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Recently, many state-of-the-art results for remote sensing image scene classification have been achieved by convolutional neural networks (CNNs) due to their large learning capability. However, in the forward process of CNNs, the high-frequency/texture features are gradually blurred with hierarchical downsampling and convolution operations. High-frequency features are important to capture the diversity within a class and the similarity between classes. For example, the line features are crucial to distinguish a tennis court from a basketball court. For tennis court in different scenes, the highlight of line features can effectively avoid the influence of diverse backgrounds. As a consequence, we propose a Laplacian high-frequency convolutional block (LHCB) based on CNN to extract useful high-frequency features by trainable Laplacian operator. To propagate high-frequency features, we embed LHCB into the existing CNN structures and obtain LHNet. In LHNet, there are two pathways. The original CNN architecture can be taken as the low-frequency pathway, and we propose a high-frequency pathway (HFP) based on LHCB that propagates the residual high-frequency features blurred in each low-frequency layer. Considering that the high-frequency features usually show large variance between images of the same class, we propose a new objective for HFP to enhance the intraclass similarity of high-frequency features. The final objective function is obtained by combining the new objective and the baseline classification objective. Numerous experiments on three public available remote sensing image scene classification datasets, the Northwestern Polytechnical University-Remote Sensing Image Scene Classification (NWPU-RESISC45), Aerial Image Dataset (AID), and the University of California at Merced (UC Merced), demonstrate the superior performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this work, we find that the matrix representing the curl–curl operator in a partial differential equation solver of Maxwell’s equations can be analytically decomposed into a gradient divergence operator and a Laplacian, both of which can be constructed from the mesh information without any need for computation. The curl–curl operator can hence be replaced by the Laplacian to find the divergence-free component of the field solution. The Laplacian is positive definite and well-conditioned. As a result, the convergence of an iterative solution of Maxwell’s equations can be guaranteed, and also significantly accelerated. Based on the finding, we represent the divergence-free component of the unknown field solution by deducting its curl-free component. The curl-free component resides in the nullspace of the curl–curl operator, which is also analytically known from the mesh information no matter it is a regular grid or an unstructured mesh. After the divergence-free component is rapidly solved from a Laplacian counterpart of the original system matrix, the curl-free component can also be solved from a Laplacian matrix, and hence having fast and guaranteed convergence. The total computational cost of the proposed method is simply a small number of sparse matrix-vector multiplications. The proposed method has been successfully applied to solve ill-conditioned on-chip, packaging, and antenna radiation problems at both low and high frequencies, involving both inhomogeneous dielectrics and lossy conductors. Numerical experiments have demonstrated its fast and guaranteed convergence, as well as trivial computational cost independent of problem size. [ABSTRACT FROM AUTHOR]

The unsplit complex frequency-shifted perfectly matched layer (CFS-PML) has been widely used in the first-order wave equation in velocity and stress while rarely formulated for the wave equation recast as a second-order system in displacement. Among different variants of PML, the unsplit CFS-PML for the second-order wave equation enjoys better absorbing performance and numerical stability, compared to the traditional PML, due to the presence of the general form of CFS stretching factors, as well as higher computational efficiency over the split PMLs since it avoids wave equation order reduction and splitting the state variables into multiple directional components. This study aims to develop an unsplit CFS-PML scheme for the second-order wave equation and devote specific attention to fractional viscoacoustic simulation where fractional time derivatives are involved and hard to be reformulated into a first-order form. In the complex space, PML is typically regarded as an analytical continuation of the real coordinates; thus, we define an explicit coordinate stretching operator acting on the Laplacian operator. This stretching operator consists of several convolution terms; each of them can be efficiently resolved by a recursive convolution updating strategy. Viscoacoustic simulations on homogeneous Pierre Shale, Marmousi model, and 3-D SEG/EAGE overthrust model verify the feasibility and absorbing the performance of our proposed scheme. [ABSTRACT FROM AUTHOR]

The ill-conditioned numerical system arising from an electromagnetic analysis is often due to the discretized curl–curl operator which has both zero eigenvalues and large ones inversely proportional to the square of the smallest feature size. In this work, we analytically decompose the discretized curl–curl operator into a gradient divergence operator and a Laplacian without numerical computation. We further split the field solution into a gradient field (curl-free component) and a divergence-free one to take advantage of the decomposition. The gradient divergence operator vanishes when acting on the divergence-free component of the field solution. As a result, we can replace the highly ill-conditioned curl–curl operator with a Laplacian for computing the divergence-free component regardless of inhomogeneity and source settings. Since the Laplacian is positive definite and well-conditioned, the new system matrix can converge quickly in a small number of iterations. The method is applied to accelerate time-domain solutions of Maxwell’s equations in ill-conditioned problems such as integrated circuits (ICs). Numerical results have validated its accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated computational tools whose performance strongly depends on how good the training data reflect a sought image pattern. Moreover, poor adherence to the image contours, lack of unique solution, and high computational cost are other common issues present in most seeded segmentation methods. In this work we introduce Laplacian Coordinates, a quadratic energy minimization framework that tackles the issues above in an effective and mathematically sound manner. The proposed formulation builds upon graph Laplacian operators, quadratic energy functions, and fast minimization schemes to produce highly accurate segmentations. Moreover, the presented energy functions are not prone to local minima, i.e., the solution is guaranteed to be globally optimal, a trait not present in most image segmentation methods. Another key property is that the minimization procedure leads to a constrained sparse linear system of equations, enabling the segmentation of high-resolution images at interactive rates. The effectiveness of Laplacian Coordinates is attested by a comprehensive set of comparisons involving nine state-of-the-art methods and several benchmarks extensively used in the image segmentation literature. [ABSTRACT FROM AUTHOR]

