Face recognition under varying illumination based on singular value decomposition and retina modeling

In this paper, a unified algebraic transformation approach is presented for designing parallel recursive and adaptive digital filters and singular value decomposition (SVD) algorithms. The approach is based on the explorations of some algebraic properties of the target algorithms' representations. Several typical modern digital signal processing examples are presented to illustrate the applications of the technique. They include the cascaded orthogonal recursive digital filter, the Givens rotation-based adaptive inverse QR algorithm for channel equalization, and the QR decomposition-based SVD algorithms. All three examples exhibit similar throughput constraints. There exist long feedback loops in the algorithms' signal flow graph representation, and the critical path is proportional to the size of the problem. Applying the proposed algebraic transformation techniques, parallel architectures are obtained for all three examples. For cascade orthogonal recursive filter, retiming transformation and orthogonal matrix decompositions (or pseudo-commutativity) are applied to obtain parallel filter architectures with critical path of five Givens rotations. For adaptive inverse QR algorithm, the commutativity and associativity of the matrix multiplications are applied to obtain parallel architectures with critical path of either four Givens rotations or three Givens rotations plus two multiply-add operations, whichever turns out to be larger. For SVD algorithms, retiming and associativity of the matrix multiplications are applied to derive parallel architectures with critical path of eight Givens rotations. The critical paths of all parallel architectures are independent of the problem size as compared with being proportional to the problem size in the original sequential algorithms. Parallelism is achieved at the expense of slight increase (or the same for the SVD case) in the algorithms' computational complexity.

Singular Value Decomposition (SVD) algorithm is a good method in Collaborative Filtering (CF) algorithm. But the traditional SVD method faces the matrix sparse problem, people solve this problem by Latent Factor Model (LMF). The data imbalances problem also troubles us. The algorithm of this paper combines Slope One and SVD algorithm to solve the data imbalances problem. First, we use Slope One algorithm to deal with the users who have few rating records. Then this kind of user will have more rating records. And we can use new data set to train the SVD model to predict the final results. The experiment results show that our algorithm is better than the traditional Slope One and SVD algorithm.

The purpose of this research is to present Symmetrical Singular Value Decomposition Representation (SSVDR) method with Gabor Filter under illumination effect for face recognition. SSVDR method was proposed to normalize illuminated face images caused by the difference of light. SSVDR method represented characteristics of face images on low-intensity combined with the symmetrical reversed part of the face based on Singular Value Decomposition (SVD). Gabor Filter was used to extract the face images which were already processed using SSVDR. In order to do the face recognition, PCA and LDA methods were used with Nearest Neighbor as the classifier. The result showed that face recognition with SSVDR based on Gabor Filter was quite good on face images with low-intensity, but the recognition were not good enough on face images with extreme illumination. Overall, the accuracy of face recognition scored 91.86% with PCA and 91.57% with LDA.

This paper concerns accurate computation of the singular value decomposition (SVD) of an $m\times n$ matrix $A$ . As is well known, cross-product matrix based SVD algorithms compute large singular values accurately but generally deliver poor small singular values. A new novel cross-product matrix based SVD method is proposed: (a) Use a backward stable algorithm to compute the eigenpairs of $A^{\rm T}A$ and take the square roots of the large eigenvalues of it as the large singular values of $A$ ; (b) form the Rayleigh quotient of $A^{\rm T}A$ with respect to the matrix consisting of the computed eigenvectors associated with the computed small eigenvalues of $A^{\rm T}A$ ; (c) compute the eigenvalues of the Rayleigh quotient and take the square roots of them as the small singular values of $A$ . A detailed quantitative error analysis is conducted on the method. It is proved that if small singular values are well separated from the large ones then the method can compute the small ones accurately up to the order of the unit roundoff $\epsilon$ . An algorithm is developed that is not only cheaper than the standard Golub–Reinsch and Chan SVD algorithms but also can update or downdate a new SVD by adding or deleting a row and compute certain refined Ritz vectors for large matrix eigenproblems at very low cost. Several variants of the algorithm are proposed that compute some or all parts of the SVD. Typical numerical examples confirm the high accuracy of our algorithm.

