‘Symmetrical face’ based improved LPP method for face recognition

As one of the most important branches of pattern recognition and computer vision, face recognition has more and more become the focus of researches. In real word applications, the face image might have various changes owing to varying illumination, facial expression and poses, so we need sufficient training samples to convey these possible changes. However, most face recognition systems cannot capture many face images of every user for training, non-sufficient training samples have become one bottleneck of face recognition. In this paper, we propose to exploit the symmetry of the face to generate ‘symmetrical face’ samples and use an improved LPP method to perform classification. Experimental results show that our method can get a high accuracy.     

A sparse representation method based on kernel and virtual samples for face recognition

To improve the classification accuracy of face recognition, a sparse representation method based on kernel and virtual samples is proposed in this paper. The proposed method has the following basic idea: first, it extends the training samples by copying the left side of the original training samples to the right side to form virtual training samples. Then the virtual training samples and the original training samples make up a new training set and we use a kernel-induced distance to determine M nearest neighbors of the test sample from the new training set. Second, it expresses the test sample as a linear combination of the selected M nearest training samples and finally exploits the determined linear combination to perform classification of the test sample. A large number of face recognition experiments on different face databases illustrate that the error ratios obtained by our method are always lower more or less than face recognition methods including the method mentioned in Xu and Zhu [21], the method proposed in Xu and Zhu [39], sparse representation method based on virtual samples (SRMVS), collaborative representation based classification with regularized least square (CRC_RLS), two-phase test sample sparse representation (TPTSSR), and the feature space-based representation method.     

Producing virtual face images for single sample face recognition

For single sample face recognition, there are limited training samples, so the traditional face recognition methods are not applicable to this problem. In this paper we propose to combine two methods to produce virtual face images for single sample face recognition. We firstly use a symmetry transform to produce symmetrical face images. We secondly use the linear combination of two samples to generate virtual samples. As a result, we convert the special single sample problem into a non-single sample problem. We then use the 2DPCA method to extract features from the samples and use the nearest neighbor classifier to perform classification. Experimental results show that the proposed method can effectively improve the recognition rate of single sample face recognition.     

Face image recognition via collaborative representation on selected training samples

In this paper, we present a collaborative representation-based classification on selected training samples (CRC_STS) for face image recognition. The CRC_STS uses a two stage scheme: The first stage is to select some most significant training samples from the original training set by using a multiple round of refining process. The second stage is to use collaborative representation classifier to perform classification on the selected training samples. Our method can be regarded as a sparse representation approach but without imposing l₁-norm constraint on representation coefficients. The experimental results on three well known face databases show that our method works very well.     

Quaternion-based improved LPP method for color face recognition

In recent years, pattern recognition and computer vision have increasingly become the focus of research. Locality preserving projection (LPP) is a very important learning method in these two fields and has been widely used. Using LPP to perform face recognition, we usually can get a high accuracy. However, the face recognition application of LPP suffers from a number of problems and the small sample size is the most famous one. Moreover, though the face image is usually a color image, LPP cannot sufficiently exploit the color and we should first convert the color image into the gray image and then apply LPP to it. Transforming the color image into the gray image will cause a serious loss of image information. In this paper, we first use the quaternion to represent the color pixel. As a result, an original training or test sample can be denoted as a quaternion vector. Then we apply LPP to the quaternion vectors to perform feature extraction for the original training and test samples. The devised quaternion-based improved LPP method is presented in detail. Experimental results show that our method can get a higher classification accuracy than other methods.     

A two-phase face recognition method in frequency domain

In this paper, we propose a two-phase face recognition method in frequency domain using discrete cosine transform (DCT) and discrete Fourier transform (DFT). The absolute values of DCT coefficients or DFT amplitude spectra are used to represent the face image, i.e. the transformed image. Then a two-phase face classification method is applied to the transformed images. This method is as follows: its first phase uses the Euclidean distance formula to calculate the distance between a test sample and each sample in the training sets, and then exploits the Euclidean distance of each training sample to determine K nearest neighbors for the test sample. Its second phase represents the test sample as a linear combination of the determined K nearest neighbors and uses the representation result to perform classification. In addition, we use various numbers of DCT coefficients and DFT amplitude spectra to test the effect on our algorithms. The experimental results show that our method outperforms the two-phase face recognition method based on space domain of face images.     