In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (s $\boldsymbol {\alpha }\text{s}$) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as s $\boldsymbol {\alpha }\text{s}$ distribution. We applied fractional Laplacian operator to image and fitted s $\boldsymbol {\alpha }\text{s}$ to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled s $\boldsymbol {\alpha }\text{s}$ distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities. [ABSTRACT FROM AUTHOR]

This paper tackles the problem of millimeter-wave (mmWave) channel estimation in massive MIMO communication systems. A new Bayes-optimal channel estimator is derived using recent advances in the approximate belief propagation Bayesian inference paradigm. By leveraging the inherent sparsity of the mmWave MIMO channel in the angular domain, we recast the underlying channel estimation problem into that of reconstructing a compressible signal from a set of noisy linear measurements. Then, the generalized approximate message passing (GAMP) algorithm is used to find the entries of the unknown mmWave MIMO channel matrix. Unlike all the existing works on the same topic, we model the angular-domain channel coefficients by Laplacian distributed random variables. Furthermore, we establish the closed-form expressions for the various statistical quantities that need to be updated iteratively by GAMP. To render the proposed algorithm fully automated, we also develop an expectation-maximization (EM) based procedure that can be easily embedded within GAMP’s iteration loop in order to learn all the unknown parameters of the underlying Bayesian inference problem. The computer simulations show that the proposed combined EM-GAMP algorithm under a Laplacian prior exhibits improvements both in terms of channel estimation accuracy, achievable rate, and computational complexity, as compared to the Gaussian mixture prior that has been advocated in the recent literature. In addition, it is found that the Laplacian prior speeds up the convergence time of GAMP over the entire signal-to-noise ratio range. [ABSTRACT FROM AUTHOR]

Spectral unmixing (SU) methods incorporating the spatial regularizations have demonstrated increasing interest. Although spatial regularizers that promote smoothness of the abundance maps have been widely used, they may overly smooth these maps and, in particular, may not preserve edges present in the hyperspectral image. Existing unmixing methods usually ignore these edge structures or use edge information derived from the hyperspectral image itself. However, this information may be affected by the large amounts of noise or variations in illumination, leading to erroneous spatial information incorporated into the unmixing procedure. This paper proposes a simple yet powerful SU framework that incorporates external data [i.e. light detection and ranging (LiDAR) data]. The LiDAR measurements can be easily exploited to adjust the standard spatial regularizations applied to the unmixing process. The proposed framework is rigorously evaluated using two simulated data sets and a real hyperspectral image. It is compared with methods that rely on spatial information derived from a hyperspectral image. The results show that the proposed framework can provide better abundance estimates and, more specifically, can significantly improve the abundance estimates for the pixels affected by shadows. [ABSTRACT FROM AUTHOR]

The image of secondary arc, which is a common phenomenon in ultrahigh voltage power system, contains a wealthy of information. To determine its geometrical characteristics, the secondary arc image is systematically processed involving gray scale, noise filtering, and image segmentation. To overcome the discontinuous and false edge caused by conventional operators, an improved algorithm is employed; the unrelated edges are fully removed, and the interrupted endpoints are dilated. Based on the results, the component and evolution of secondary arc are discussed; the correlation of the arc luminance and arc current is revealed. Occasionally, the arc roots and arc column have irregular motion behavior. Using the edge-detection technique, the detailed jumping location and velocity of anode arc root are tracked; the life expectancy and stability of coexistence of multicathode arc roots are determined; the morphology of short circuit of arc column is ascertained. Furthermore, the secondary arc dimension is estimated in this paper, including the arc radius and arc length. A number of formulas have been presented to predict the dimension. The obtained results are more accuracy than previous works. [ABSTRACT FROM AUTHOR]

Multisatellite measurements of altimeter-derived sea surface height (SSH) have provided a wealth of information on the ocean. Yet, horizontal scales below 100 km remain scarcely resolved. Especially, in the Mediterranean Sea, an important fraction of the mesoscale range, characterized by a small Rossby radius of deformation of 15–20 km, is not properly retrieved by altimeter-derived gridded products. Here, we investigate a novel processing of AVISO products with a view to resolving the horizontal scales sensed by current along-track altimeter data. The key feature of our framework is the use of linear convolutional operators to model the fine-scale SSH detail as a function of different sea surface fields, especially optimally interpolated SSH and sea surface temperature (SST). The proposed model embeds the surface quasi-geostrophic SST–SSH synergy as a special case. Using an observing system simulation experiment with simulated SSH data from model outputs in the Western Mediterranean Sea, we show that the proposed approach has the potential for improving current optimal interpolations of gridded altimeter-derived SSH fields by more than 20% in terms of relative SSH and kinetic energy mean square error, as well as in terms of spectral signatures for horizontal scales ranging from 30 to 100 km. Our results also suggest that SST–SSH relationship may only play a secondary role compared with the interscale SSH cascade. We further discuss the relevance of the proposed approach in the context of future altimetric satellite missions. [ABSTRACT FROM AUTHOR]

