Geometric Point Research Articles

Tuned hybrid nonuniform subdivision surfaces with optimal convergence rates

AbstractThis article presents an enhanced version of our previous work, hybrid nonuniform subdivision (HNUS) surfaces, to achieve optimal convergence rates in isogeometric analysis (IGA). We introduce a parameter () to control the rate of shrinkage of irregular regions, so the method is called tuned hybrid nonuniform subdivision (tHNUS). Thus, HUNS is a special case of tHNUS when . While introducing in hybrid subdivision significantly complicates the theoretical proof of G1 continuity around extraordinary vertices, reducing can recover optimal convergence rates when tHNUS functions are used as a basis in IGA. From the geometric point of view, tHNUS retains comparable shape quality as HNUS under nonuniform parameterization. Its basis functions are refinable and the geometric mapping stays invariant during refinement. Moreover, we prove that a tHNUS surface is globally G1‐continuous. From the analysis point of view, tHNUS basis functions form a nonnegative partition of unity, are globally linearly independent, and their spline spaces are nested. In the end, we numerically demonstrate that tHNUS basis functions can achieve optimal convergence rates for the Poisson's problem with nonuniform parameterization around extraordinary vertices.

On Curvature and Torsion in Courant Algebroids

We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly restrict to Dirac structures. Depending on an auxiliary affine connection K, we introduce the K-curvature and K-torsion of a Courant algebroid connection. These are conventional tensors on the body. Finally, we compute their Ricci and scalar curvature.

A new geometrical perspective on Bohr-equivalence of exponential polynomials

Based on Bohr’s equivalence relation for general Dirichlet series, in this paper we connect the families of equivalent exponential polynomials with a geometrical point of view related to lines in crystal-like structures. In particular we characterize this equivalence relation, and give an alternative proof of Bochner’s property referring to these functions, through this new geometrical perspective.

Age prediction based on a small number of facial landmarks and texture features.

BACKGROUND:Age is an essential feature of people, so the study of facial aging should have particular significance.OBJECTIVE:The purpose of this study is to improve the performance of age prediction by combining facial landmarks and texture features.METHODS:We first measure the distribution of each texture feature. From a geometric point of view, facial feature points will change with age, so it is essential to study facial feature points. We annotate the facial feature points, label the corresponding feature point coordinates, and then use the coordinates of feature points and texture features to predict the age.RESULTS: We use the Support Vector Machine regression prediction method to predict the age based on the extracted texture features and landmarks. Compared with facial texture features, the prediction results based on facial landmarks are better. This suggests that the facial morphological features contained in facial landmarks can reflect facial age better than facial texture features. Combined with facial landmarks and texture features, the performance of age prediction can be improved.CONCLUSIONS:According to the experimental results, we can conclude that texture features combined with facial landmarks are useful for age prediction.

Análise hidrogeomorfométrica da microbacia do rio Mutum: informações para auxiliar o manejo de recursos hídricos na Amazônia Ocidental

O desenvolvimento sustentável de sistemas agropecuários tem como base o planejamento e a gestão dos recursos naturais, logo, é essencial conhecer as características da paisagem. Em face ao exposto, o presente trabalho tem como objetivo fornecer informações sobre as características hidrogeomorfométricas da microbacia do rio Mutum. A análise da paisagem foi realizada com os softwares Google Earth, QGIS e TrackMaker Free, imagens altimétricas dos satélites Alos, e dados da literatura. A microbacia tem área de 8,64 km2, perímetro de 15,26 km, formata alongada e baixa a média suscetibilidade a inundações (ponto de vista geométrico), altitudes de 228 a 322 m, predominância de relevos suave ondulado (50,81%) e ondulado (30,67%), 92,93% de sua área com baixa propensão a influência a propagação de incêndios e 92,94% apta à extremamente apta a mecanização agrícola, rede de drenagem de 17,30 km com padrão dendrítico de 4ª ordem, densidades de nascentes média, densidade de drenagem média, coeficiente de manutenção de 499,4 m2 m-1, canal principal reto e baixo tempo de concentração. A microbacia tem potencial para o desenvolvimento agropecuário, no entanto, a adoção de práticas de manejo conservacionista do solo é necessário para mitigar os impactos desta atividade no meio ambiente. É recomendado o estudo da dinâmica temporal e espacial da cobertura do solo, para analisar a qualidade e a quantidade de vegetação nativa na microbacia, e assim, delimitar áreas prioritárias para a manutenção e/ou recuperação dessa vegetação.

