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Many emerging cyber-physical systems, such as autonomous vehicles and robots, rely heavily on artificial intelligence and machine learning algorithms to perform important system operations. Since these highly parallel applications are computationally intensive, they need to be accelerated by graphics processing units (GPUs) to meet stringent timing constraints. However, despite the wide adoption of GPUs, efficiently scheduling multiple GPU applications while providing rigorous real-time guarantees remains a challenge. In this paper, we propose RTGPU, which can schedule the execution of multiple GPU applications in real-time to meet hard deadlines. Each GPU application can have multiple CPU execution and memory copy segments, as well as GPU kernels. We start with a model to explicitly account for the CPU and memory copy segments of these applications. We then consider the GPU architecture in the development of a precise timing model for the GPU kernels and leverage a technique known as persistent threads to implement fine-grained kernel scheduling with improved performance through interleaved execution. Next, we propose a general method for scheduling parallel GPU applications in real time. Finally, to schedule multiple parallel GPU applications, we propose a practical real-time scheduling algorithm based on federated scheduling and grid search (for GPU kernel segments) with uniprocessor fixed priority scheduling (for multiple CPU and memory copy segments). Our approach provides superior schedulability compared with previous work, and gives real-time guarantees to meet hard deadlines for multiple GPU applications according to comprehensive validation and evaluation on a real NVIDIA GTX1080Ti GPU system.

Varied edge bundling methods have been used to reduce visual clutter in parallel coordinates plots (PCP). However, existing edge-bundled PCP do not scale well for visual analysis of multidimensional big data and often overplot the bundles in the area near the axes. In this study, we propose a scalable lightweight bundling method to support visual analysis of multidimensional big data in PCP. It helps the users discover trends and detect outliers in the data by bundling the edges between each two adjacent axes independently. We integrate human judgments into the two-dimensional data binning by novel interactions to accelerate the clustering process of the data. We use the frequency-based representation to render the clusters as histogram-like bundles to reveal the distribution of the data and eliminate the overplotting of the bundles. Based on our method, we build a lightweight web-based visual analytics system for exploring multidimensional big data in PCP. The scalability analysis of our method shows that its clustering time increases linearly with the size of the data. Its rendering time is independent of the size of the data. We conduct two case studies and a user study to compare our method with classic PCP and two state-of-the-art edge-bundled PCP.

We propose and numerically validate a patch reflectarray modeling approach suitable for small patches that describes each patch as a pair of polarizable magnetic dipoles. We introduce an extraction technique to obtain the effective polarizability of the patch dipoles via full-wave simulations on individual patches, followed by a beamforming design routine valid under weakly scattering configurations. This dipole framework serves as an alternative to the ray tracing model often used in reflectarray designs, in which rays are drawn from the feed point and scattered off of the patch elements. Whereas the ray tracing method solves the design problem in terms of phase delays, the dipole framework presented here has the potential to accurately design and predict beam patterns using a fully dipolar treatment of empirically characterized patches. We illustrate this technique by applying it to two modulation strategies: a variable patch size reflectarray in which the phase can be continuously tuned (grayscale patch response), and a fixed patch size (binary patch response) in which on/off modulation is achieved through selective patch electrical shorting. Methods for incorporating these cases into the dipole design framework are discussed and the results compared to those from full wave simulation., 10 pages, 10 figures

Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology changes. Implicit representations like signed-distance functions, on the other hand, offer better support of topology changes but are much more difficult to use for physics-based differentiable rendering. We introduce a new physics-based inverse rendering pipeline that uses both implicit and explicit representations. Our technique enjoys the benefit of both representations by supporting both topology changes and differentiable rendering of complex effects such as environmental illumination, soft shadows, and interreflection. We demonstrate the effectiveness of our technique using several synthetic and real examples.

In order to effectively solve the problems of high error rate, long time consuming, and low accuracy of feature extraction in current painting image classification methods, a painting image classification method based on transfer learning and feature fusion was proposed. The global characteristics of the painting picture, such as color, texture, and form, are extracted. The SIFT method is used to extract the painting’s local features, and the global and local characteristics are normalized and merged. The painting images are preliminarily classified using the result of feature fusion, the deterministic and nondeterministic samples are divided, and the estimated Gaussian model parameters are transferred to the target domain via a transfer learning algorithm to alter the distribution of nondeterministic samples, completing the painting image classification. Experimental results show that the proposed method has a low error rate and low feature extraction time and a high accuracy rate of painting image classification.

A new family of combined subdivision schemes with one tension parameter is proposed by the interpolatory and approximating subdivision schemes. The displacement vectors between the points of interpolatory and approximating subdivision schemes provide the flexibility in designing the limit curves and surfaces. Therefore, the limit curves generated by the proposed subdivision schemes variate in between or around the approximating and interpolatory curves. We also design few analytical algorithms to study the properties of the proposed schemes theoretically. The efficiency of these algorithms is analyzed by calculating their time complexity. The graphical representations and graphical properties of the proposed schemes are also analyzed.

