying a Euclidean metric-based learning algorithm to histograms-representing frequency data. Aiming to the problems of above visual features appeared in the processes of recognition and learning, we consider the probabilistic generative models of pixel-by-pixel features or co-occurring features of images (or filtered images) in the framework of statistical manifolds. By using the techniques of the models'discretization (only to nonparametric probability models) and the compactified embedding, the similarity metrics of generative models are built by the Fisher-Riemannian geometries on multinomial manifolds. We present the recognition methods of matching generative models of features or co-occurring features, and the learning method based on stochastic histogram embedding in the framework of statistical manifold. The novelties and main results of the associated work in this thesis include:
(1) Object representation in the form of probabilistic generative model of features or co-occurring features is presented. That is, objects are represented as (product) the points of a nonparameteric (product) statistical manifold with the joint (or marginal) generative models of pixel-by-pixel feature sets of object images or the filtered images. Using the generative models of co-occurring features on object images or filtered images, objects are represented as the points on a (product) multinomial manifold. The presented object representations are the foundations to formulate our recognition algorithms in this thesis.
(2) Theoretically, we prove the rationality to study a submanifold of a nonparemeteric statistical manifold by the Fisher geometry on multinomial manifold. As to application, we present the partition scheme on feature space with the quantiles learned in unsupervised manner. For designing model geometry-adaptive information metric, the techniques of maximum likelihood embedding and compactified embedding are adopted for the discretized models. In addition, we equip the embedded (product) submanifold with the information metric built by the geodesic distance metrics of factor multinomial manifolds. In this way, we present the object recognition method by matching probabilistic generative models of images' features. Experiments showed that the method gained the better recognition performances on several different types of object databases by using multichannel Gabor features or Gaussian differential features.
(3) Object recognition approach matching gray level co-occurrence matrix or color co-occurrence matrices on (product) multinomial manifold is presented, by introducing (product) co-occurrence matrix (matrices) embedding and the compactification. In order to generalize the approach, a novel image descriptor, i.e. Gabor magnitude co-occurrence matrix was designed in this thesis. Using the extension technique of geodesic distance metrics on multinomial manifolds, we also generalized the method for object recognition by matching Gabor magnitude co-occurrence matrices on product multinomial manifold with boundary. Experimental results showed that these methods significantly outperformed classic (kernel) subspace methods and Haralick features based method with the higher recognition accuracy.
(4) The statistical manifold learning method based on stochastic histogram embedding is presented. This method does not pursue the optimal histogram binning scheme, but stress the extraction of multiple low-resolution stochastic histograms and information integration on product multinomial manifold based on the compactified embedding. The classical manifold learning algorithms and the intrinsic dimension estimation algorithms can be adjusted to the derived metric-adaptive form, for learning on the embedded product submanifold for lower-dimensional Euclidean embedding. Experimental results show this learning algorithm can gain promising performances on feature extraction and data visualization.
(1)提出了基于特征/共生特征概率生成模型的目标表示。即利用目标图像/滤波图像上逐像素点的特征集的联合(或边际)生成模型,将目标表示成为某个(积)非参数统计流形上的点。利用图像/滤波图像上共生特征的生成模型,将目标表示成一个(积)多项流形上的点。这些目标表示方法是本文算法设计的基础。
(2)理论上,证明了用多项流形的费舍尔几何来研究无限维非参数统计流形的某个子流形的合理性。应用上,给出了由非监督学习的分位点确定的模型离散化方法。为了获得与模型几何相适应的信息度量,采用了离散化模型的极大似然嵌入和嵌入的紧化技术。并对嵌入的(积)子流形赋予了由(因子)多项流形上测地距离导出的信息度量。由此,提出了基于特征概率生成模型匹配的目标识别方法。实验结果表明：当应用多通道Gabor特征或高斯微分特征进行目标识别时,该方法能在不同类型的目标库上获得较好的识别性能。
(3)通过引入紧化的(积)共生矩阵嵌入,提出了在嵌入(积)子流形上匹配灰度/颜色共生矩阵的目标识别方法。为了将这种方法加以推广,本文设计了一种新颖的图像描述子—Gabor幅值共生矩阵。通过对多项流形上的测地距离度量的延拓,提出了匹配Gabor幅值共生矩阵的目标识别方法。实验结果验证：本文提出的识别方法在性能上明显优于经典(核)子空间方法和Haralick特征匹配的方法。
(4)提出了基于随机直方图嵌入的统计流形学习方法。该方法不刻意追求从数据或特征集中抽取最优直方图,而是强调通过抽取多个低分辨率的随机直方图和紧致化嵌入,在积多项流形上对其判别信息加以整合。在嵌入积子流形上将经典流形学习算法和本征维数估计算法调整成与导出度量相适应的形式,由此实现积子流形的低维欧氏嵌入。实验结果证实,该方法在特征提取以及目标或数据集的可视化方面均有很好的表现。