Características hidrogeomorfométricas da microbacia Três Galhos, Amazônia Ocidental, Brasil

A aquisição de informações sobre as características da paisagem é essencial para o planejamento de uso e conservação dos recursos naturais. Em face ao exposto, o presente estudo tem como objetivo disponibilizar informações geométricas, topográficas e hidrográficas da microbacia do rio Três Galhos. Para a aquisição das informações foram utilizados softwares (QGIS, Google Earth e TrackMaker Free), imagens altimétricas (satélite ALOS) e equações, e para a discussão dos resultados foram utilizados dados da literatura. A microbacia do rio Três Galhos tem área de 23,24 km2, perímetro de 26,13 km, forma alongada, baixa suscetibilidade a inundações (ponto de vista geométrico), altitudes de 247 a 444 m, predominância do relevo suave ondulado (45,1%), rede de drenagem de 91,33 km, padrão dendrítico, 6ª ordem de drenagem (elevada condição para habitação de peixes), 12,62 nascentes km-2 (alta), densidade de drenagem de 3,93 km km-2 (muito alta), índice de sinuosidade de 39,94% (canal principal sinuoso), coeficiente de manutenção de 254,5 m2 m-1 e tempo de concentração de 2,28 h (baixo). Portanto, as informações obtidas da microbacia do rio Três Galhos, podem auxiliar no planejamento e gestão dos recursos naturais na região, através de instituições (públicas e privadas) e proprietários de imóveis rurais, possibilitando a manutenção ou melhoria da qualidade de vida das gerações atuais e futuras.

Seismic assessment of a reconstructed historic masonry structure: A case study on the ruins of Bigali castle mosque built in the early 1800s

Architectural and cultural heritage structures that have provided important services in the past may lose their functions over time and become out of service due to possible reasons. The loss of the structural integrity in these structures is mostly connected to the material damages due to long-term exposure to environmental conditions and human intervention. Despite the negative period that these structures have been faced with since they are out of service, they need to be protected due to their historical importance and cultural identity. Therefore, the survival of the heritage of these structures can be possible through on-site observations and subsequent analysis and restoration/reconstruction process. This paper focuses on the seismic assessment of a reconstructed historic ruined mosque located in a castle constructed between 1807 and 1820. The study consists of four stages: on-site examinations, laboratory tests, reconstruction process and seismic performance analyses of the examined structure. The field study involves the visual inspection of structural deterioration and gathering of representative samples from various parts of the structure. The laboratory study includes mechanical, chemical and mineralogical analyses of the samples obtained from the structure. Reconstruction process of the mosque considering its original form are presented in the third stage. Finally, the seismic performance level of the structure against seismic effects is determined by performing linear, pushover and kinematic analyses. The presentation of the processes within this study on the reconstruction of the structural integrity of a historic structure that has suffered from deterioration over time into its original form will add valuable information to the literature. The adopted methodology and presented findings can be used as a guide for similar studies from a geometric and material point of view. All of the essential steps used for the reconstruction of the originality of the structure including obtaining the data related to the history of the structure, field studies, laboratory tests, numerical analyses, and the stages of the reconstruction process are presented on an example case study.

IoT based Smart Grid Attack Resistance in AC and DC State Estimation

Use of automation and intelligence in smart grids has led to implementation in a number of applications. When internet of things is incorporated it will result in the significant improvement a number of factors such as fault recovery, energy delivery efficiency, demand response and reliability. However, the collaboration of internet of things and smart grid gives rise to a number of security issues and threats. This is especially the case when using internet based protocols and public communication infrastructure. To address these issues we should ensure that the data stored is secure and critical information from the data is extracted in a careful manner. If any threat to its security is detective an early blackout warning should be issued immediately. In this paper we have proposed a geometric view point for big data attacks which is capable of bypassing bad data detection. We have created an environment where replay scheme is used launch blind energy big data attack. The defence mechanism of our proposed work is studied and found to be efficient. Experimental evidence supports our theory and we have found our methodology to efficiently improve error detection rate.