In this article, barycentric rational collocation method is introduced to solve Burgers’ equation. The algebraic equations of the barycentric rational collocation method are presented. Numerical analysis and error estimates are established. With the help of the barycentric rational interpolation theory, the convergence rates of the barycentric rational collocation method for Burgers’ equation are proved. Numerical experiments are carried out to validate the convergence rates and show the efficiency.

This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that share them. The algorithm is termed Polylla and is divided into three phases. The first phase consists of labeling each edge of the input triangulation according to its size; the second phase builds polygons (simple or not) from terminal-edges regions using the label system; and the third phase transforms each non simple polygon into simple ones. The final mesh contains polygons with convex and non convex shape. Since Voronoi based meshes are currently the most used polygonal meshes, we compare some geometric properties of our meshes against constrained Voronoi meshes. Several experiments were run to compare the shape and size of polygons, the number of final mesh points and polygons. For the same input, Polylla meshes contain less polygons than Voronoi meshes, and the algorithm is simpler and faster than the algorithm to generate constrained Voronoi meshes. Finally, we have validated Polylla meshes by solving the Laplace equation on an L-shaped domain using the Virtual Element Method (VEM). We show that the numerical performance of the VEM using Polylla meshes and Voronoi meshes is similar.

Many real world applications require large-scale sensor networks deployed on the surface of a complex 3D terrain. Compared with planar and 3D network localizations, terrain surface network localization generates unique and fundamental hardness. We explore 3D surface network localization with terrain models. A digital terrain model (DTM), available to public with a variable resolution up to one meter, is a 3D representation of a terrain's surface. The constraint that the sensors must be on the known 3D terrain's surface ensures that the triangular meshes of the network and the terrain's surface overlap and approximate the same geometric shape. The basic idea of both the anchor-based and anchor-free localization algorithms is to map the two triangular meshes extracted from the connectivity graph of a sensor network and the DTM of its deployed terrain surface to plane. With the well-aligned triangular meshes of a network and its deployed terrain surface on plane, each sensor node of the network can easily locate reference grid points from the DTM of the terrain to calculate its own geographic location.

We present the design of a mesh quality indicatorthat can predict the behavior of the Virtual Element Method (VEM) on a given mesh family or a finite sequence of polyhedral meshes (dataset). The mesh quality indicator is designed to measure the violation of the mesh regularity assumptions that are normally considered in the convergence analysis. We investigate the behavior of this new mathematical tool on the lowest-order conforming approximation of the three-dimensional Poisson equation. This work also assesses the convergence rate of the VEM when applied to very general polyhedral meshes, including non-convex and skewed three-dimensional elements. Such meshes are created within an original mesh generation framework, which is designed to allow the generation of meshes with very different sizes, connectivity, and geometrical properties. The obtained results show a significant correlation between the quality measured a priori by the indicator and the effective performance of the VEM.

In this paper, we present a new approach to the Mandelbrot set via fuzzy set theory. We introduce and characterize the fuzzy Mandelbrot set by describing its membership function that determines the degrees of belonging of the points to this set under the iteration even if the orbit of the point is not limited. Then we investigate the basic topological properties of the fuzzy Mandelbrot set and its strong α-cut such as closedness, openness, boundness, connectedness and simply connectedness.

In this paper has been considered the main content and distinctive features of the “Geometric Modeling” training course for the “Mathematics and Computer Science” training program 02.03.01 (“Mathematical and Computer Modeling” specialization). The goal of the “Geometric Modeling” course study is the assimilation of mathematical methods for construction of geometric objects with complex curved shapes, and techniques for their computer visualization by using polygons of curves and surfaces. Methods for construction of structures’ curved shapes using spline representations, as well as techniques for construction of surfaces and volumetric geometries using motion operations and basic logical operations on geometric objects are considered. The spline representations include linear and bilinear splines, Hermite cubic splines and Hermite surfaces, natural cubic and bicubic interpolation splines, Bezier curves and surfaces, rational Bezier splines, B-splines and B-spline surfaces, NURBS-curves and NURBS-surfaces, transfinite interpolation methods, and splines of surfaces with triangular form. Logical operations for intersection of two spline curves, and intersection of two parametric surfaces are considered. The principles of scientific visualization and computer animation are considered in this course as well. Some examples for visualization of initial data and results of curves and surfaces construction in two- and three-dimensional spaces through the software shell developed by authors and used by students while doing tests have been demonstrated. The software shell has a web interface with the WebGL library graphic support. Tasks for four practical studies in a computer classroom, as well as several variations of homework are represented. The problems occurring in preparation materials for some course sections are discussed, as well as the practical importance of acquired knowledge for the further progress of students. The paper may be interesting for teachers of “Geometric Modeling” and “Computer Graphics” courses aimed to students with a specialization in mathematics and information, as well as to those who independently develop software interfaces for algorithms of geometric modeling.