As the basic visual features, color, texture and shape are usually adopted to describe image properities and applied to object recognition tasks. Gabor filter and Gaussian derivative filter are two kinds of tools to construct multispectral texture and local shape descriptors of image. For any input image, the collection of filtered images outputted from a bank of Gabor filters or Gaussian derivative filters used to be viewed as a multichannel or multispectral image for alanysis and application. This sort of multichannel image owns the global high-dimensional and local multi-dimensional natures similar to common color image. Global approaches are accustomed to concatenating all channels of pixel-by-pixel filtered responses to form a high-dimensional vector. But, the high-dimensional nature of feature vectors tends to cause "the curse of dimensionality" in a learning or recognition task, which makes algorithm invalid or only output suboptimal result. Although sampling and other compression techniques can solve the problem to certain extent, it is often at the cost of multitudinous information loss. A co-occurrence matrix is essentially a discrete probability distribution that describes image texture with spatial co-occurrence information of pixel features. The classical methods use Haralick features, but then the complete information of the co-occurrence matrix can not be summarized into these features. Histograms are a kind of widely used image descriptors, but the response sets obtained by convoluting an image with a bank of Gabor or Gaussian derivative filters have complex distributions in most cases. Then it is necessary to extract discriminative histograms and endow them with appropriate information metric. In addition, the non-Euclidean structured histograms determine that it is hard to get satisfactory results as applying a Euclidean metric-based learning algorithm to histograms-representing frequency data. Aiming to the problems of above visual features appeared in the processes of recognition and learning, we consider the probabilistic generative models of pixel-by-pixel features or co-occurring features of images (or filtered images) in the framework of statistical manifolds. By using the techniques of the models'discretization (only to nonparametric probability models) and the compactified embedding, the similarity metrics of generative models are built by the Fisher-Riemannian geometries on multinomial manifolds. We present the recognition methods of matching generative models of features or co-occurring features, and the learning method based on stochastic histogram embedding in the framework of statistical manifold. The novelties and main results of the associated work in this thesis include:
(1) Object representation in the form of probabilistic generative model of features or co-occurring features is presented. That is, objects are represented as (product) the points of a nonparameteric (product) statistical manifold with the joint (or marginal) generative models of pixel-by-pixel feature sets of object images or the filtered images. Using the generative models of co-occurring features on object images or filtered images, objects are represented as the points on a (product) multinomial manifold. The presented object representations are the foundations to formulate our recognition algorithms in this thesis.
(2) Theoretically, we prove the rationality to study a submanifold of a nonparemeteric statistical manifold by the Fisher geometry on multinomial manifold. As to application, we present the partition scheme on feature space with the quantiles learned in unsupervised manner. For designing model geometry-adaptive information metric, the techniques of maximum likelihood embedding and compactified embedding are adopted for the discretized models. In addition, we equip the embedded (product) submanifold with the information metric built by the geodesic distance metrics of factor multinomial manifolds. In this way, we present the object recognition method by matching probabilistic generative models of images' features. Experiments showed that the method gained the better recognition performances on several different types of object databases by using multichannel Gabor features or Gaussian differential features.
(3) Object recognition approach matching gray level co-occurrence matrix or color co-occurrence matrices on (product) multinomial manifold is presented, by introducing (product) co-occurrence matrix (matrices) embedding and the compactification. In order to generalize the approach, a novel image descriptor, i.e. Gabor magnitude co-occurrence matrix was designed in this thesis. Using the extension technique of geodesic distance metrics on multinomial manifolds, we also generalized the method for object recognition by matching Gabor magnitude co-occurrence matrices on product multinomial manifold with boundary. Experimental results showed that these methods significantly outperformed classic (kernel) subspace methods and Haralick features based method with the higher recognition accuracy.
(4) The statistical manifold learning method based on stochastic histogram embedding is presented. This method does not pursue the optimal histogram binning scheme, but stress the extraction of multiple low-resolution stochastic histograms and information integration on product multinomial manifold based on the compactified embedding. The classical manifold learning algorithms and the intrinsic dimension estimation algorithms can be adjusted to the derived metric-adaptive form, for learning on the embedded product submanifold for lower-dimensional Euclidean embedding. Experimental results show this learning algorithm can gain promising performances on feature extraction and data visualization.
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