Illumination variations significantly affect the performance of the automatic face recognition system. To achieve optimum contrast enhancement, contrast limiting adaptive histogram equalization (CLAHE) has been used in this work. Histogram Equalization (HE) modifies the histogram of the image globally based on intensity distribution of an entire image. However, the feature of interest in an image needs enhancement locally. CLAHE is based on the intensity distribution in a neighborhood of every pixel in the image. Further, for removing the illumination variations in the face image, the appropriate number of low frequency DCT coefficients has been scaled down as illumination variations mainly lie in the low-frequency band. After eliminating illumination variations effect, mapping of the data on to another feature space is done using Kernel PCA (KPCA), which extract higher order statistics. KPCA has the advantage of less computation time and improve performance level. Classification is done by using nearest neighbor classifier. Experiments are performed on Extended Yale B database. The experimental results show that the performance of our method is significantly better than that of any existing state-of-art technique.

Change point detection is essential to understand the time-evolving structure of dynamic networks. Recent research shows that a latent semantic indexing (LSI)-based algorithm effectively detects the change points of a dynamic network. The LSI-based method involves a singular value decomposition (SVD) on the data matrix. In a dynamic scenario, recomputing the SVD of a large matrix each time new data arrives is prohibitively expensive and impractical. A more efficient approach is to incrementally update the decomposition. However, in the classical incremental SVD (incSVD) algorithm, the information of the newly added columns is not fully considered in updating the right singular space, resulting in an approximation error which cannot be ignored. This paper proposes an enhanced incSVD (EincSVD) algorithm, in which the right singular matrix is calculated in an alternative way. An adaptive EincSVD (AEincSVD) algorithm is also proposed to further reduce the computational complexity. Theoretical analysis proves that the approximation error of the EincSVD is smaller than that of the incSVD. Simulation results demonstrate that the EincSVD and the AEincSVD perform much better than the incSVD on change point detection, and the performance of the EincSVD is comparable to the batch SVD algorithm.

Estimates of the past thermal state of the land surface are crucial to assess the magnitude of current anthropogenic climate change, as well as to assess the ability of Earth System Models to forecast the evolution of the climate near the ground, not included in standard meteorological records. Subsurface temperature data are able to retrieve long-term changes in surface energy balance –from decadal to millennial time scales, thus constituting an important record of the dynamics of the climate system that contributes low-frequency information to proxy-based paleoclimatic reconstructions. A broadly used technique to retrieve past temperature and heat flux histories from subsurface temperature profiles based on a Singular Value Decomposition (SVD) algorithm was able to take into account a limited number of sources of uncertainty, with recent works attempting to increase the number of factors considered in uncertainty estimates. Nevertheless, the SVD methodology did not define a statistical framework for aggregating inversions of individual profiles to derive global results, which lead to estimates of global and regional uncertainties that are difficult to interpret. To alleviate the lack of a conceptual framework for estimating uncertainties in past temperature and heat flux histories at regional and global scales, we combine a new bootstrapping sampling strategy with the broadly used SVD algorithm, and assess its performance against the original SVD technique and another technique based on generating perturbed parameter ensembles of inversions. The new bootstrap approach is able to reproduce the prescribed surface temperature series used to derive an artificial profile. Bootstrap results are also in agreement with the global mean surface temperature history and the global mean heat flux history retrieved in previous studies. Furthermore, the new bootstrap technique provides with a meaningful uncertainty range for the inversion of large sets of subsurface temperature profiles. We suggest the use of this new approach particularly for aggregating results from a number of individual profiles, and to this end, we release the programs used to derive all inversions in this study as a suite of codes labelled CIBOR 1.0: Codes for Inverting BORholes, version 1.0.

A combination of a multiresolution (MR) preconditioner and matrix decomposition algorithm – singular value decomposition (MDA-SVD) algorithm is proposed for the analysis of densely discretised electromagnetic (EM) scatterers. In realistic EM scattering problems, the discretisation may be very dense to accurately describe the geometric shape of targets. However, dense discretisations will generate two major drawbacks: (i) the badly conditioned method of moments (MoM) matrix which makes iterative solvers difficult to converge; (ii) the dense near-field MoM matrix for which the computational cost is large, even multilevel fast multipole algorithm (MLFMA) is applied. To remedy the first shortcoming of dense discretisations, an MR preconditioner can be applied to improve the condition of MoM matrices. To reduce the computational cost in solving the MoM matrix equation, an MDA-SVD algorithm can be applied to accelerate the matrix−vector multiplication. Compared with the traditional MLFMA, the MDA-SVD algorithm has no limit on the size of octree boxes which makes the MDA-SVD algorithm suitable for the analysis of dense discretisations. Therefore an MR preconditioner is combined with the MDA-SVD algorithm for fast analysis of dense discretisations. Numerical results indicate that the combination of the MR preconditioner and the MDA-SVD algorithm is efficient.