Various computer simulations regarding, e.g., the weather or structural mechanics, solve complex problems on a two-dimensional domain. They mostly do so by splitting the input domain into a finite set of smaller and simpler elements on which the simulation can be run fast and efficiently. This process of splitting can be automatized by using subdivision schemes. Given the wide range of simulation problems to be tackled, an equally wide range of subdivision schemes is available. They create subdivisions that are (mainly) comprised of triangles, quadrilaterals, or hexagons. Furthermore, they ensure that (almost) all vertices have the same number of neighboring vertices. This paper illustrates a subdivision scheme that splits the input domain into pentagons. Repeated application of the scheme gives rise to fractal-like structures. Furthermore, the resulting subdivided domain admits to certain weaving patterns. These patterns are subsequently generalized to several other subdivision schemes. As a final contribution, we provide paper models illustrating the weaving patterns induced by the pentagonal subdivision scheme. Furthermore, we present a jigsaw puzzle illustrating both the subdivision process and the induced weaving pattern. These transform the visual and abstract mathematical algorithms into tactile objects that offer exploration possibilities aside from the visual., Comment: Submitted for publication to the Journal of Mathematics and the Arts (2022)

Monte Carlo integration is an established method in simulating light transport. However, due to its stochastic nature, it requires copious amounts of samples to eliminate the estimation error, and variance reduction techniques such as importance sampling are used to improve the convergence speed as a remedy. Path guiding is a class of adaptive importance sampling methods devised specifically for light transport simulation, which demonstrates significant improvements over classical sampling techniques. Yet most of the previous path guiding methods only account for the radiance term, omitting the bidirectional scattering distribution function (BSDF) term. This results in suboptimal sample quality for non-diffuse light transport. This paper presents a path guiding method which guides paths according to the full product of the BSDF and radiance terms in light transport equation. Extending a spatio-directional tree based path guiding method, we use a semi-adaptive grid-quadtree hybrid subdividing the directional domain in a spatial subdomain to learn and represent the radiance field. With the help of BSDF lookup tables used to accelerate BSDF evaluations, this grid-quadtree allows us to efficiently construct approximate product distributions and guide paths according to the product of incident radiance and cosine-weighted BSDF at each path vertex. The resulting method is relatively simple to implement and enables more robust sampling on scenes with many glossy surfaces.

We construct examples of non-schematic algebraic spaces that become schemes after finite ground field extensions., 7 pages

Due to the diversity of defocus blurred images, causing the unsatisfied effect of sharpness enhancement of the defocused and blurred image. On this basis, the paper has proposed an enhancement algorithm of defocused and blurred image base on non-local constraints. The estimated results similar to the original image was acquired, the actual defocus blur optical transfer function was calculated and the low inverter over-amplifying the noise was avoided through the improvement of inverse filtering by the Wiener filter. Based on the symmetry of a defocused and blurred circular, the diffusion curve of straight marginal function was filtered and restored to eliminate the noise in the image. On this basis, the non-local self-similarity and total variational regularity of the defocused and blurred image were complemented, and the sharpness of the defocused and blurred image was finally enhanced by using the non-local model to restore the marginal and detailed texture information of the defocused and blurred image. The results of the simulation have shown that the proposed method could not only increase the computational efficiency, but also obtain satisfactory sharpness enhancement of the defocused and blurred image, and a better retain effect of the marginal information.

Computational mesh is an important ingredient that affects the accuracy and efficiency of CFD numerical simulation. In light of the introduced large amount of computational costs for many adaptive mesh methods, moving mesh methods keep the number of nodes and topology of a mesh unchanged and do not increase CFD computational expense. As the state-of-the-art moving mesh method, the variational mesh adaptation approach has been introduced to CFD calculation. However, quickly estimating the flow field on the updated meshes during the iterative algorithm is challenging. A mesh optimization method, which embeds a machine learning regression model into the variational mesh adaptation, is proposed. The regression model captures the mapping between the initial mesh nodes and the flow field, so that the variational method could move mesh nodes iteratively by solving the mesh functional which is built from the estimated flow field on the updated mesh via the regression model. After the optimization, the density of the nodes in the high gradient area increases while the density in the low gradient area decreases. Benchmark examples are first used to verify the feasibility and effectiveness of the proposed method. And then we use the steady subsonic and transonic flows over cylinder and NACA0012 airfoil on unstructured triangular meshes to test our method. Results show that the proposed method significantly improves the accuracy of the local flow features on the adaptive meshes. Our work indicates that the proposed mesh optimization approach is promising for improving the accuracy and efficiency of CFD computation.

Premature wear, fatigue and other failures caused by non-linear vibration are one of the key problems of aerodynamic power transmission in spline coupling which maybe suffer from abnormal meshing effects due to misalignment between internal spline and external spline. A non-linear dynamic model of the misaligned spline coupling is established, which involves the calculation of dynamic meshing behavior of misaligned tooth pairs. The movement state of spline coupling can change from a periodic state to a chaotic state with the increase of speed. Under light load, the main resonance speed of system may be modified due to changes in the load. The existence of misalignment promotes the vibration intensity, advances the main resonance speed and increases the instability of spline coupling. In addition, a test bench for the misalignment spline coupling was developed to measure the vibration acceleration signal, and the effect of the misalignment on the dynamic behavior of spline coupling was discussed.

Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms of a so-called multi-degree Tchebycheffian B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis. We present a practical framework to compute MDTB-splines, and provide an object-oriented implementation in Matlab . The implementation supports the construction, differentiation, and visualization of MDTB-splines whose pieces belong to Tchebycheff spaces that are null-spaces of constant-coefficient linear differential operators. The construction relies on an extraction operator that maps local Tchebycheffian Bernstein functions to the MDTB-spline basis of interest.

In this study, a filtering method based on the threshold value of normalized synthetic aperture radar (SAR) data is proposed to eliminate clutter in millimeter wave ground based synthetic aperture radar (GB-SAR) images. In the proposed method, first, stepped frequency continuous wave SAR data are reconstructed by using the back-projection algorithm and focused complex SAR data are obtained. Then, the amplitude values of the complex SAR data are normalized and the best threshold values to distinguish the target from clutter is determined by the OTSU’s thresholding method. Next, a filter mask is created that cancels all data below the computed threshold values. The mask matrix is finally multiplied with the resulted GB-SAR data to eliminate all clutter from the image. With the proposed technique, the best threshold value is determined automatically by directly processing the raw data without converting the SAR data into any RGB images. The proposed technique is validated through real GB-SAR experiments that were carried out in the frequency band of 78-81 GHz. In the experiments, challenging GB-SAR data are obtained using high cluttered background materials, and very successful filtering operations are performed with the proposed technique.

Gradient meshes, an advanced vector graphics primitive, are widely used by designers for creating scalable vector graphics. Traditional variants require a regular rectangular topology, which is a severe design restriction. The more advanced subdivision gradient mesh allows for an arbitrary manifold topology and is based on subdivision techniques to define the resulting colour surface. This also allows the artists to manipulate the geometry and colours at various levels of subdivision. Recent advances allow for the interpolation of both geometry and colour, local detail following edits at coarser subdivision levels and sharp colour transitions. A shortcoming of all existing methods is their dependence on global refinement, which makes them unsuitable for real-time (commercial) design applications. We present a novel method that incorporates the idea of feature-adaptive subdivision and uses approximating patches suitable for hardware tessellation with real-time performance. Further novel features include multiple interaction mechanisms and self-intersection prevention during interactive design/editing.

Although various deep neural networks such as convolutional neural networks (CNNs) have been suggested for classification of polarimetric synthetic aperture radar (PolSAR) images, but, they have several deficiencies. CNNs have weakness in producing classification maps with reduced noise and also are disabled in extraction of polarimetric/scattering information to explore the physical characteristics of the radar image. A deep neural network based on convolutional blocks is proposed for PolSAR image classification in this work that deals with the above difficulties. The low frequency components of the PolSAR image are added to the output of convolutional blocks to help the network to learn noise reduction. Moreover, eight fuzzy clustering maps obtained by the polarimetric entropy and averaged alpha angle are extracted as radar’s physical feature maps which concatenated with the spatial features extracted by convolutional blocks. So, the proposed network while learns to reduce the speckle noise, learns to simultaneously extract the spatial-physical characteristics of the PolSAR cube. The experiments on two real PolSAR datasets show superior performance of the proposed network compared to CNN, residual network and some other well-done networks.

Synthetic aperture radar (SAR) images are widely used for Earth observation to complement optical imaging. By combining information on the polarization and the phase shift of the radar echos, SAR images offer high sensitivity to the geometry and materials that compose a scene. This information richness comes with a drawback inherent to all coherent imaging modalities: a strong signal-dependent noise called "speckle". This paper addresses the mathematical issues of performing speckle reduction in a transformed domain: the matrix-log domain. Rather than directly estimating noiseless covariance matrices, recasting the denoising problem in terms of the matrix-log of the covariance matrices stabilizes noise fluctuations and makes it possible to apply off-the-shelf denoising algorithms. We refine the method MuLoG by replacing heuristic procedures with exact expressions and improving the estimation strategy. This corrects a bias of the original method and should facilitate and encourage the adaptation of general-purpose processing methods to SAR imaging.

Fluid structural interactions involve temporal change of the boundaries of the computational domain as a result of the fluid forces acting on the solid structure. In order to take into account this change, OpenFOAM offers two different methods: the overset method and the morphing mesh method. The morphing mesh method takes into account the boundary movement by changing the topology of the mesh but keeping the connectivity between cells unchanged. The overset methods consists in non overlapping meshes which are moving relative to a background mesh. Usually the meshes do not change the topology. The coupling between meshes is achieved by interpolation of the variables between the meshes. Both methods are compared with each other and reference experiments and simulation by taking a two-dimensional laminar flow around a cylinder. The results are found to agree reasonable well with the references. Both mesh types give similar results for similar number of cells.

