СИНГУЛЯРНОЕ РАЗЛОЖЕНИЕ МАТРИЦ В АНАЛИЗЕ ЦИФРОВЫХ ИЗОБРАЖЕНИЙ

The paper describes new properties of the singular matrix decomposition. It is shown that permutation of rows or columns of the matrix or matrix rotation by 90 degrees does not change the set of its singular numbers. However, variation the value of at least one matrix element or permutation of any two matrix elements leads to a modification of the whole set of the singular numbers. Examples of image sharpening and contrast enhancement by modification of the singular numbers are given.Описываются новые свойства сингулярных чисел, вычисляемых для матриц цифровых изо-бражений. Показано, что перестановка строк или столбцов матрицы и ее поворот на 90° не меняют множества сингулярных чисел, однако изменение значения одного элемента или перестановка местами двух элементов матрицы могут привести к изменению всего множества сингулярных чисел. Приводятся примеры повышения резкости и контраста изображений путем модификации множества сингулярных чисел

A perceptual quality metric for 3D triangle meshes based on spatial pooling

© 2018, Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature. In computer graphics, various processing operations are applied to 3D triangle meshes and these processes often involve distortions, which affect the visual quality of surface geometry. In this context, perceptual quality assessment of 3D triangle meshes has become a crucial issue. In this paper, we propose a new objective quality metric for assessing the visual difference between a reference mesh and a corresponding distorted mesh. Our analysis indicates that the overall quality of a distorted mesh is sensitive to the distortion distribution. The proposed metric is based on a spatial pooling strategy and statistical descriptors of the distortion distribution. We generate a perceptual distortion map for vertices in the reference mesh while taking into account the visual masking effect of the human visual system. The proposed metric extracts statistical descriptors from the distortion map as the feature vector to represent the overall mesh quality. With the feature vector as input, we adopt a support vector regression model to predict the mesh quality score.We validate the performance of our method with three publicly available databases, and the comparison with state-of-the-art metrics demonstrates the superiority of our method. Experimental results show that our proposed method achieves a high correlation between objective assessment and subjective scores

A deep evaluator for image retargeting quality by geometrical and contextual interaction

An image is compressed or stretched during the multidevice displaying, which will have a very big impact on perception quality. In order to solve this problem, a variety of image retargeting methods have been proposed for the retargeting process. However, how to evaluate the results of different image retargeting is a very critical issue. In various application systems, the subjective evaluation method cannot be applied on a large scale. So we put this problem in the accurate objective-quality evaluation. Currently, most of the image retargeting quality assessment algorithms use simple regression methods as the last step to obtain the evaluation result, which are not corresponding with the perception simulation in the human vision system (HVS). In this paper, a deep quality evaluator for image retargeting based on the segmented stacked AutoEnCoder (SAE) is proposed. Through the help of regularization, the designed deep learning framework can solve the overfitting problem. The main contributions in this framework are to simulate the perception of retargeted images in HVS. Especially, it trains two separated SAE models based on geometrical shape and content matching. Then, the weighting schemes can be used to combine the obtained scores from two models. Experimental results in three well-known databases show that our method can achieve better performance than traditional methods in evaluating different image retargeting results

No reference quality assessment of stereo video based on saliency and sparsity

With the popularity of video technology, stereoscopic video quality assessment (SVQA) has become increasingly important. Existing SVQA methods cannot achieve good performance because the videos' information is not fully utilized. In this paper, we consider various information in the videos together, construct a simple model to combine and analyze the diverse features, which is based on saliency and sparsity. First, we utilize the 3-D saliency map of sum map, which remains the basic information of stereoscopic video, as a valid tool to evaluate the videos' quality. Second, we use the sparse representation to decompose the sum map of 3-D saliency into coefficients, then calculate the features based on sparse coefficients to obtain the effective expression of videos' message. Next, in order to reduce the relevance between the features, we put them into stacked auto-encoder, mapping vectors to higher dimensional space, and adding the sparse restraint, then input them into support vector machine subsequently, and finally, get the quality assessment scores. Within that process, we take the advantage of saliency and sparsity to extract and simplify features. Through the later experiment, we can see the proposed method is fitting well with the subjective scores

Low-Rank Matrix Approximations with Flip-Flop Spectrum-Revealing QR Factorization

We present Flip-Flop Spectrum-Revealing QR (Flip-Flop SRQR) factorization, a significantly faster and more reliable variant of the QLP factorization of Stewart, for low-rank matrix approximations. Flip-Flop SRQR uses SRQR factorization to initialize a partial column pivoted QR factorization and then compute a partial LQ factorization. As observed by Stewart in his original QLP work, Flip-Flop SRQR tracks the exact singular values with "considerable fidelity". We develop singular value lower bounds and residual error upper bounds for Flip-Flop SRQR factorization. In situations where singular values of the input matrix decay relatively quickly, the low-rank approximation computed by SRQR is guaranteed to be as accurate as truncated SVD. We also perform a complexity analysis to show that for the same accuracy, Flip-Flop SRQR is faster than randomized subspace iteration for approximating the SVD, the standard method used in Matlab tensor toolbox. We also compare Flip-Flop SRQR with alternatives on two applications, tensor approximation and nuclear norm minimization, to demonstrate its efficiency and effectiveness