In this paper, to solve nonlinear optimal control problems which can be modeled as Markov decision processes (MDPs), we present an online self-learning control algorithm called dual heuristic programming with global Laplacian Eigenmaps (GLEM-DHP). The GLEM-DHP algorithm makes use of GLEM, which is an improved manifold learning approach with global information, to learn the features for value function approximation of the MDP. Different from traditional feature representation methods using neural networks, the manifold-based features can be learned before the online learning process by collecting samples from the MDP. More importantly, in addition to local features, global information can also be utilized by using the geodesic minimum spanning tree (GMST) approach. Based on the theoretical property of GMST, it is shown that the GLEM-based features can represent the intrinsic geometric property of MDP states, which is beneficial to improve the performance of value function approximation and, hence, leads to better learning control properties. To compare the proposed method with previous learning control algorithms, the performance of GLEM-DHP is evaluated on two nonlinear control problems, which include the cart-pole problem and the ball-plate control problem. Simulation and experimental results show that the GLEM-DHP algorithm can obtain better learning control performance than previous learning control algorithms with manually designed features, as well as manifold features only with local information. [ABSTRACT FROM AUTHOR]

Visual tracking is complicated due to factors, such as occlusion, background clutter, abrupt target motion, and illumination variations, among others. In recent years, subspace representation and sparse coding techniques have demonstrated significant improvements in tracking. However, performance gain in tracking has been at the expense of losing locality and similarity attributes among the instances to be encoded. In this paper, a graph regularized and locality-constrained coding (GRLC) technique that encapsulates local manifold structure of the data in order to preserve locality and similarity information among instances is proposed. The GRLC methodology incorporates a similarity-preserving term within the objective function of the locality-constrained linear coding model, thereby overcoming some of the inherent instability issues common to such coding methods. In the proposed GRLC scheme, a graph Laplacian regularizer is chosen as a smoothing operator to learn both the representation dictionary and the coefficients by preserving the local structure of the data. This graph Laplacian smoothing operator ensures that the representations vary smoothly along the geodesics of the data manifold. Thus, by deriving the objective function of the GRLC method, a discriminative dictionary of instances can be iteratively obtained and the corresponding coefficients for each candidate can be computed using this learned dictionary. Finally, an effective observation likelihood function based on reconstruction error and a simple dictionary update scheme for visual target tracking are also proposed. Experimental results on the CVPR2013 visual tracker benchmark have demonstrated a favorable performance of the proposed technique both in terms of accuracy and robustness. [ABSTRACT FROM PUBLISHER]

Objective: We propose two electrocardiogram (ECG)-derived markers of T-wave morphological variability in the temporal, d_w, and amplitude, d_a, domains. Two additional markers, d_w^\mathrmNL and d_a^\mathrmNL, restricted to measure the nonlinear information present within d_w and d_a are also proposed. Methods: We evaluated the accuracy of the proposed markers in capturing T-wave time and amplitude variations in 3 situations: 1) In a simulated set up with presence of additive Laplacian noise, 2) when modifying the spatio-temporal distribution of electrical repolarization with an electro-physiological cardiac model, and 3) in ECG records from healthy subjects undergoing a tilt table test. Results: The metrics d_w, d_a , and d_a^{\mathrm{NL}} followed T-wave time- and amplitude-induced variations under different levels of noise, were strongly associated with changes in the spatio-temporal dispersion of repolarization, and showed to provide additional information to differences in the heart rate, QT$ and T_{\mathrm{pe}} intervals, and in the T-wave width and amplitude. Conclusion: The proposed ECG-derived markers robustly quantify T-wave morphological variability, being strongly associated with changes in the dispersion of repolarization. Significance: The proposed ECG-derived markers can help to quantify the variability in the dispersion of ventricular repolarization, showing a great potential to be used as arrhythmic risk predictors in clinical situations. [ABSTRACT FROM AUTHOR]

Efficient and accurate detection of cell nuclei is an important step toward automatic analysis in histopathology. In this work, we present an automatic technique based on generalized Laplacian of Gaussian (gLoG) filter for nuclei detection in digitized histological images. The proposed technique first generates a bank of gLoG kernels with different scales and orientations and then performs convolution between directional gLoG kernels and the candidate image to obtain a set of response maps. The local maxima of response maps are detected and clustered into different groups by mean-shift algorithm based on their geometrical closeness. The point which has the maximum response in each group is finally selected as the nucleus seed. Experimental results on two datasets show that the proposed technique provides a superior performance in nuclei detection compared to existing techniques. [ABSTRACT FROM AUTHOR]

This paper studies the problem of object tracking in challenging scenarios by leveraging multimodal visual data. We propose a grayscale-thermal object tracking method in Bayesian filtering framework based on multitask Laplacian sparse representation. Given one bounding box, we extract a set of overlapping local patches within it, and pursue the multitask joint sparse representation for grayscale and thermal modalities. Then, the representation coefficients of the two modalities are concatenated into a vector to represent the feature of the bounding box. Moreover, the similarity between each patch pair is deployed to refine their representation coefficients in the sparse representation, which can be formulated as the Laplacian sparse representation. We also incorporate the modal reliability into the Laplacian sparse representation to achieve an adaptive fusion of different source data. Experiments on two grayscale-thermal datasets suggest that the proposed approach outperforms both grayscale and grayscale-thermal tracking approaches. [ABSTRACT FROM AUTHOR]

Pansharpened images are widely used synthetic representations of the Earth surface characterized by both a high spatial resolution and a high spectral diversity. They are usually generated by extracting spatial details from a high-resolution PANchromatic image and by injecting them into a low spatial resolution multispectral image. The details injection is performed through injection coefficients, whose values can be either uniform for the whole image (global methods) or spatially variant (context-adaptive (CA) approaches). In this paper, we propose a CA approach in which the injection coefficients are estimated over image segments achieved through a binary partition tree segmentation algorithm. The approach is applied to two credited pansharpening algorithms based on the Gram–Schmidt orthogonalization procedure and the generalized Laplacian pyramid technique. The performance assessment is performed using two different data sets acquired by the QuickBird and the WorldView-3 satellites. The validation procedure, both at full and at reduced resolution, shows the suitability of the proposed approach, which reaches a good tradeoff between accuracy and computational burden. [ABSTRACT FROM PUBLISHER]