Synthetic aperture Radar (SAR) uses the relative movement of the Radar and the target to pick up echoes of the detected area and image it. In contrast to optical imaging, SAR imaging systems are not affected by weather and time and can detect targets in harsh conditions. Therefore, the SAR image has important application value in military and civilian purposes. This paper introduces the classification of Gaussian process. Gaussian process classification is a probabilistic classification algorithm based on Bass frame. This is a complete probability expression. Based on Gaussian process and SAR data, Gaussian process classification algorithm for SAR images is studied in this paper. In this paper, we introduce the basic principle of Gaussian process, briefly analyze the basic theory of classification and the characteristics of SAR images, provide the evaluation index system of image classification, and give the SAR classification model of Gaussian process. Taking Laplace approximation as an example, several classification algorithms are introduced directly. Based on the two classifications, we propose an indirect multipurpose classification method and a multifunction classification method for two-pair two-Gaussian processes. The SAR image algorithm based on the two categories is relatively simple and achieves certain results.

Synthetic aperture radar (SAR), due to its inherent characteristics, will produce speckle noise, which results in the deterioration of image quality, so the removal of speckle in SAR image is very important for the subsequent high-level image processing. In order to balance the relationship between denoising and texture preservation, we propose a multiscale residual dense dual attention network (MRDDANet) for SAR image denoising. This algorithm can effectively suppress the speckle while fully retaining the texture details of the image. In MRDDANet, shallow features are extracted from the noisy images by multiscale modules with different kernel sizes, and then, the extracted shallow features are mapped to the residual dense dual-attention network to obtain the deep features of SAR image. Finally, the final denoising image is generated through global residual learning. MRDDANet has advantages of both multiscale blocks and residual dense dual attention networks. The dense connection can fully extract features in the image, and the dual-channel attention enables MRDDANet to pay more attention to noise information, which is beneficial to remove noise and keep the details of the original image at the same time. Compared with state-of-the-art algorithms, the results of the experiment indicate that our method not only improves various objective indicators but also shows great advantages in visual effects.

Unlike geocoded images, slant-range (SR) synthetic aperture radar (SAR) images vary from imaging resolution to angles, which are difficult to be registered directly using the traditional SAR image registration methods. A possible way is to match their corresponding geocoded images and to project the correspondences to SR images. However, this way is time consuming and suffers from both registration and projection errors. In this letter, an automatic and efficient method is proposed to directly match multiview SR SAR images. We first estimate the scale and rotation differences between two SR images from the metadata delivered by vendors alongside the image file. Specifically, the scale differences of the range and azimuth directions are estimated by transforming the range and azimuth pixel intervals into a uniform geographical resolution, and the rotation differences are estimated by comparing the azimuth angles of an image-pair. A global-to-local framework is then implemented to accelerate the registration process. In the global stage, we fix the scale and rotation parameters in SAR-scale-invariant-feature-transform (SAR-SIFT) method to avoid mismatches. In the local stage, the phase correlation of cropped patches is parallelized to generate accurate matches. Experimental results on 13 multiview SAR images of the Omaha city show that the proposed method can provide accurate and efficient registration results for each pair of the 13 images, and outperforms the state-of-the-art methods both in accuracy and in efficiency.

The proliferation of synthetic aperture radar (SAR) imagery, its accessibility in open platforms like Google Earth Engine, and the development of automated classification and geophysical information extraction algorithms have prompted the need for understanding the role of incidence angle (IA) on radar scattering mechanism, backscatter intensity, and classification accuracy. This letter demonstrates the dependence of image texture parameters on SAR IA, using Arctic landfast sea ice samples extracted from C-band frequency Sentinel-1 SAR scenes collected during the winter period. Gray-level cooccurrence matrix (GLCM) derived texture parameters, and occurrence texture parameters, derived from undeformed first-year sea ice and multi-year sea ice, which are dominated by surface and volume scattering mechanisms, respectively, were analyzed. All GLCM texture parameters were found to be dependent on IA, highlighting the need for consideration of angular dependence in texture parameters, particularly in the development of image classification and inversion algorithms utilizing them. Occurrence texture parameters showed negligible influence by IA; however, feature discrimination capability was also lost. Some GLCM parameters had similar angular dependencies for both sea ice types, suggesting that, in some cases, global image normalization approaches for texture may be applied to account for the IA effect.

We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish to replace them by a new glyph that captures the information of the intersecting glyphs. We present a fully dynamic kinetic data structure that maintains a set of $n$ disjoint growing squares. Our data structure uses $O(n (\log n \log\log n)^2)$ space, supports queries in worst case $O(\log^3 n)$ time, and updates in $O(\log^7 n)$ amortized time. This leads to an $O(n\alpha(n)\log^7 n)$ time algorithm to solve the agglomerative clustering problem. This is a significant improvement over the current best $O(n^2)$ time algorithms., Comment: 14 pages, 7 figures

A $(m,n)$ sonar sequence is an $m\times n$ array with exactly one dot in each column and where all lines connecting two dots in the array are distinct as vectors. These arrays are known to have many applications such as sonar and radar detection and these are studied as a particular case of Golomb rectangles or two-dimensional Sidon sets. The main open problem for sonar sequences is: for fixed $m$ , find the largest $n$ for which there is an $(m,n)$ sonar sequence, these sequences are called the best sonar sequences. The extended sonar sequences are generalizations of sonar sequences where each column has at most one dot, the motivation to study these arrays are the best results obtained when applied to radar and sonar detection. In this paper, we give the best sonar sequences with $m\leq 100$ obtained from an exhaustive computational search based on the Caicedo, Ruiz and Trujillo constructions and we present new constructions of extended sonar sequences that use Sidon sets.