A novel virtual samples-based sparse representation method for face recognition

A limited training set usually limits the performance of face recognition in practice. Even sparse representation-based methods which outperform in face recognition cannot avoid such situation. In order to effectively improve recognition accuracy of sparse representation-based methods on a limited training set, a novel virtual samples-based sparse representation (VSSR) method for face recognition is proposed in this paper. In the proposed method, virtual training samples are constructed to enrich the size and diversity of a training set and a sparse representation-based method is used to classify test samples. Extensive experiments on different face databases confirm that VSSR is robust to illumination variations and works better than many representative representation-based face recognition methods.     

Modular Fisher Discriminant Sparse Representation for robust face recognition

This paper proposes a novel framework for robust face recognition based on sparse representation and discrimination ranking. This method consists of three stages. The first stage partitions each training sample into some overlapped modules and then computes each module's Fisher ratio, respectively. The second stage selects modules which have higher Fisher ratios to comprise a template to filter training and test images. The dictionary is constructed by the filtered training images. The third stage computes the sparse representation of filtered test sample on the dictionary to perform identification. The advantages of the proposed method are listed as follows: the first stage can preserve the local structure. The second stage removes the modules that have little contribution for classification. Then the method uses the retaining modules to classify the test sample by SRC which makes the method robust. Compared with the related methods, experimental results on benchmark face databases verify the advancement of the proposed method. The proposed method not only has a high accuracy but also can be clearly interpreted.     

基于WSSRC单样本人脸识别及样本扩充方法研究

由于传统的SRC方法的实时性不强、单样本条件下算法性能低等缺点,提出了融合全局和局部特征的加权超级稀疏表示人脸识别方法(WSSRC),同时采用一种三层级联的虚拟样本产生方法获取冗余样本,将生成的多种表情和多种姿态的新样本当成训练样本,运用WSSRC算法进行人脸识别分类。在单样本的情况下,实验证实在ORL人脸库上该方法比传统的SRC方法提高了15.53%的识别率,使用在FERET 人脸库上则提高7.67%。这样的方法与RSRC 、SSRC、DMMA、DCT-based DMMA、I-DMMA相比,一样具备较好的识别性能。     

Quantum dice

In a letter to Born, Einstein wrote  [42]: “Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one.’ I, at any rate, am convinced that He does not throw dice.” In this paper we take seriously Einstein’s famous metaphor, and show that we can gain considerable insight into quantum mechanics by doing something as simple as rolling dice. More precisely, we show how to perform measurements on a single die, to create typical quantum interference effects, and how to connect (entangle) two identical dice, to maximally violate Bell’s inequality.     

A hierarchical structure with improved OMP sparse representation used with face recognition

With the rapid development of the face recognition technology, more and more optical products are applied in people's real life. The recognition accuracy can be improved by increasing the number of training samples, but the colossal training samples will result in the increase of computational complexity. In recent years, sparse representation method becomes a research hot spot on face recognition. In this paper we propose an energy constrain orthogonal matching pursuit (ECOMP) algorithm for sparse representation to select the few training samples and a hierarchical structure for face recognition. We filter the training samples with ECOMP algorithm and then we compute the weights by all selected training samples. At last we find the closest recovery sample to the test sample. Simultaneously the experimental results in AR, ORL and FERET database also show that our proposed method has better recognition performance than the LRC and SRC_OMP method.     

A novel method for recognizing face with partial occlusion via sparse representation

In this paper, we propose a novel method to recognize the partially occluded face images based on sparse representation. Generally, occlusions, such as glasses and scarf, fall on some random patch of image's pixels of test images, but which is known to be connected. In our method, all images are divided into several blocks and then an indicator based on linear regression technique is presented to determine whether a block is occluded. We utilize those uncontaminated blocks as the new feature of an image. Finally, the sparse representation-based classification (SRC) method serves as the classifier to recognize unknown faces. In the original work of SRC, the extended SRC (eSRC) scheme is presented to deal with occlusions, which has very heavy computational cost. The experimental results show that our method can achieve good recognition accuracy and has much lower computational cost than eSRC.     

A face recognition algorithm based on collaborative representation

In this paper, we propose a face recognition algorithm by incorporating a neighbor matrix into the objective function of sparse coding. We first calculate the neighbor matrix between the test sample and each training sample by using the revised reconstruction error of each class. Specifically, the revised reconstruction error (RRE) of each class is the division of the l₂-norm of reconstruction error to the l₂-norm of reconstruction coefficients, which can be used to increase the discrimination information for classification. Then we use the neighbor matrix and all the training samples to linearly represent the test sample. Thus, our algorithm can preserve locality and similarity information of sparse coding. The experimental results show that our algorithm achieves better performance than four previous algorithms on three face databases.     