Razlike u brzini šuta između pozicija šuta u vrhunskom rukometu

Shooting velocity is one of the most important features that influence successful shooting performance in handball. Therefore, the aim of this study was to determine differences in shooting velocity between shooting positions in top level handball. A total of 784 shots were analyzed. Shooting velocity was measured with iBall (SELECT, Denmark), that has a built-in chip for tracking and distributing data in real time regarding ball velocity, shot detection, shot position and the position of the ball in the goal (Kinexon, Germany). Shooting position (SP) is defined as a geometrical point and a tactical situation from which a shot was taken. Differences between shooting positions were calculated using the Kruskal-Wallis test. Significant difference in shooting velocity was noticed between shooting positions (Chi-Square=95.83). Post-hoc analysis revealed that shots executed outside the nine meter perimeter are significantly faster than from other shooting positions. Shots taken outside the 9-meter perimeter require the fastest shots since players cannot outsmart goalkeepers with modified slow shots (e.g. lob shot, shot with rotation or "dry leaf" shot). Modified slow shots are commonly used in closer distance shots like wing shot, fast break shot, breakthrough shot or penalty shot. In these situations, players have more demanding angle in which shooting velocity is not always an advantage.

Scene Semantic Recognition Based on Modified Fuzzy C-Mean and Maximum Entropy Using Object-to-Object Relations

With advances in machine vision systems (e.g., artificial eye, unmanned aerial vehicles, surveillance monitoring) scene semantic recognition (SSR) technology has attracted much attention due to its related applications such as autonomous driving, tourist navigation, intelligent traffic and remote aerial sensing. Although tremendous progress has been made in visual interpretation, several challenges remain (i.e., dynamic backgrounds, occlusion, lack of labeled data, changes in illumination, direction, and size). Therefore, we have proposed a novel SSR framework that intelligently segments the locations of objects, generates a novel Bag of Features, and recognizes scenes via Maximum Entropy. First, denoising and smoothing are applied on scene data. Second, modified Fuzzy C-Means integrates with super-pixels and Random Forest for the segmentation of objects. Third, these segmented objects are used to extract a novel Bag of Features that concatenate different blobs, multiple orientations, Fourier transform and geometrical points over the objects. An Artificial Neural Network recognizes the multiple objects using the different patterns of objects. Finally, labels are estimated via Maximum Entropy model. During experimental evaluation, our proposed system illustrated a remarkable mean accuracy rate of 90.07% over the MSRC dataset and 89.26% over the Caltech 101 for object recognition, and 93.53% over the Pascal-VOC12 dataset for scene recognition, respectively. The proposed system should be applicable to various emerging technologies, such as augmented reality, to represent the real-world environment for military training and engineering design, as well as for entertainment, artificial eyes for visually impaired people and traffic monitoring to avoid congestion or road accidents.

Automatic Road Extraction From Remote Sensing Imagery Using Ensemble Learning and Postprocessing

High-resolution satellite images contain valuable road semantic information, but the occlusion of vegetation and buildings and the sparse distribution and heterogeneous appearance of roads limit the accuracy of road extraction models. In this article, we propose a novel method for extracting roads using an ensemble learning model with a postprocessing stage. The network weights and biases of our proposed deep learning model are transmitted through the random combination of layers of different submodels during forward and backward propagation. In the gradient descent process, a superior loss function is designed to solve the problem of class imbalance caused by road sparseness, and more attention is given to hard classification samples to extract narrow and covered roads. In addition, we solve road disconnection issues in the results obtained with the neural network by extracting and analyzing the geometric structures and feature points of the roads. Experiments on two challenging datasets of remote sensing imagery show that the proposed method performs better than other models and can extract road information from complex scenes.

Aromatic nature of neutral and dianionic 1,4-diaza-2,3,5,6-tetraborinine derivatives.

