High-order sum-of-squares structured tensors:theory and applications

Tensor decomposition is an important research area with numerous applications in data mining and computational neuroscience.An important class of tensor decomposition is sum-of-squares(SOS)tensor decomposition.SOS tensor decomposition has a close connection with SOS polynomials,and SOS polynomials are very important in polynomial theory and polynomial optimization.In this paper,we give a detailed survey on recent advances of high-order SOS tensors and their applications.It first shows that several classes of symmetric structured tensors available in the literature have SOS decomposition in the even order symmetric case.Then,the SOS-rank for tensors with SOS decomposition and the SOS-width for SOS tensor cones are established.Further,a sharper explicit upper bound of the SOS-rank for tensors with bounded exponent is provided,and the exact SOS-width for the cone consists of all such tensors with SOS decomposition is identified.Some potential research directions in the future are also listed in this paper.

Contour tracking using weighted structure tensor based variational level set

A novel contour tracking method using weighted structure tensor based variational level set is proposed in this paper.The image is first converted to weighted structure tensor field by extracting apositive definite symmetric covariance matrix for each pixel.Then,a level set method is employed to represent object contour implicitly which separates the image domain into two areas each modeled by tensor field based Gaussian mixture model separately.By solving agradient flow equation of energy functional with respect to the level set,the object contour will converge to its real profile in the newly arrived frame.Experimental results on several video sequences demonstrate the better performance of our method than the other two contour tracking algorithms.

Application of 3D stereotomography to the deep-sea data acquired in the South China Sea:a tomography inversion case

A 3D stereotomography algorithm, which is derived from the 3D Cartesian coordinate, is applied for the first time to the deep-sea data acquired in the LH area, South China Sea, to invert a macro velocity model for pre-stack depth migration. The successful implementation of stereotomography is highly dependent on the correct extraction of slowness components and the proper application of regularization terms. With the help of the structure tensor algorithm, a high-quality 3D stereotomography data space is achieved in a very efficient manner. Then, considering that the horizontal slowness in cross-line direction is usually unavailable for 3D narrow-azimuth data, the regularization terms must be enhanced to guarantee a stable convergence of the presented algorithm. The inverted model serves as a good model for the 3D pre-stack depth migration. The synthetic and real data examples demonstrated the robustness and effectiveness of the presented algorithm and the related schemes.

A Convolutional Neural Network Classifier VGG-19 Architecture for Lesion Detection and Grading in Diabetic Retinopathy Based on Deep Learning

Diabetic Retinopathy(DR)is a type of disease in eyes as a result of a diabetic condition that ends up damaging the retina,leading to blindness or loss of vision.Morphological and physiological retinal variations involving slowdown of blood flow in the retina,elevation of leukocyte cohesion,basement membrane dystrophy,and decline of pericyte cells,develop.As DR in its initial stage has no symptoms,early detection and automated diagnosis can prevent further visual damage.In this research,using a Deep Neural Network(DNN),segmentation methods are proposed to detect the retinal defects such as exudates,hemorrhages,microaneurysms from digital fundus images and then the conditions are classified accurately to identify the grades as mild,moderate,severe,no PDR,PDR in DR.Initially,saliency detection is applied on color images to detect maximum salient foreground objects from the background.Next,structure tensor is applied powerfully to enhance the local patterns of edge elements and intensity changes that occur on edges of the object.Finally,active contours approximation is performed using gradient descent to segment the lesions from the images.Afterwards,the output images from the proposed segmentation process are subjected to evaluate the ratio between the total contour area and the total true contour arc length to label the classes as mild,moderate,severe,No PDR and PDR.Based on the computed ratio obtained from segmented images,the severity levels were identified.Meanwhile,statistical parameters like the mean and the standard deviation of pixel intensities,mean of hue,saturation and deviation clustering,are estimated through K-means,which are computed as features from the output images of the proposed segmentation process.Using these derived feature sets as input to the classifier,the classification of DR was performed.Finally,a VGG-19 deep neural network was trained and tested using the derived feature sets from the KAGGLE fundus image dataset containing 35,126 images in total.The VGG-19 is trained with features extracted from 20,000 images and tested with features extracted from 5,000 images to achieve a sensitivity of 82%and an accuracy of 96%.The proposed system was able to label and classify DR grades automatically.

Study of formation boundary and dip attribute extraction based on edge detection technology

In the seismic profile interpretation process,as the seismic data are big and the small geological features are difficult to identify,improvement of the efficiency is needed. In this study,structure tensor method in computer image edge detection processing is applied into the 2D seismic profile. Coherent attribute is used to extract formation edge. At the same time,extracting the eigenvalues and eigenvectors to calculate the seismic geometric properties which include dip and apparent dip,automatic identification is achieved. Testing the Gaussian kernel function with synthetic models and comparing the coherent attribute and dip attribute extraction results before and after,the conclusion that Gaussian filter can remove the random noise is obtained.