Effective feature selection plays a vital role in anterior segment imaging for determining the mechanism involved in angle-closure glaucoma (ACG) diagnosis. This research focuses on the use of redundant features for complex disease diagnosis such as ACG using anterior segment optical coherence tomography images. Both supervised [minimum redundancy maximum relevance (MRMR)] and unsupervised [Laplacian score (L-score)] feature selection algorithms have been cross-examined with different ACG mechanisms. An AdaBoost machine learning classifier is then used for classifying the five various classes of ACG mechanism such as iris roll, lens, pupil block, plateau iris, and no mechanism using both feature selection methods. The overall accuracy has shown that the usefulness of redundant features by L-score method in improved ACG diagnosis compared to minimum redundant features by MRMR method. [ABSTRACT FROM PUBLISHER]

Scale-space behavior of corners is important for developing an efficient corner detection algorithm. In this paper, we analyze the scale-space behavior with the Laplacian of Gaussian (LoG) operator on a planar curve which constructs Laplacian Scale Space (LSS). The analytical expression of a Laplacian Scale-Space map (LSS map) is obtained, demonstrating the Laplacian Scale-Space behavior of the planar curve corners, based on a newly defined unified corner model. With this formula, some Laplacian Scale-Space behavior is summarized. Although LSS demonstrates some similarities to Curvature Scale Space (CSS), there are still some differences. First, no new extreme points are generated in the LSS. Second, the behavior of different cases of a corner model is consistent and simple. This makes it easy to trace the corner in a scale space. At last, the behavior of LSS is verified in an experiment on a digital curve. [ABSTRACT FROM PUBLISHER]

Polyhedral meshes (PM)—meshes having planar faces—have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate. Previous methods start with a smooth surface and then apply elaborate meshing schemes to create polyhedral meshes approximating the surface. In this paper, we describe a reverse approach: given the topology of a mesh, we explore the space of possible planar meshes having that topology. Our approach is based on a complete characterization of the maximal linear spaces of polyhedral meshes contained in the curved manifold of polyhedral meshes with a given topology. We show that these linear spaces can be described as nullspaces of differential operators, much like harmonic functions are nullspaces of the Laplacian operator. An analysis of this operator provides tools for global and local design of a polyhedral mesh, which fully expose the geometric possibilities and limitations of the given topology. [ABSTRACT FROM AUTHOR]

We present a semisupervised method for single-pixel classification of hyperspectral images. The proposed method is designed to address the special problematic characteristics of hyperspectral images, namely, high dimensionality of hyperspectral pixels, lack of labeled samples, and spatial variability of spectral signatures. To alleviate these problems, the proposed method features the following components. First, being a semisupervised approach, it exploits the wealth of unlabeled samples in the image by evaluating the confidence probability of the predicted labels, for each unlabeled sample. Second, we propose to jointly optimize the classifier parameters and the dictionary atoms by a task-driven formulation, to ensure that the learned features (sparse codes) are optimal for the trained classifier. Finally, it incorporates spatial information through adding a Laplacian smoothness regularization to the output of the classifier, rather than the sparse codes, making the spatial constraint more flexible. The proposed method is compared with a few comparable methods for classification of several popular data sets, and it produces significantly better classification results. [ABSTRACT FROM PUBLISHER]

In this paper, we study transmission of a memoryless Laplacian source over three types of channels: additive white Laplacian noise (AWLN), additive white Gaussian noise (AWGN), and slow flat-fading Rayleigh channels under both bandwidth compression and bandwidth expansion. For this purpose, we analyze two well-known hybrid digital–analog (HDA) joint source–channel coding schemes for bandwidth compression and one for bandwidth expansion. Then we obtain achievable (absolute-error) distortion regions of the HDA schemes for the matched signal-to-noise ratio (SNR) case as well as the mismatched SNR scenario. Using numerical examples, it is shown that these schemes can achieve a distortion very close to the provided lower bound (for the AWLN channel) and to the optimum performance theoretically attainable bound (for AWGN and Rayleigh fading channels) on mean-absolute error distortion under matched SNR conditions. In addition, a non-linear analog coding scheme is analyzed, and its performance is compared to the HDA schemes for bandwidth compression under both matched and mismatched SNR scenarios. The results show that the HDA schemes outperform the non-linear analog coding over the whole CSNR region. [ABSTRACT FROM AUTHOR]

One of the important tasks for bridge maintenance is bridge deck crack inspection. Traditionally, a human inspector detects cracks using his/her eyes and marks the location of cracks manually. However, the accuracy of the inspection result is low due to the subjective nature of human judgement. We propose a crack inspection system that uses a camera-equipped mobile robot to collect images on the bridge deck. In this method, the Laplacian of Gaussian (LoG) algorithm is used to detect cracks and a global crack map is obtained through camera calibration and robot localization. To ensure that the robot collects all the images on the bridge deck, a path planning algorithm based on the genetic algorithm is developed. The path planning algorithm finds a solution which minimizes the number of turns and the traveling distance. We validate our proposed system through both simulations and experiments. [ABSTRACT FROM PUBLISHER]

Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In recent years, significant attention has been devoted to descriptors obtained from the spectral decomposition of the Laplace-Beltrami operator associated with the shape. Notable examples in this family are the heat kernel signature (HKS) and the recently introduced wave kernel signature (WKS). The Laplacian-based descriptors achieve state-of-the-art performance in numerous shape analysis tasks; they are computationally efficient, isometry-invariant by construction, and can gracefully cope with a variety of transformations. In this paper, we formulate a generic family of parametric spectral descriptors. We argue that to be optimized for a specific task, the descriptor should take into account the statistics of the corpus of shapes to which it is applied (the "signal") and those of the class of transformations to which it is made insensitive (the "noise"). While such statistics are hard to model axiomatically, they can be learned from examples. Following the spirit of the Wiener filter in signal processing, we show a learning scheme for the construction of optimized spectral descriptors and relate it to Mahalanobis metric learning. The superiority of the proposed approach in generating correspondences is demonstrated on synthetic and scanned human figures. We also show that the learned descriptors are robust enough to be learned on synthetic data and transferred successfully to scanned shapes. [ABSTRACT FROM AUTHOR]

Hodge theory provides a unifying view of the various line, surface, and volume integrals that appear in physics and engineering applications. Hodge theory on graphs develops discrete versions of the differential forms found in the continuous theory and enables a graph decomposition into gradient, solenoidal, and harmonic components. Interpreted via similarity to gradient, curl, and Laplacian operators on vector fields, these components are useful in solving certain ranking and approximations problems that arise naturally in a graph context. This tutorial develops the rudiments of discrete Hodge theory and provides several example applications. [ABSTRACT FROM AUTHOR]

The slow wave activity was measured in the magnetoenterogram (MENG) of normal porcine subjects ( N = 5) with segmental intestinal ischemia. The correlation changes in enteric slow wave activity were determined in MENG and serosal electromyograms (EMG). MENG recordings show significant changes in the frequency and power distribution of enteric slow-wave signals during segmental ischemia, and these changes agree with changes observed in the serosal EMG. There was a high degree of correlation between the frequency of the electrical activity recorded in MENG and in serosal EMG (r = \0.97). The percentage of power distributed in brady- and normoenteric frequency ranges exhibited significant segmental ischemic changes. Our results suggest that noninvasive MENG detects ischemic changes in isolated small bowel segments. [ABSTRACT FROM PUBLISHER]

The objective of this paper was to investigate the effects of surface Laplacian processing on gross and persistent electromyographic (EMG) contamination of electroencephalographic (EEG) signals in electrical scalp recordings. We made scalp recordings during passive and active tasks, on awake subjects in the absence and in the presence of complete neuromuscular blockade. Three scalp surface Laplacian estimators were compared to left ear and common average reference (CAR). Contamination was quantified by comparing power after paralysis (brain signal, B) with power before paralysis (brain plus muscle signal, B+M). Brain:Muscle (B:M) ratios for the methods were calculated using B and differences in power after paralysis to represent muscle (M). There were very small power differences after paralysis up to 600 Hz using surface Laplacian transforms (B:M > 6 above 30 Hz in central scalp leads). Scalp surface Laplacian transforms reduce muscle power in central and pericentral leads to less than one sixth of the brain signal, two to three times better signal detection than CAR. Scalp surface Laplacian transformations provide robust estimates for detecting high-frequency (gamma) activity, for assessing electrophysiological correlates of disease, and also for providing a measure of brain electrical activity for use as a standard in the development of brain/muscle signal separation methods. [ABSTRACT FROM PUBLISHER]

Sparse coding exhibits good performance in many computer vision applications. However, due to the overcomplete codebook and the independent coding process, the locality and the similarity among the instances to be encoded are lost. To preserve such locality and similarity information, we propose a Laplacian sparse coding (LSc) framework. By incorporating the similarity preserving term into the objective of sparse coding, our proposed Laplacian sparse coding can alleviate the instability of sparse codes. Furthermore, we propose a Hypergraph Laplacian sparse coding (HLSc), which extends our Laplacian sparse coding to the case where the similarity among the instances defined by a hypergraph. Specifically, this HLSc captures the similarity among the instances within the same hyperedge simultaneously, and also makes the sparse codes of them be similar to each other. Both Laplacian sparse coding and Hypergraph Laplacian sparse coding enhance the robustness of sparse coding. We apply the Laplacian sparse coding to feature quantization in Bag-of-Words image representation, and it outperforms sparse coding and achieves good performance in solving the image classification problem. The Hypergraph Laplacian sparse coding is also successfully used to solve the semi-auto image tagging problem. The good performance of these applications demonstrates the effectiveness of our proposed formulations in locality and similarity preservation. [ABSTRACT FROM AUTHOR]

The Web as a graph can be embedded in a low-dimensional space where its geometry can be visualized and studied in order to mine interesting patterns such as web communities. The existing algorithms operate on small-to-medium-scale graphs; thus, we propose a close to linear time algorithm called Mani-Web suitable for large-scale graphs. The result is similar to the one produced by the manifold-learning technique Laplacian eigenmap that is tested on artificial manifolds and real web-graphs. Mani-Web can also be used as a general-purpose manifold-learning/dimensionality-reduction technique as long as the data can be represented as a graph. [ABSTRACT FROM PUBLISHER]

