摘要
特征提取是人脸识别研究的核心问题。通过采集设备所获得的人脸图像构成了高维的人脸观测空间,而人脸的鉴别特征则分布在高维空间中人脸样本所形成的低维流形(子空间)上。特征提取就是从高维观测空间搜寻低维的人脸鉴别子空间(流形)的过程。在这一过程中,光照处理和维数约简是两个关键的步骤。在观测空间中,人脸样本数据的分布在本质上是稀疏的,但各类别分布之间又是高度交叠的,造成了人脸样本的类内差异大于类间差异。对人脸图像进行光照处理,可以有效地调整观测空间中人脸样本的分布形态,缩小样本的类内差异,增大类间差异,为随后的维数约简(特征提取)奠定良好的基础。经过光照处理的人脸图像仍然位于高维的观测空间,向量的高维性质会造成“维数灾难”和“测度集中”现象,在这种情况下,直接利用分类器进行分类难以取得好的效果。因此,如何针对高维、小样本的人脸识别问题,设计出有效的维数约简算法,以便从高维的观测空间中提取的最具鉴别力的低维人脸特征,便成为人脸识别研究的中心任务。遵循这一思路,本文围绕着光照处理和特征提取这两个关键步骤,从理论和技术两个层面进行了深入的研究,在现有的研究基础上,提出了一些新的观点和解决方案。
针对光照变化处理,论文分别提出了基于Gabor小波和基于NSCT (Nonsubsampled Contourlet Transform, NSCT)变换的光照处理算法。
(1)基于Gabor小波的光照变化处理：Gabor小波内核类似于哺乳动物的视觉皮层感知细胞的响应曲线,因此图像的Gabor特征对光照、姿态和表情的变化不敏感。基于Gabor小波的这一特性,本文首先对人脸图像进行Gabor变换,得到人脸的Gabor表征,之后针对高维的Gabor特征,提出基于保持局部线性关系的监督流形学习算法：监督邻域保持嵌入算法(Supervised Neighborhood Preserving Embedding, SNPE),进行了有效的维数约简。在Yale和ORL两个人脸数据库上进行了实验,结果验证了算法的可行性。
(2)基于NSCT变换的光照变化处理：类似于Gabor小波,NSCT变换(Nonsubsampled Contourlet Transform, NSCT)也是一种多尺度、多方向的2D小波变换,但和Gabor小波不同,NSCT的基函数之间是相互正交的。因此,NSCT各子图之间所包含的冗余信息最小,而且可以通过重构算法由子图得到原始图像。基于NSCT变换的这种优良性质,本文在Retinex光照模型的基础上,将人脸图像变换到NSCT域,采用自适应阈值对各高频子图进行滤波,通过逆NSCT变换重构得到人脸图像的光照不变量(特征)。实验结果表明,本文所提算法可以非常有效地削弱光照变化对人脸图像的影响,在很大程度上提高了算法的识别率。
流形学习的核心思想是在降维的过程中保持数据空间局部的几何性质,是目前主流的非线性子空间方法,已经被广泛地应用到了人脸识别问题中。本文根据人脸样本分布的特点,基于现行方法提出了3种应用于人脸识别问题的监督流形学习算法：
(1)自适应监督局部保持最优投影算法(Adaptive Supervised Locality Optimal Preserving Projection, ASLOPP):ASLOPP算法在构造样本空间特征图时,首先采用自适应邻域算法来确定样本空间中每个数据点邻域的大小,增强了对数据分布稀疏性的表征；其次通过改变权值来抑制邻域内不同样本之间的相似度,并通过增加约束条件,采用迭代算法进行目标函数的优化,使得低维嵌入空间的基向量之间相互正交,减少了嵌入空间中信息的冗余,同时也提高鉴别能力。在Extended Yale B和CMU PIE两个人脸库上进行了实验,结果表明该算法可以有效地提高人脸识别效果。
(2)监督局部保持投影算法(Supervised Locality Preserving Proj ection, SLPP):该算法也是在LPP算法的基础上,根据人脸图像特征空间的分布特点,在构造样本空间特征图的过程中,首先利用自适应邻域算法确定样本点邻域大小,之后利用样本的先验类标信息,分布构造了类内图和类外图,用来表征样本空间中各类样本的分布情况。目标函数则融入了线性鉴别分析(Linear Discriminant Analysis, LDA)的思想,使得优化后的嵌入空间不仅最优保持了原始样本空间的局部几何结构,同时各类样本的类内散度最小化,类间散度最大化,大幅度增强了嵌入空间的鉴别能力。
(3)监督邻域保持嵌入算法(Supervised Neighborhood Preserving Embedding):监督邻域保持嵌入则是在NPE算法(Neighborhood Preserving Embedding, NPE)的基础上,在构造样本空间的邻域图的过程中,利用样本的类标信息将邻域内样本分为内类样本和外类样本,通过目标函数的优化,使得嵌入空间在最优保持样本空间局部线性关系的同时,同类数据之间距离缩小,不同类数据之间距离增大,从而嵌入空间在最优保持各类数据子流形的基础上,减少了数据的类内散度,增大了数据的类间散度,提高了鉴别能力。
Feature extraction is a key problem in the study of face recognition. Face images obtained by image acquisition equipment construct the high-dimensional face observation space, and discriminative features of human face lie on the low manifold (subspace) formed by face samples. What is the feature extraction is the process of searching the low-dimensional discriminative subspace (manifold) from the high-dimensional observation space. During this process, illumination processing and dimensionality reduction is the two crucial steps. The distribution of face sample data in the observation space is sparse essentially, while that of each class is highly overlapping with each other, resulting that the differences of face samples within classes are larger than that between classes. Processing the illumination of face images effectively can adjust the distribution form of face samples in the observation space, reducing the differences within classes, increasing those between classes, and thus laying a good foundation for the followed dimensionality reduction (feature extraction). However, face images, after handling lighting, still stay in the observation space, and the high-dimensional property of vectors will incur'Curse of Dimensionality' and 'measure concentration', in which case it is hard to achieve good results by using classifiers to classify the samples directly. Therefore, it becomes the central task in the study of face recognition how to design effective algorithms of reducing dimensionality to extract the low-dimensional face features from the high-dimensional observation space with the most powerful discriminative. Followed this idea, we made an intensive study on these two crucial steps of processing illumination and extracting features from the view of theory and technology, and proposed some new idea and solutions based on the existing research results.