The Generalized Order Tensor Complementarity Problems

The main propose of this paper is devoted to study the solvability of the generalized order tensor complementarity problem.We define two problems:the generalized order tensor complementarity problem and the vertical tensor comple-mentarity problem and show that the former is equivalent to the latter.Using the degree theory,we present a comprehensive analysis of existence,uniqueness and stability of the solution set of a given generalized order tensor complementarity problem.

A novel dense descriptor based on structure tensor voting for multi-modal image matching

Automatic and robust matching of multi-modal images can be challenging owing to the nonlinear intensity differences caused by radiometric variations among these images.To address this problem,a novel dense feature descriptor and improved similarity measure are proposed for enhancing the matching performance.The proposed descriptor is built on a voting scheme of structure tensor that can effectively capture the geometric structural properties of images.It is not only illumination and contrast invariant but also robust against the degradation caused by significant noise.Further,the similarity measure is improved to adapt to the reversal of orientation caused by the intensity inversion between multi-modal images.The proposed dense feature descriptor and improved similarity measure enable the development of a robust and practical templatematching algorithm for multi-modal images.We verify the proposed algorithm with a broad range of multi-modal images including optical,infrared,Synthetic Aperture Radar(SAR),digital surface model,and map data.The experimental results confirm its superiority to the state-of-the-art methods.

GrabCut image segmentation algorithm based on structure tensor

This paper attempts to present an interactive color natural images segmentation method. This method extracts the feature of images by using the nonlinear compact structure tensor （NCST） and then uses GrabCut method to obtain the segmentation. This method not only realizes the non-parametric fusion of texture information and color information, but also improves the efficiency of the calculation. Then, the improved GrabCut algorithm is used to evaluate the foreground target segmentation. In order to calculate the simplicity and efficiency, this paper also extends the Gaussian mixture model （GMM） constructed base on the GrabCut to the tensor space, and uses the Kullback-Leibler （KL） divergence instead of the usual Riemannian geometry. Lastly, an iteration convergence criterion is proposed to reduce the time of the iteration of GrabCut algorithm dramatically with satisfied segmentation accuracy. After conducting a large number of experiments on synthetic texture images and natural images, the results demonstrate that this method has a more accurate segmentation effect.

Image Inpainting Based on Structural Tensor Edge Intensity Model

In the exemplar-based image inpainting approach,there are usually two major problems:the unreasonable calculation of priority and only considering the color features in the patch lookup strategy.In this paper,we propose an image inpainting approach based on the structural tensor edge intensity model.First,we use the progressive scanning inpainting method to avoid the image filling order being affected by the priority function.Then,we use the edge intensity model to build the patches similarity function for correctly identifying the local image structure.Finally,the balance operator is used to restrict the excessive propagation of structural information to ensure the correct structural reconstruction.The experimental results show that the our approach is comparable and even superior to some state-of-the-art inpainting algorithms.

Airframe Damage Region Division Method Based on Structure Tensor Dynamic Operator

In order to improve the accuracy of damage region division and eliminate the interference of damage adjacent region,the airframe damage region division method based on the structure tensor dynamic operator is proposed in this paper.The structure tensor feature space is established to represent the local features of damage images.It makes different damage images have the same feature distribution,and transform varied damage region division into consistent process of feature space division.On this basis,the structure tensor dynamic operator generation method is designed.It integrates with bacteria foraging optimization algorithm improved by defining double fitness function and chemotaxis rules,in order to calculate the parameters of dynamic operator generation method and realize the structure tensor feature space division.And then the airframe damage region division is realized.The experimental results on different airframe structure damage images show that compared with traditional threshold division method,the proposed method can improve the division quality.The interference of damage adjacent region is eliminated.The information loss caused by over-segmentation is avoided.And it is efficient in operation,and consistent in process.It also has the applicability to different types of structural damage.

Massively efficient filter for topology optimization based on the splitting of tensor product structure

In this work,we put forward a massively efficient filter for topology optimization(TO)utilizing the splitting of tensor product structure.With the aid of splitting technique,the traditional weight matrices of B-splines and non-uniform rational B-spline implicit filters are decomposed equivalently into two or three submatrices,by which the sensitivity analysis is reformulated for the nodal design variables without altering the optimization process.Afterwards,an explicit sensitivity filter,which is decomposed by the splitting pipeline as that applied to implicit filter,is established in terms of the tensor product of the axial distances between adjacent element centroids,and the corresponding sensitivity analysis is derived for elemental design variables.According to the numerical results,the average updating time for the design variables is accelerated by two-order-of-magnitude for the decomposed filter compared with the traditional filter.In addition,the memory burden and computing time of the weight matrix are decreased by six-and three-order-of-magnitude for the decomposed filter.Therefore,the proposed filter is massively improved by the splitting of tensor product structure and delivers a much more efficient way of solving TO problems in the frameworks of isogeometric analysis and finite element analysis.