A modified Galam’s model for word-of-mouth information exchange

In this paper we analyze the stochastic model proposed by Galam in [S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Physica A 320 (2003), 571-580], for information spreading in a ‘word-of-mouth’ process among agents, based on a majority rule. Using the communications rules among agents defined in the above reference, we first perform simulations of the ‘word-of-mouth’ process and compare the results with the theoretical values predicted by Galam’s model. Some dissimilarities arise in particular when a small number of agents is considered. We find motivations for these dissimilarities and suggest some enhancements by introducing a new parameter dependent model. We propose a modified Galam’s scheme which is asymptotically coincident with the original model in the above reference. Furthermore, for relatively small values of the parameter, we provide a numerical experience proving that the modified model often outperforms the original one.     

Double fusion filtering based multi-view face recognition

Two-dimensional (2D) face recognition by correlation is a key challenge of telecommunication and optical information processing. Although this issue has been the focus of intense research, its utilization still has some drawbacks especially when the face is in rotation. In this paper, we propose an alternative method based on a newly designed optical correlation filter which allows recognizing faces with different view angles. This filter called “Multi-View Binary Phase-Only Filter” is based on a double fusion of reference images allowing an optimisation of the use of the spatial-bandwidth product (SBWP) in the filter Fourier plane. The first fusion is performed in the image (space) domain, and the second one is conducted in the spectral domain. Simulations results with the Pointing Head Pose Image Database illustrate the performance of the designed correlation filter for multi-view face recognition.     

Semi-supervised Discriminant Analysis and Sparse Representation-based self-training for Face Recognition

In this paper, we consider the problem of automatic face recognition with limited manually labeled training data. We propose a new semi-supervised self-training approach which is used to automatically augment the manually labeled training set with new unlabeled data. Semi-supervised Discriminant Analysis is used in each iteration of self-training for discriminative dimensionality reduction by making use of both labeled and unlabeled training data. Sparse representation is applied for classification. Experimental results on four independent databases show that our algorithm outperforms other face recognition methods under 3 different configurations, namely transductive, semi-supervised and single training image.     

Complexity reduced coding of binary pattern units in image classification

The ability to simulate and control complex physical situations in real time is an important element of many engineering and robotics applications, including pattern recognition and image classification. One of the ways to meet specific requirements of a process is a reduction of computational complexity of algorithms. In this work we propose a new coding of binary pattern units (BPU) that reduces the time and spatial complexity of algorithms of image classification significantly. We apply this coding to a particular but important case of the coordinated clusters representation (CCR) of images. This algorithm reduces the dimension of the CCR feature space and, as a consequence, the time and space complexity of the CCR based methods of image classification, exponentially. In addition, the new coding preserves all the fundamental properties of the CCR that are successfully used in the recognition, classification and segmentation of texture images. The same approach to the coding of BPUs can be used in the Local Binary Pattern (LBP) method. In order to evaluate the reduction of time and space complexity, we did an experiment on multiclass classification of images using the “traditional” and the new coding of the CCR. This test showed very effective reduction of the computing time and required computer memory with the use of the new coding of BPUs of the CCR, retaining 100% or a little less efficiency of classification at the time.     

Robust face recognition based on sparse representation in 2D Fisherface space

Sparse representation is being proved to be effective for many tasks in the field of face recognition. In this paper, we will propose an efficient face recognition algorithm via sparse representation in 2D Fisherface space. We firstly transformed the 2D image into 2D Fisherface in preprocessing, and classify the testing image via sparse representation in the 2D Fisherface space. Then we extend the proposed method using some supplementary matrices to deal with random pixels corruption. For face image with contiguous occlusion, we partition each image into some blocks, and define a new rule combining sparsity and reconstruction residual to discard the occluded blocks, the final result is aggregated by voting the classification result of the valid individual block. The experimental results have shown that the proposed algorithm achieves a satisfying performance in both accuracy and robustness.     

Econophysical visualization of Adam Smith’s invisible hand

Consider a complex system whose macrostate is statistically observable, but yet whose operating mechanism is an unknown black-box. In this paper we address the problem of inferring, from the system’s macrostate statistics, the system’s intrinsic force yielding the observed statistics. The inference is established via two diametrically opposite approaches which result in the very same intrinsic force: a top-down approach based on the notion of entropy, and a bottom-up approach based on the notion of Langevin dynamics. The general results established are applied to the problem of visualizing the intrinsic socioeconomic force–Adam Smith’s invisible hand–shaping the distribution of wealth in human societies. Our analysis yields quantitative econophysical representations of figurative socioeconomic forces, quantitative definitions of “poor” and “rich”, and a quantitative characterization of the “poor-get-poorer” and the “rich-get-richer” phenomena.