Images obtained in dim light do not clearly represent the target scene, limiting information transmission on the image carrier. This study proposes a texture‐preserving image enhancement method, i.e. ETPR. The proposed method draws the illumination map of a low light image by Max‐RGB, and then applies the weighted median filter algorithm and Retinex to improve the illumination map further. Then, the enhanced image is changed from RGB mode to YCbCr mode and the texture of the luminance component Y is described. It is achieved by denoising the texture of the image to be enhanced, and then the final enhanced image is obtained by the method of sub‐region image fusion denoising. The effectiveness of ETPR is established by comparing it with existing enhancement technologies using public data and real images.

Synthetic aperture radar (SAR) image registration is still a challenging task in remote sensing. The scale-invariant feature transform (SIFT) method and its extensions are most widely used feature detectors in SAR images. However, due to the presence of nonlinear speckle noise, some wrong features are chosen which directly influence the feature matching process. In this article, for the first time, the KAZE algorithm with a modified version of speeded-up robust features (SURF) descriptor is used for SAR image registration. It uses discrete stochastic second order nonlinear partial differential equations (PDEs) to model the SAR image's edge structure. KAZE uses nonlinear diffusion filtering to build up the scale levels of the SIFT descriptor. It preserves the edges while simultaneously decreasing the speckle noise in smoothing the image. Therefore, it captures the exact location of features in down-sampling and filtering stages of SIFT. Experimental results show that our proposed method has increased the localization accuracy and distinctiveness of feature extraction through the use of KAZE detector. Our method is also able to handle challenging cases in different image sources, different view angles, different image times, complex affine mapping, presence of blurring, and noise.

Due to the severe speckle noise and complex local deformation in synthetic aperture radar (SAR) images, robust pixelwise registration with high accuracy is an important problem but is far from being resolved. The core of this problem is how to establish a precise deformation field that maps every pixel to its corresponding pixel with high accuracy. To address this problem, a novel SAR dense-matching algorithm, which includes high-accuracy landmark generation and a precise deformation field parameter estimation, is proposed in this article. First, a strategy for generating enough well-distributed landmarks is proposed by designing patch matching of improved scale-invariant feature transform features based on phase correlation and the gradient method. Furthermore, a multiscale coherent point drift (MCPD), powered by iterative residual map minimization, is designed to reliably match landmarks and estimate precise field parameters. Both simulated deformed SAR images and real SAR images are utilized to evaluate the performance of the proposed method, and the experimental results demonstrate that the proposed method provides better registration performance than previous methods in terms of both accuracy and robustness.

Let $G$ be an additive group of order $v$ . A $k$ -element subset $D$ of $G$ is called a $(v, k, \lambda, t)$ -almost difference set if the expressions $g-h$ , for $g$ and $h$ in $D$ , represent $t$ of the non-identity elements in $G$ exactly $\lambda $ times and every other non-identity element $\lambda + 1$ times. Almost difference sets are highly sought after as they can be used to produce functions with optimal nonlinearity, cyclic codes, and sequences with three-level autocorrelation. A set of positive integers $A$ is called a Golomb ruler if the difference between two distinct elements of $A$ are different. In this paper, we use Singer type Golomb rulers to construct new families of almost difference sets. Additionally, we constructed 2-adesigns from these almost difference sets.

In this paper, we introduce projective inertial parallel subgradient extragradient-line algorithm for solving variational inequalites of L-Lipschitz continuous and monotone mappings which L is unknown. We prove a strong convergence result under some mild conditions in Hilbert space. We also present some numerical examples in Euclidean space R3 compared with Parallel-Viscosity-Type Subgradient Extragradient-Line Method. Finally, we deblur the Grey and RGB images from common types of blur matrixes Gaussian blur, Out of focus blur and Motion blur using our proposed algorithm and show the better efficeincy when the number of types of blur matrixes is large.

Publisher Copyright: Author We present design, simulation, and experimental characterization of dual-band frequency-diverse holograms for distributed beamforming. The holograms operate in the 50-75 GHz (WR-15) and 220-330 GHz (WR-3.4) bands for millimeter-and submillimeter-wave imaging. The holograms are designed to create a dispersive field in the region of interest (RoI) located 600 mm from the aperture. The holograms lie in the front end of an imaging setup and modulate the phase of the incident collimated beam from a parabolic mirror. The distributed beamforming enables interrogation of the RoI so that the measured reflection through the dispersive propagation path conveys the spatial information of the target. Different phase modulation schemes are evaluated, and two prototype holograms are manufactured. The dispersive operation and efficiency of the hologram are characterized with both simulations and measurements. The frequency diversity of the holograms is quantified using singular-value decomposition and spatial-spectral correlation coefficient methods. The results identified a design frequency of 120 GHz, a phase quantization step of π/2 radians, and an added phase of 1.9π radians as a good dispersion-efficiency compromise. A fully connected neural network is trained to localize a corner-cube reflector in the RoI illuminated by the hologram. The localization accuracy follows the diffraction-limited resolution and confirms the best performance for the hologram considered optimal in the design metrics.