ACTIVE CONTOUR BASED ON 3D STRUCTURE TENSOR APPLIED IN MEDICAL IMAGE SEGMENTATION

The paper presents an improved tensor-based active contour model in a variational level set formulation for medical image segmentation. In it, a new energy function is defined with a local intensity fitting term in intensity inhomogeneity of the image, and with a global intensity fitting term in intensity homogeneity domain. Weighting factor is chosen to balance these two intensity fitting terms, which can be calculated automatically by local entropy. The level set regularization term is to replace contour curve to find the minimum of the energy function. Particularly, structure tensor is applied to describe the image, which overcomes the disadvantage of image feature without structure information.The experimental results show that our proposed method can segment image efficiently whether it presents intensity inhomogeneity or not and wherever the initial contour is. Moreover, compared with the Chan-Vese model and local binary fitting model, our proposed model not only handles better intensity inhomogeneity, but also is less sensitive to the location of initial contour.

Candidate Biomarkers in Children with Autism Spectrum Disorder: A Review of MRI Studies

Searching for effective biomarkers is one of the most challenging tasks in the research ？eld of Autism Spectrum Disorder（ASD）. Magnetic resonance imaging（MRI） provides a non-invasive and powerful tool for investigating changes in the structure, function, maturation,connectivity, and metabolism of the brain of children with ASD. Here, we review the more recent MRI studies in young children with ASD, aiming to provide candidate biomarkers for the diagnosis of childhood ASD. The review covers structural imaging methods, diffusion tensor imaging, resting-state functional MRI, and magnetic resonance spectroscopy. Future advances in neuroimaging techniques, as well as cross-disciplinary studies and largescale collaborations will be needed for an integrated approach linking neuroimaging, genetics, and phenotypic data to allow the discovery of new, effective biomarkers.

Quantum correlations relativity for continuous variable systems

It is shown that a choice of degrees of freedom of a bipartite continuous variable system determines the amount of non-classical correlations (quantified by discord) in the system's state. Non-classical correlations (that include entanglement as a special kind of correlations) are ubiquitous for such systems. For a quantum state, if there are not non-classical correlations (quantum discord is zero) for one, there are in general non-classical correlations (quantum discord is non-zero) for another set of the composite system's degrees of freedom. The physical relevance of this "quantum correlations relativity" is emphasized also in the more general context.

Can multi-modal neuroimaging evidence from hippocampus provide biomarkers for the progression of amnestic mild cognitive impairment?

Impaired structure and function of the hippocampus is a valuable predictor of progression from amnestic mild cognitive impairment（a MCI） to Alzheimer＇s disease（AD）. As a part of the medial temporal lobe memory system,the hippocampus is one of the brain regions affected earliest by AD neuropathology,and shows progressive degeneration as a MCI progresses to AD. Currently,no validated biomarkers can precisely predict the conversion from a MCI to AD. Therefore,there is a great need of sensitive tools for the early detection of AD progression. In this review,we summarize the specifi c structural and functional changes in the hippocampus from recent a MCI studies using neurophysiological and neuroimaging data. We suggest that a combination of advanced multi-modal neuroimaging measures in discovering biomarkers will provide more precise and sensitive measures of hippocampal changes than using only one of them. These will potentially affect early diagnosis and disease-modifying treatments. We propose a new sequential and progressive framework in which the impairment spreads from the integrity of fibers to volume and then to function in hippocampal subregions. Meanwhile,this is likely to be accompanied by progressive impairment of behavioral and neuropsychological performance in the progression of a MCI to AD.

Real-Time Image and Video Artistic Style Rendering System Based on GPU

Aiming at the practical engineering application of video stylization,in this paper, a GPU-based video art stylization algorithm is proposed, and areal-time video art stylization rendering system is implemented. The four mostcommon artistic styles including cartoon, oil painting, pencil painting and watercolorpainting are realized in this system rapidly. Moreover, the system makesgood use of the GPU’s parallel computing characteristics, transforms the videostylized rendering algorithm into the texture image rendering process, acceleratesthe time-consuming pixel traversal processing in parallel and avoids the loop processingof the traditional CPU. Experiments show that the four art styles achievedgood results, and the system has a good interactive experience.