In this paper, first, a new Laplacian kernel is developed to integrate into it the anisotropic behavior to control the process of forward diffusion in horizontal and vertical directions. It is shown that, although the new kernel reduces the process of edge distortion, it nonetheless produces artifacts in the processed image. After examining the source of this problem, an analytical scheme is devised to obtain a spatially varying kernel that adapts itself to the diffusivity function. The proposed spatially varying Laplacian kernel is then used in various nonlinear diffusion filters starting from the classical Perona–Malik filter to the more recent ones. The effectiveness of the new kernel in terms of quantitative and qualitative measures is demonstrated by applying it to noisy images. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel scheme of polarimetric synthetic aperture radar (PolSAR) image classification. We apply Laplacian eigenmaps (LE), a nonlinear dimensionality reduction (NDR) technique, to a high-dimensional polarimetric feature representation for PolSAR land-cover classification. A wide variety of polarimetric signatures are chosen to construct a high-dimensional polarimetric manifold which can be mapped into the most compact low-dimensional structure by manifold-based dimensionality reduction techniques. This NDR technique is employed to obtain a low-dimensional intrinsic feature vector by the LE algorithm, which is beneficial to PolSAR land-cover classification owing to its local preserving property. The effectiveness of our PolSAR land-cover classification scheme with LE intrinsic feature vector is demonstrated with the RadarSat-2 C-band PolSAR data set and the 38th Research Institute of China Electronics Technology Group Corporation X-band PolInSAR data set. The performance of our method is measured by the separability in the feature space and the accuracy of classification. Comparisons on the feature space show that the LE intrinsic feature vector is more separable than different original feature vectors. Our LE intrinsic feature vector also improves the classification accuracy. [ABSTRACT FROM AUTHOR]

We describe a prototype ultrawideband radar. We show how the system was designed and how the hardware was developed for the radar prototype. Waveform generation, radar parameters, and signal processing for the stepped frequency waveform are discussed. The radar operates from 500 MHz to 3 GHz with a nominal resolution of 6 cm in air. The advantage of the stepped frequency approach over an impulse radar is better matching between the transmitted waveform and the receiver. We use range gating to improve the system dynamic range. The advantages are illustrated with laboratory measurements and field measurements from glacial ice and permafrost in Svalbard, showing penetration depths of 11 m. Antennas which do not require contact with the ground were developed and used in the experiments. [ABSTRACT FROM AUTHOR]

The paper investigates the mean-squared error (MSE) distortion of a variance-mismatched fixed-rate scalar quantizer that is optimal or asymptotically optimal in the minimum MSE sense for a Laplacian density with standard deviation \sigmaq but is applied to another with standard deviation \sigmap. A Nitadori-like formula is discovered for an optimal quantizer when \rho (\triangleq\sigmap/\sigmaq)=1/2. Also it is shown that the distortion expressions derived rigorously for asymptotically optimal quantile quantizers essentially confirm the heuristically obtained previous result that the distortion decreases as 1/ N^3/\rho for the heavy mismatch of \rho>3/ 2, as \ln N/ N^2 for the critical mismatch of \rho=3/2, and as 1/N^2 for the mild mismatch of \rho<3/2, where N is the number of quantization points. These asymptotic behaviors agree surprisingly well with Bennett's integral even in the critical and heavy mismatched cases. Thus, in the case of nonuniform quantizers, the long-conjectured convergence of the MSE distortion to zero at a rate other than 1/N^2 is confirmed rigorously. In addition, optimal uniform quantizers are found to be heavily mismatched when \rho>1 and the resulting distortion decreases as (\ln N/N^2)^1/\rho. [ABSTRACT FROM AUTHOR]

Optimal coefficients of the spatial finite difference (FD) operator for the complex nonstandard finite difference time-domain (CNS-FDTD) method are presented. To derive the optimal coefficients that minimize the dispersion error, we employ a semianalytical method based on the FD Laplacian. The propagation constant is a complex number in lossy media, therefore, the derivation of the coefficients is more complicated than the derivation for the NS-FDTD method. It is confirmed by numerical tests using the numerical dispersion equation that our coefficients give the CNS-FDTD method a higher accuracy than the standard FDTD method. The coefficients are used for the reflection analysis of a grid ferrite electromagnetic wave absorber, and the validity of the coefficients is shown. The calculation time to derive the coefficients is negligible compared with that for the CNS-FDTD calculations themselves. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a generic error resilient video coding (ERVC) scheme using embedded Wyner–Ziv (WZ) description. At the encoder side, a joint source-channel R-D optimized mode selection (JSC-RDO-MS) algorithm with WZ-coded anchor frames is statistically studied and developed. Given a stationary first-order Markov Gaussian source, the proposed mode optimization is justified by an analysis of the RD impact on the WZ bit-rate. JSC-RDO-MS involves in the estimation of expected rate and distortion of WZ coding with the unavailable side information, and the WZ bit-rate of each coding mode is determined based on the error correction capability of the specific WZ codec. At the decoder side, an online correlation noise model between the source and the side-information is proposed with a mixture of Laplacians whose parameters are attained to reflect the coherence of the motion field of successive frames and the energy of prediction residual. Each mixture component represents the statistical distribution of prediction residuals, and the mixing coefficients represent the amount of errors in motion compensation. The proposed scheme achieves the so-called classification gain by exploiting the spatially non-stationary characteristics of the motion field and texture. Extensive experimental results show that the proposed WZ-ERVC scheme achieves a better overall RD performance than existing ERVC schemes, and the proposed modeling algorithm also significantly outperforms the conventional Laplacian model by up to 2 dB. [ABSTRACT FROM PUBLISHER]