In image processing, removal of speckle noise from a satellite image is a challenging task for the researchers. There are various approaches for speckle noise reduction. Generally, the speckle noises are scattered, in satellite images, medical images and synthetic aperture radar (SAR) images. This paper introduces a bidimensional empirical mode decomposition (BEMD)-based adaptive filtering method for despeckling of SAR image. The noisy SAR image is decomposed into different bidimensional intrinsic mode function (BIMF) levels using BEMD and then filtering is performed on the first BIMF level, as it contains the high-frequency noise component. This adaptation process effectively filters out the noisy image component without destroying the original image component. A BEMD-based adaptive Frost filter is introduced in this paper for despeckling of SAR images. The despeckling performances of our proposed filtering method are further analyzed by visual evaluation and also using performance parameters comparatively. Our reconstructed images show better performance quantitatively and qualitatively compared to other filters.

This letter proposes a Doppler through-wall radar (TWR) positioning method based on the Hough transform of the extended Bezier model. First, the Hough transform based on the extended Bezier model is used to extract the interested target components from received echoes and estimate their instantaneous frequency (IF). Next, the real-time position of the target is estimated according to the Doppler processing. To improve the adaptability of the algorithm to different target trajectories, especially to solve the problem of asymmetric curve fitting, the proposed extended Bezier model can approach the practical IF curve by dynamically adjusting two parameters, which can not only keep the relatively low computational complexity but also significantly improve the positioning accuracy. Moreover, the proposed algorithm effectively solves the problem of ``frequency ambiguity.'' The experimental results demonstrate and validate that the proposed algorithm is effective in the field of human sensing applications of Doppler radar.

A novel spatial singularity-exponent-domain multiresolution imaging (SSMRI) method is proposed in this article. It is aimed at improving the image processing ability for the single-channel synthetic aperture radar (SAR), thereby acquiring the robust image feature for SAR target detection at the very low SNR. Combining the 2-D singularity power spectrum (SPS) and the 2-D pseudo-Wigner-Ville distribution (PWVD), the SSMRI method is derived. Consequently, the single-channel SAR images are transformed to obtain spatial multiresolution SAR images with respect to the singularity exponent. Furthermore, the separability of the SAR image target in the space of the singularity exponent is analyzed, and the separability theorem in the sense of SSMRI is proved. In particular, under the background of GWN and fractal noise, the separability of SAR image targets based on SSMRI processing is studied. In addition, the stability and robustness of SSMRI-SAR feature extraction are demonstrated. On this basis, a maritime SAR ship target detection method based on SSMRI is put forward in the extremely low SNR condition. The experiment results on the SAR-Ship-Dataset indicate that the proposed method is superior in performance to the traditional CFAR or 2-D-SPS method. Especially when SNR =-30 dB, the detection performance with more than 99.4% can be achieved.

This letter presents a ground-penetrating radar (GPR) forward model on dispersive media based on parallel conformal symplectic Euler algorithm. We developed a symplectic Euler algorithm combined with conformal meshes and graphics processing unit (GPU) acceleration technology, which proved to be an accurate and effective method to simulating GPR electromagnetic wave propagation in dispersive media.

Polarimetric synthetic aperture radar (PolSAR) image classification plays an important role in the development of remote sensing image interpretation for the rich polarization information. Generative methods learn the statistical distribution characteristic of the scattered echoes data with heavy noise. However, it is tedious to design and solve different generative likelihood functions. Discriminative methods learn image features and classifier in an end-to-end framework whose classification performance is also limited without polarization statistical characteristics. In order to make full use of the statistical characteristic of PolSAR echoes and spatial feature of PolSAR image, a novel real-value hybrid generative/discriminative (HGD) deep network is proposed to learn statistical-spatial feature for PolSAR image classification with the data expressing ability of the generative term and the end-to-end learning ability of the discriminative term. First, a derived replacement form is obtained from the typical Wishart distribution of PolSAR data with an eigenvalue generative term. In this way, the complex-value form of PolSAR data converts into real-value expression, which makes the PolSAR image classification easy to understand and implement in the deep network. Finally, these two terms are integrated from the variational Bayesian theory with an alternative optimization equation derived for PolSAR image classification. It provides a normal framework for PolSAR multifeature learning. Experiments are tested on different PolSAR datasets compared with several state-of-the-art individual generative or discriminative methods. All visual experimental results and accuracy values demonstrate the superiority of the proposed method.