In this paper, it studies two critical technical links of face detection and face recognition in the recognition of face, and conducts analyses and comparisons on some commonly used face detections and recognition algorithms. Through the collation of this information and the combination of related knowledge in the digital image processing, it proposes a face recognition algorithm based on the singular value decomposition. After preprocessing face images, by the use of the projection method, it obtains positions of five sense organs, and then extracts local feature values near five sense organs as the main features of faces by using the singular value decomposition. For different face images of the same individual, the matching degree of feature values will be very high.KeywordsFace recognitionimage recognitionlocal informationfeature extraction

Purpose: Segmentation of the vessel tree from retinal fundus images can be used to track changes in the retina and be an important first step in a diagnosis. Manual segmentation is a time-consuming process that is prone to error; effective and reliable automation can alleviate these problems but one of the difficulties is uneven image background, which may affect segmentation performance. Approach: We present a patch-based deep learning framework, based on a modified U-Net architecture, that automatically segments the retinal blood vessels from fundus images. In particular, we evaluate how various pre-processing techniques, images with either no processing, N4 bias field correction, contrast limited adaptive histogram equalization (CLAHE), or a combination of N4 and CLAHE, can compensate for uneven image background and impact final segmentation performance. Results: We achieved competitive results on three publicly available datasets as a benchmark for our comparisons of pre-processing techniques. In addition, we introduce Bayesian statistical testing, which indicates little practical difference ( ) between pre-processing methods apart from the sensitivity metric. In terms of sensitivity and pre-processing, the combination of N4 correction and CLAHE performs better in comparison to unprocessed and N4 pre-processing ( ); but compared to CLAHE alone, the differences are not significant ( to 0.88). Conclusions: We conclude that deep learning is an effective method for retinal vessel segmentation and that CLAHE pre-processing has the greatest positive impact on segmentation performance, with N4 correction helping only in images with extremely inhomogeneous background illumination.

We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the matrix product operator (MPO) format, also called the tensor train matrix format. Our tensor network randomized SVD (TNrSVD) algorithm is an MPO implementation of the randomized SVD algorithm that is able to compute dominant singular values and their corresponding singular vectors. In contrast to the state-of-the-art tensor-based alternating least squares SVD (ALS-SVD) and modified alternating least squares SVD (MALS-SVD) matrix approximation methods, TNrSVD can be up to 13 times faster while achieving better accuracy. In addition, our TNrSVD algorithm also produces accurate approximations in particular cases where both ALS-SVD and MALS-SVD fail to converge. We also propose a new algorithm for the fast conversion of a sparse matrix into its corresponding MPO form, which is up to 509 times faster than the standard tensor train SVD method while achieving machine precision accuracy. The efficiency and accuracy of both algorithms are demonstrated in numerical experiments.

In spite of the differences in visual stimulus of human beings such as ageing, changing conditions of a person, and occlusion, recognition can even be done at a glance by the human eye many years after the previous encounter. It has been established that facial differences like the hairstyle changes, growing of one’s beard, wearing of glasses, and other forms of occlusions can hardly hinder the power of the human brain from making a face recognition. However, the same cannot easily be said about automated intelligent systems which have been developed to mimic the skill of the human brain to aid in recognition. There have been growing interests in developing a resilient and efficient recognition system mainly because of its numerous application areas (access control, entertainment/leisure, security system based on biometric data, and user-friendly human-machine interfaces). Although there have been numerous researches on face recognition under varying pose, illumination, expression, and image degradations, problems caused by occlusions are mostly ignored. This study thus focuses on facial occlusions and proposes an enhancement mechanism through face image augmentation to improve the recognition of occluded face images. This study assessed the performance of Principal Component Analysis with Singular Value Decomposition using Fast Fourier Transform (FFT-PCA/SVD) for preprocessing face recognition algorithm on face images with missingness and augmented face image database. It was found that the average recognition rates for the FFT-PCA/SVD algorithm were the same ( 90 % ) when face images with missingness and augmented face images were used as test images, respectively. The statistical evaluation revealed that there exists a significant difference in the average recognition distances for the face images with missingness and augmented face images when FFT-PCA/SVD is used for recognition. Augmented face images tend to have a relatively lower average recognition distance when used as test images. This finding is contrary to the equal performance assessment by the adopted numerical technique. The MICE algorithm is therefore recommended as a suitable imputation mechanism for enhancing/improving the performance of the face recognition system.