Support vector machine (SVM), as one of the most popular classifiers, aims to find a hyperplane that can separate two classes of data with maximal margin. SVM classifiers are focused on achieving more separation between classes than exploiting the structures in the training data within classes. However, the structural information, as an implicit prior knowledge, has recently been found to be vital for designing a good classifier in different real-world problems. Accordingly, using as much prior structural information in data as possible to help improve the generalization ability of a classifier has yielded a class of effective structural large margin classifiers, such as the structured large margin machine (SLMM) and the Laplacian support vector machine (LapSVM). In this paper, we unify these classifiers into a common framework from the concept of “structural granularity” and the formulation for optimization problems. We exploit the quadratic programming (QP) and second-order cone programming (SOCP) methods, and derive a novel large margin classifier, we call the new classifier the structural regularized support vector machine (SRSVM). Unlike both SLMM at the cross of the cluster granularity and SOCP and LapSVM at the cross of the point granularity and QP, SRSVM is located at the cross of the cluster granularity and QP and thus follows the same optimization formulation as LapSVM to overcome large computational complexity and non-sparse solution in SLMM. In addition, it integrates the compactness within classes with the separability between classes simultaneously. Furthermore, it is possible to derive generalization bounds for these algorithms by using eigenvalue analysis of the kernel matrices. Experimental results demonstrate that SRSVM is often superior in classification and generalization performances to the state-of-the-art algorithms in the framework, both with the same and different structural granularities. [ABSTRACT FROM AUTHOR]

In this paper, we examine the Green's function and Z-matrix models commonly used in calculations for microwave planar circuits. We prove, for the first time, the pointwise convergence of the Green's function and the interchangeability of the integration and infinite summation used in deriving the Z-matrix model. We also show the validity of interchanging the order of the double summation of the Z-matrix. In a related vein, we point out some potential problem of performing series rearrangements in evaluating infinite sums. Through computational analysis, we will demonstrate that a stable and efficient algorithm for the Green's function and Z-matrix calculations can be optimally obtained for all practical boundary port configurations of rectangular planar circuits. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel predictive model, active volume model (AVM), for object boundary extraction. It is a dynamic “object” model whose manifestation includes a deformable curve or surface representing a shape, a volumetric interior carrying appearance statistics, and an embedded classifier that separates object from background based on current feature information. The model focuses on an accurate representation of the foreground object's attributes, and does not explicitly represent the background. As we will show, however, the model is capable of reasoning about the background statistics thus can detect when is change sufficient to invoke a boundary decision. When applied to object segmentation, the model alternates between two basic operations: 1) deforming according to current region of interest (ROI), which is a binary mask representing the object region predicted by the current model, and 2) predicting ROI according to current appearance statistics of the model. To further improve robustness and accuracy when segmenting multiple objects or an object with multiple parts, we also propose multiple-surface active volume model (MSAVM), which consists of several single-surface AVM models subject to high-level geometric spatial constraints. An AVM's deformation is derived from a linear system based on finite element method (FEM). To keep the model's surface triangulation optimized, surface remeshing is derived from another linear system based on Laplacian mesh optimization (LMO) refid="ref26"/, refid="ref27"/ . Thus efficient optimization and fast convergence of the model are achieved by solving two linear systems. Segmentation, validation and comparison results are presented from experiments on a variety of 2-D and 3-D medical images. [ABSTRACT FROM AUTHOR]

In this paper, a novel motion-tracking scheme using scale-invariant features is proposed for automatic cell motility analysis in gray-scale microscopic videos, particularly for the live-cell tracking in low-contrast differential interference contrast (DIC) microscopy. In the proposed approach, scale-invariant feature transform (SIFT) points around live cells in the microscopic image are detected, and a structure locality preservation (SLP) scheme using Laplacian Eigenmap is proposed to track the SIFT feature points along successive frames of low-contrast DIC videos. Experiments on low-contrast DIC microscopic videos of various live-cell lines shows that in comparison with principal component analysis (PCA) based SIFT tracking, the proposed Laplacian-SIFT can significantly reduce the error rate of SIFT feature tracking. With this enhancement, further experimental results demonstrate that the proposed scheme is a robust and accurate approach to tackling the challenge of live-cell tracking in DIC microscopy. [ABSTRACT FROM AUTHOR]

This paper presents two semisupervised one-class support vector machine (OC-SVM) classifiers for remote sensing applications. In one-class image classification, one tries to detect pixels belonging to one of the classes in the image and reject the others. When few labeled pixels of only one class are available, obtaining a reliable classifier is a difficult task. In the particular case of SVM-based classifiers, this task is even harder because the free parameters of the model need to be finely adjusted, but no clear criterion can be adopted. In order to improve the OC-SVM classifier accuracy and alleviate the problem of free-parameter selection, the information provided by unlabeled samples present in the scene can be used. In this paper, we present two state-of-the-art algorithms for semisupervised one-class classification for remote sensing classification problems. The first proposed algorithm is based on modifying the OC-SVM kernel by modeling the data marginal distribution with the graph Laplacian built with both labeled and unlabeled samples. The second one is based on a simple modification of the standard SVM cost function which penalizes more the errors made when classifying samples of the target class. The good performance of the proposed methods is illustrated in four challenging remote sensing image classification scenarios where the goal is to detect one of the classes present on the scene. In particular, we present results for multisource urban monitoring, hyperspectral crop detection, multispectral cloud screening, and change-detection problems. Experimental results show the suitability of the proposed techniques, particularly in cases with few or poorly representative labeled samples. [ABSTRACT FROM AUTHOR]

Laplacian matrices play an important role in linear-consensus algorithms. This paper studies optimal linear-consensus algorithms for multivehicle systems with single-integrator dynamics in both continuous-time and discrete-time settings. We propose two global cost functions, namely, interaction-free and interaction-related cost functions. With the interaction-free cost function, we derive the optimal (nonsymmetric) Laplacian matrix by using a linear-quadratic-regulator-based method in both continuous-time and discrete-time settings. It is shown that the optimal (nonsymmetric) Laplacian matrix corresponds to a complete directed graph. In addition, we show that any symmetric Laplacian matrix is inverse optimal with respect to a properly chosen cost function. With the interaction-related cost function, we derive the optimal scaling factor for a prespecified symmetric Laplacian matrix associated with the interaction graph in both continuous-time and discrete-time settings. Illustrative examples are given as a proof of concept. [ABSTRACT FROM AUTHOR]