Different from the object motion blur, the defocus blur is caused by the limitation of the cameras' depth of field. The defocus amount can be characterized by the parameter of point spread function and thus forms a defocus map. In this paper, we propose a new network architecture called Defocus Image Deblurring Auxiliary Learning Net (DID-ANet), which is specifically designed for single image defocus deblurring by using defocus map estimation as auxiliary task to improve the deblurring result. To facilitate the training of the network, we build a novel and large-scale dataset for single image defocus deblurring, which contains the defocus images, the defocus maps and the all-sharp images. To the best of our knowledge, the new dataset is the first large-scale defocus deblurring dataset for training deep networks. Moreover, the experimental results demonstrate that the proposed DID-ANet outperforms the state-of-the-art methods for both tasks of defocus image deblurring and defocus map estimation, both quantitatively and qualitatively. The dataset, code, and model is available on GitHub: https://github.com/xytmhy/DID-ANet-Defocus-Deblurring.

Extracting quadrilateral layouts from surface triangulations is an important step in texture mapping, semi-structured quadrilateral meshing for traditional analysis and spline reconstruction for isogeometric analysis. Current methods struggle to yield high-quality layouts with appropriate connectivity between singular nodes (known as “extraordinary points” for spline representations) without resorting to either mixed-integer optimization or manual constraint prescription. The first of these is computationally expensive and comes with no guarantees, while the second is laborious and error-prone. In this work, we rigorously characterize curves in a quadrilateral layout up to homotopy type and use this information to quickly define high-quality connectivity constraints between singular nodes. The mathematical theory is accompanied by appropriate computational algorithms. The efficacy of the proposed method is demonstrated in generating quadrilateral layouts on the United States Army’s DEVCOM Generic Hull vehicle and parts of a bilinear quadrilateral finite element mesh (with some linear triangles) of a 1996 Dodge Neon.

In this paper we present a method to fit missing data – i.e., to fit a dataset containing a region in which no data are provided – by means of a C 1 -quadratic patch. Such a patch is constructed to faithfully extend the shape and the geometric features of the dataset. To this end, a mesh of curves gathering the information about the shape of the dataset will be considered and extended to the interior of the hole. Next, a (unique) patch fitting such a mesh of curves will be computed. Several numerical and graphical examples showing the effectiveness of the proposed method are provided.

We study valuated matroids, their tropical incidence relations, flag matroids and total positivity. This leads to a characterization of permutahedral subdivisions, namely subdivisions of regular permutahedra into generalized permutahedra. Further, we get a characterization of those subdivisions arising from positive valuated flag matroids., Comment: long version of extended abstract (FPSAC 2022, DMD 2022)

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when a sampled occluding contour is valid, that is, when it may be assigned consistent visibility. Previous methods do not guarantee these conditions, which helps explain why smooth contour visibility has been such a challenging problem in the past. The paper then proposes an algorithm that, given a subdivision surface, finds sampled contours satisfying these conditions, and then generates a new triangle mesh matching the given occluding contours. The contours of the output triangle mesh may then be rendered with standard non-photorealistic rendering algorithms, using the mesh for visibility computation. The method can be applied to any triangle mesh, by treating it as the base mesh of a subdivision surface., Accepted to ACM Transactions on Graphics (TOG)

Subdivision surface is a versatile tool for representing a smooth surface with any topology. This research explains how a smooth polyhedron surface is made using the Catmull-Clark subdivision method. The approach is based on the consideration of the regular topological entities of polyhedron on a cube. Construction is seen as a generalization of an arbitrary control point mesh recurrent subdivision algorithm. For faces, edges and arbitrary net points, the process uses the same expression that is formed in the cube. The process of the scheme will produce a smooth surface as the result. The important criteria for the construction also presented.

This work presents a novel approach for monocular dense Simultaneous Localization and Mapping. The surface to be estimated is represented as a piecewise planar surface, defined as a group of surfels each having as parameters its position and normal. These parameters are then directly estimated from the raw camera pixels measurements, by a Gauss-Newton iterative process. The representation of the surface as a group of surfels has several advantages. It allows the recovery of robust and accurate pixel depths, without the need to use a computationally demanding depth regularization schema. This has the further advantage of avoiding the use of a physically unlikely surface smoothness prior. New surfels can be correctly initialized from the information present in nearby surfels, avoiding also the need to use an expensive initialization routine commonly needed in Gauss-Newton methods. The method was written in the GLSL shading language, allowing the usage of GPU thus achieving real-time. The method was tested against several datasets, showing both its depth and normal estimation correctness, and its scene reconstruction quality. The results presented here showcase the usefulness of the more physically grounded piecewise planar scene depth prior, instead of the more commonly pixel depth independence and smoothness prior.

In the field of subdivision, the smoothness increases as the arity of schemes increases. The family of high arity schemes gives high smoothness comparative to low arity schemes. In this paper, we propose a simple and generalized formula for a family of multiparameter quaternary subdivision schemes. The conditions for convergence of subdivision schemes are also presented. Moreover, we derive subdivision schemes after substituting the different values of parameters. We also analyzed the important properties of the proposed family of subdivision schemes. After comparison with existing schemes, we analyze that the proposed family of subdivision schemes gives better smoothness and approximation compared with the existing subdivision schemes.

We present a sufficient condition for recovering unique texture and viewpoints from unknown orthographic projections of a flat texture process. We show that four observations are sufficient in general, and we characterize the ambiguous cases. The results are applicable to shape from texture and texture-based structure from motion.