The aromatically relevant parameters of boron-rich inorganic benzenes—neutral and dianionic 1,4-diaza-2,3,5,6-tetraborinine derivatives (B4N2R6)—have been computationally estimated and evaluated from geometric, electronic, magnetic, and energetic points of view. The majority of the criteria (ASE, NICSzz, ELF, and PDI) indicate that the aromaticity of the neutral B4N2 benzene analogue stabilized by Lewis bases lies in between those of benzene and borazine. On the other hand, the aromaticity of the dianionic B4N2 benzene analogue 4′ is controversial. The pronounced aromatic nature of 4′ is supported by ELFπ, PDI, and NICSπzz, but ASE, the FiPC-NICS plot, and ACID oppose this. These data confirm that even with the same B4N2-skeletal framework of a 6π-system, the aromatic feature varies depending on the overall charge of the B4N2 systems.

Geometric conditions for injectivity of 3D Bézier volumes

<abstract><p>The one-to-one property of injectivity is a crucial concept in computer-aided design, geometry, and graphics. The injectivity of curves (or surfaces or volumes) means that there is no self-intersection in the curves (or surfaces or volumes) and their images or deformation models. Bézier volumes are a special class of Bézier polytope in which the lattice polytope equals $ \Box_{m, n, l}, (m, n, l\in Z) $. Piecewise 3D Bézier volumes have a wide range of applications in deformation models, such as for face mesh deformation. The injectivity of 3D Bézier volumes means that there is no self-intersection. In this paper, we consider the injectivity conditions of 3D Bézier volumes from a geometric point of view. We prove that a 3D Bézier volume is injective for any positive weight if and only if its control points set is compatible. An algorithm for checking the injectivity of 3D Bézier volumes is proposed, and several explicit examples are presented.</p></abstract>

TRAVELING WAVE SOLUTIONS OF TWO TYPES OF GENERALIZED BREAKING SOLITON EQUATIONS

<abstract> In this paper, the bifurcation theory of dynamical system is applied to study traveling waves of two types of generalized breaking soliton (GBS) equations which include many famous partial differential equation models. Without any parameter constraints, we investigate their traveling wave systems in detail from the geometric point of view. Due to the existence of a two dimensional invariant manifold, all bounded and unbounded orbits are identified and studied in different parameter bifurcation sets. Furthermore, by calculating complicated elliptic integrals along these orbits, we obtain exact expressions of all possible single wave solutions of two types of GBS equations. </abstract>

Оценка фрактальной размерности поверхности разрушения образцов горных пород

An approach to estimate fractal dimension of a microphotograph of rock sample fracture surface using the Differential Box Counting (DBC) method is presented. The difference between this algorithm and the classical method for fractal dimension calculation is in that the grayscale levels of pixels of analyzed image are taken into account. This approach does not require initial binarization of the image, which is poorly applicable for estimation of fractal dimension of real objects, such as microphotographs of rock sample surface, which in turn does not lead to the loss of useful information. Testing the method on a set of images generated with different content of pixels of gray levels showed that there is a steady increase in fractal dimension values with increase in the number of added pixels. It is shown that fractal dimension for a set of images simulating crack propagation also demonstrates growth with increasing of fracturing. From a geometric point of view, this feature is a consequence of increase of roughness of the surface, which is a set of rectangles, the height of which corresponds to gray level of pixels of analyzed image. This approach can be used to quantify changes in sample surface structure before and after load action, as well as in real time using high-speed photography of the sample surface or radioscopy of internal cracks. Keywords: fractal analysis, fractal dimension, differential box-counting, fracture surface.

Dimensionality Reduction of Spectral Reflectance by Dividing the Error Space of Principal Component Analysis

A method based on the error space division of principal component analysis (PCA) is proposed to improve both the spectral and colorimetric reconstruction accuracy in spectral dimensionality reduction. Founded on the error source analysis of PCA from a geometric point of view, an objective function minimizing the within-cluster spectral reconstruction error is established to divide the error space of PCA. PCA is implemented again to each divided cluster to reduce the dimensionality of spectral reflectance. The proposed method, error-space-divided PCA (ESDPCA), is tested using four different spectral datasets. The root mean squared error (RMSE) and CIEDE2000 colour difference are adopted as the spectral and colorimetric evaluation metric respectively. Statistical results indicate that ESDPCA can outperform PCA by at least one principal component (PC) in colorimetric accuracy, while it can outperform PCA by at least two or three PCs in spectral accuracy. Comparisons with other three representative methods (i.e., LabPQR, LabRGB, and XYZLMS) show that ESDPCA outperforms them both in spectral and colorimetric accuracy significantly. In addition, the proposed method is robust for spectral datasets and compatible with few other methods involving PCA. Moreover, the computation complexity of ESPCA has the same order of magnitude as that of PCA.