We compare and contrast from a geometric perspective a number of low-dimensional signal models that support stable information-preserving dimensionality reduction. We consider sparse and compressible signal models for deterministic and random signals, structured sparse and compressible signal models, point clouds, and manifold signal models. Each model has a particular geometrical structure that enables signal information to be stably preserved via a simple linear and nonadaptive projection to a much lower dimensional space; in each case the projection dimension is independent of the signal's ambient dimension at best or grows logarithmically with it at worst. As a bonus, we point out a common misconception related to probabilistic compressible signal models, namely, by showing that the oft-used generalized Gaussian and Laplacian models do not support stable linear dimensionality reduction. [ABSTRACT FROM AUTHOR]

Extracting information from multitrial magnetoen-cephalography or electroencephalography (EEG) recordings is challenging because of the very low SNR, and because of the inherent variability of brain responses. The problem of low SNR is commonly tackled by averaging multiple repetitions of the recordings, also called trials, but the variability of response across trials leads to biased results and limits interpretability. This paper proposes to decode the variability of neural responses by making use of graph representations. Our approach has several advantages compared to other existing methods that process single-trial data: first, it avoids the a priori definition of a model for the waveform of the neural response; second, it does not make use of the average data for parameter estimation; third, it does not suffer from initialization problems by providing solutions that are global optimum of cost functions; and last, it is fast. We proceed in two steps. First, a manifold learning algorithm, based on a graph Laplacian, offers an efficient way of ordering trials with respect to the response variability, under the condition that this variability itself depends on a single parameter. Second, the estimation of the variability is formulated as a combinatorial optimization that can be solved very efficiently using graph cuts. Details and validation of this second step are provided for latency estimation. Performance and robustness experiments are conducted on synthetic data, and results are presented on EEG data from a P300 oddball experiment. [ABSTRACT FROM AUTHOR]

The bit error rate performance of Rake reception of impulse radio ultra-wide bandwidth signals over the IEEE 802.15.3a channel models is evaluated. Instead of using Gaussian approximation for the probability density function of the total disturbance which includes the multi-user interference and the background additive white Gaussian noise, two new models dubbed the "composite lognormal-Gaussian" and the "composite lognormal-Laplacian" are proposed for modeling the multi-user interference and shadowing in ultra-wide bandwidth multipath fading channels. Tractable formulae for bit error rate evaluation of Rake reception in ultra-wide bandwidth multipath channels are derived for both models. Numerical results indicate that these formulae predict the bit error rate performance with good accuracy, and can be rapidly and easily evaluated using commonplace computer resources. [ABSTRACT FROM AUTHOR]

This paper proposes a non-orthogonal view iris recognition system comprising a new iris imaging module, an iris segmentation module, an iris feature extraction module and a classification module. A dual-charge-coupled device camera was developed to capture four-spectral (red, green, blue, and nearinfrared) iris images which contain useful information for simplifying the iris segmentation task. An intelligent random sample consensus iris segmentation method is proposed to robustly detect iris boundaries in a four-spectral iris image. In order to match iris images acquired at different off-axis angles, we propose a circle rectification method to reduce the off-axis iris distortion. The rectification parameters are estimated using the detected elliptical pupillary boundary. Furthermore, we propose a novel iris descriptor which characterizes an iris pattern with multiscale step/ridge edge-type maps. The edge-type maps are extracted with the derivative of Gaussian and the Laplacian of Gaussian filters. The iris pattern classification is accomplished by edge-type matching which can be understood intuitively with the concept of classifier ensembles. Experimental results show that the equal error rate of our approach is only 0.04% when recognizing iris images acquired at different off-axis angles within ±30°. [ABSTRACT FROM AUTHOR]

Nodule growth as observed in computed tomography (CT) scans acquired at different times is the primary feature to malignancy of indeterminate small lung nodules. In this paper, we propose the estimation of nodule size through a scale-space representation which needs no segmentation and has high intraand inter-operator reproducibility. Lung nodules usually appear in CT images as blob-like patterns and can be analyzed in the scale-space by Laplacian of Gaussian (LoG ) kernels. For each nodular pattern the LoG scale-space signature was computed and the related characteristic scale adopted as measurement of nodule size. Both in vitro and in vivo validation of LoG characteristic scale were carried out. In vitro validation was done by 40 nondeformable phantoms and 10 deformable phantoms. A close relationship between the characteristic scale and the equivalent diameter, i.e., the diameter of the sphere having the same volume of nodules, (Pearson correlation coefficient was 0.99) and, for nodules undergoing little deformations (obtained at constant volume), small variability of the characteristic scale was observed. The in vivo validation was performed on low and standard-dose CT scans collected from the ITALUNG screening trial (86 nodules) and from the LIDC public data set (89 solid nodules and 40 part-solid nodules or ground-glass opacities). The Pearson correlation coefficient between characteristic scale and equivalent diameter was 0.83-0.93 for ITALUNG and 0.68-0.83 for LIDC data set. Intra- and inter-operator reproducibility of characteristic scale was excellent: on a set of 40 lung nodules of ITALUNG data, two radiologists produced identical results in repeated measurements. The scan-rescan variability of the characteristic scale was also investigated on 86 two-year-stable solid lung nodules (each one observed, on average, in four CT scans) identified in the ITALUNG screening trial: a coefficient of repeatability of about 0.9 mm was observed. Experimental evidence supports the clinical use of the LoG characteristic scale to measure nodule size in CT imaging. [ABSTRACT FROM AUTHOR]