The kernels of Gabor wavelet are similar to the response of the two-dimensional receptive field profiles of the mammalian simple cortical cell, and exhibit the desirable characteristics of capturing salient visual properties such as spatial localization, orientation selectivity, and spatial frequency selectivity. Therefore, the Gabor features of images are insensitive to the variations of illumination, pose and expression. Based on this property of Gabor wavelet, we first made a Gabor transform to face images, with the facial Gabor features obtained; and then proposed a locality preserving based supervised manifold learning algorithm designed for the high-dimensional Gabor features, called Supervised Neighborhood Preserving Embedding, by which the dimensionality is reduced effectively. Experimental results on the two face databases of Yale and ORL show the feasibility of the proposed algorithm.
Similar to the Gabor wavelet, Nonsubsampled Contourlet Transform (NSCT) is also a multi-scale and multi-direction2D wavelet transform. The difference from the Gabor wavelet is that the basis functions of NSCT is orthogonal to each other, with the least redundant information contained by the sub-bands of NSCT. In consideration of this good feature of NSCT, we transformed, based on the Retinex illumination model, the face image into NSCT domain, used adaptive threshold to filter each high-frequency sub-band, and obtained the illumination invariant of face images by using inverse NSCT. Experimental results indicated that the proposed algorithm can very effectively reduce the effect of illumination variation on face images, improving the recognition rate of the algorithm to a large extent.
Manifold learning has a core idea of preserving the local geometric properties of the data space during the process of reducing the dimensionality, which is now a mainstream nonlinear subspace method and wildly applied to face recognition. In this paper, according to the distribution feature of face samples, we proposed3kinds of supervised learning algorithms for face recognition based on an analysis of limits of some manifold learning algorithms.
(1) Adaptive Supervised Locality Optimal Preserving Projection (ASLOPP). After investigating some drawbacks of existing supervised LPP algorithms in classification problem, ASLOPP method determines the neighborhood size of each data in sample space by using adaptive neighborhood algorithm, adds constraint conditions, and employs iterative method to optimize the objective function, which leads to orthogonal basis vectors in low-dimensional embedding, decreasing the information redundancy in the embedding while increasing the discriminative power. We conducted experiments on Extended Yale B and CMU PIE face databases, with good results improving the face recognition rates obviously.
(2) Supervised Locality Preserving Projection (SLPP). This algorithm is also based on LPP, which first employs adaptive neighborhood method for determining the sample neighborhood size in the process of constructing the eigenmap of sample space, in terms of the distribution of facial feature space. Then the prior class label information of samples is used to construct within-class and between-class maps, respectively, by which the distribution of each class is represented. And the objective function absorbs the idea of LDA, which allows the optimized embedding not only maintain the local geometry of the original sample space, but also minimize the within-class variance while maximize the between-class one, greatly enhancing the discriminative of the embedding.
(3) Supervised Neighborhood Preserving Embedding. On the basis of the Neighborhood Preserving Embedding (NPE), this algorithm determines the link mode between samples by the class label in constructing the neighborhood map of the sample space. By optimization of the objective function, the embedding holds the local linearity of the sample space optimally, and also greatly improve the discriminative power.
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