Resistance spot welding particularities of the nickel alloy Nimonic 80 A

The resistance spot welding of nickel Nimonic80 A alloy is a critical welding technology for components manufacturing for nuclear (for construction elements with not subject to irradiation) and aeronautic industry. The present paper highlights the effect of base welding process parameters (welding current, welding time, electrode force) on the geometrical characteristics of the weld nugget. From geometrical point of view, the size of the fusion area beside the interface of the two sheets and the electrode indentation depth are key factors for controlling the welded nugget geometry. Joining of sheets with 1.6 mm width, by applying a force of 450 daN, a current of 6000 A and a welding time of 0.3–0.4 s, provides an optimal size of the fusion area and of the electrode indentation depth.

Hyper-Laplacian Regularized Multi-View Subspace Clustering With a New Weighted Tensor Nuclear Norm

In this paper, we present a hyper-Laplacian regularized method WHLR-MSC with a new weighted tensor nuclear norm for multi-view subspace clustering. Specifically, we firstly stack the subspace representation matrices of the different views into a tensor, which neatly captures the higher-order correlations between the different views. Secondly, in order to make all the singular values have different contributions in tensor nuclear norm based on tensor-Singular Value Decomposition (t-SVD), we use weighted tensor nuclear norm to constrain the constructed tensor, which can obtain the class discrimination information of the sample distribution more accurately. Third, from a geometric point of view, the data are usually sampled from a low-dimensional manifold embedded in a high-dimensional ambient space, the WHLR-MSC model uses hyper-Laplacian graph regularization to capture the local geometric structure of the data. An effective algorithm for solving the optimization problem of WHLR-MSC model is proposed. Extensive experiments on five benchmark image datasets show the effectiveness of our proposed WHLR-MSC method.

A Novel 3D LiDAR SLAM Based on Directed Geometry Point and Sparse Frame

Simultaneous localization and mapping is an indispensable yet challenging direction for mobile robots. Attracted by 3D LiDAR with accurate depth information and robustness to illumination variations, many 3D LiDAR SLAM methods based on scan-to-map matching have been developed. However, there is a critical issue of existing approaches, where a large and dense map is generally required to achieve satisfactory localization accuracy, leading to low efficiency of scan-to-map matching. To solve this problem, in this letter, we propose a novel 3D LiDAR SLAM based on directed geometry point (DGP) and sparse frame. The former is used to provide a sparse distribution of points in the spatial dimension and the latter gives rise to a sparse distribution of frames in the temporal sequence. The sparsity of points and frames impove the efficiency of 3D LiDAR SLAM, and the strict data association based on directed geometric points also brings in good accuracy of pose estimation. To compensate the accuracy loss of the localization and mapping caused by frame sparsity, point propagation is proposed to improve the quality of directed geometric points in the map and the accuracy of scan-to-map matching. Also, loop detection and pose graph optimization are conducted for global consistency. The experimental results demonstrate the effectiveness of the proposed method in terms of accuracy and efficiency.

Small-Time Local Controllability of Switched Nonlinear Systems

This article considers the small-time local controllability (STLC) of switched nonlinear systems (SNSs). First, the original SNS is associated with a nilpotent Lie algebra, on which the solutions of the SNS are approximated by the hybrid Lie power series. Second, the concepts of high-order control variations and bad Lie brackets are defined for SNSs from a geometrical point of view. This helps to establish a new high-order sufficient STLC condition that is closely related to “neutralized” bad Lie brackets. Finally, it is shown that the obtained general condition is compatible with the existing controllability conditions of switched linear systems and nonswitched linear and nonlinear systems.