Although face recognition systems have wide application, they are vulnerable to presentation attack samples (fake samples). Therefore, a presentation attack detection (PAD) method is required to enhance the security level of face recognition systems. Most of the previously proposed PAD methods for face recognition systems have focused on using handcrafted image features, which are designed by expert knowledge of designers, such as Gabor filter, local binary pattern (LBP), local ternary pattern (LTP), and histogram of oriented gradients (HOG). As a result, the extracted features reflect limited aspects of the problem, yielding a detection accuracy that is low and varies with the characteristics of presentation attack face images. The deep learning method has been developed in the computer vision research community, which is proven to be suitable for automatically training a feature extractor that can be used to enhance the ability of handcrafted features. To overcome the limitations of previously proposed PAD methods, we propose a new PAD method that uses a combination of deep and handcrafted features extracted from the images by visible-light camera sensor. Our proposed method uses the convolutional neural network (CNN) method to extract deep image features and the multi-level local binary pattern (MLBP) method to extract skin detail features from face images to discriminate the real and presentation attack face images. By combining the two types of image features, we form a new type of image features, called hybrid features, which has stronger discrimination ability than single image features. Finally, we use the support vector machine (SVM) method to classify the image features into real or presentation attack class. Our experimental results indicate that our proposed method outperforms previous PAD methods by yielding the smallest error rates on the same image databases.

The technology of low-field nuclear magnetic resonance (LF-NMR) is commonly used in food, agriculture, energy and chemical sectors due to its non-destructive, non-invasive, in situ, green and other advantages. Recently, this technology played an increasingly large role in the field of food-safety supervision especially. In oil product quality testing, conventional T2 spectrum inversion methods such as the non-negative singular value decomposition (SVD) algorithm can only reflect T2 spectrum in a smooth model. However, for a sparse model, the inversion result of non-negative SVD algorithm is expected to be very glossy, leading to low resolution of T2 spectrum and inaccurate analysis of sample property. To solve this problem, we propose a sparse T2 spectrum inversion algorithm based on the L1 norm minimization constraint. In this paper, we establish the sparse model expression of NMR echo curve, and obtain the T2 sparse spectrum inversion results based on the inner truncated Newton-point method. Furthermore, the effectiveness of L1 sparse inversion algorithm is examined by the synthetic data of the smooth model and the spare model which have different peak numbers and signaltonoise ratios (SNRs). Synthetic results show that compared with the non-negative SVD algorithm, the L1 sparse algorithm is appropriate for both the smooth model and the sparse model with higher inversion accuracy. When the number of T2 peaks in a sparse model changes from a single peak to a quad peak, the L1 sparse algorithm can still obtain accurate inversion results, while the SVD algorithm results in a gradual deterioration, and cannot even determine the peak number. Under the sparse model, when the SNR of the measured NMR curve is gradually changed from 5 dB to 50 dB, the L1 sparse algorithm at 20 dB or more can obtain accurate inversion results which have less than 10% peak error and less than 5% peak position error and amplitude average error. However, the non-negative SVD algorithm cannot obtain accurate results at each SNR. Finally, multiple sets of frying oil samples are utilized to prove the accuracy and robustness of L1 sparse inversion algorithm. Inversion results of seven sets of frying oil samples show that the L1 sparse algorithm prefers the non-negative SVD algorithm. The obtained T2 spectrum by the L1 sparse algorithm shows three peaks obviously, and the T21 peak area ratio S21 and the single component relaxation time T2w are higher linear with respect to frying time than the results by non-negative SVD algorithm, which is useful for detecting the frying oil quality change. The inversion results of the T2 spectrum at different SNRs are consistent with the synthetic results, i.e., when the SNR is reduced, the T2 spectrum inversion results from the L1 sparse algorithm are better than those from the non-negative SVD algorithm when SNR is greater than 20 dB.

Computational complexity is a matter of great concern in real time face recognition systems. In this paper, four state hidden Markov model for face recognition has been presented whereby coefficients of feature vectors have been curtailed. Face images have been divided into a sequence of overlapping blocks. An observation sequence containing coefficients of eigen values and eigenvectors of these blocks have been used to train the model and each subject is associated with a separate hidden Markov model. The computational complexity of the proposed model has been minimized by employing discrete wavelet transform in the preprocessing stage. Furthermore, singular value decomposition has been employed on face images and a threshold singular value is determined empirically to reject or accept test images. Principal component analysis is used for feature extraction. Accepted test images are classified based on the majority vote criteria using different observation sequences of image features. Experimental findings on Yale and ORL databases in noisy such as Salt and Pepper and noise free environments reveal that the recognition accuracy of the proposed model is comparable to the existing techniques with reduced computational cost.