Subdivision based isogeometric analysis for geometric flows

We present a new isogeometric analysis (IGA) approach based on extended Loop subdivision scheme for solving various geometric flows defined on subdivision surfaces. The studied flows include the second-order, fourth-order, and sixth-order geometric flows, such as averaged mean curvature flow, constant mean curvature flow, and minimal mean-curvature-variation flow, which are generally derived by minimizing the associate energy functionals with $L^2$-gradient flow respectively. The geometric flows are discretized by means of subdivision based IGA, where the finite element space is formulated by the limit form of the extended Loop subdivision for different initial control meshes. The basis functions, consisting of quartic box-splines corresponding to each subdivided control mesh, are utilized to represent the geometry exactly. For the cases of the evolution of open surfaces with any shape boundary, high-order continuous boundary conditions derived from the mixed variational forms of the geometric flows should be implemented to be consistent with the isogeometric concept. For time discretization, we adopt an adaptive semi-implicit Euler scheme. By several numerical experiments, we study the convergence behaviors of the proposed approach for solving the geometric flows with high-order boundary conditions. Moreover, the numerical results also show the accuracy and efficiency of the proposed method.     

Multicriteria decision-making using Archimedean aggregation operators in Pythagorean hesitant fuzzy environment

In multicriteria decision-making (MCDM), the existing aggregation operators are mostly based on algebraic t-conorm and t-norm. But, Archimedean t-conorms and t-norms are the generalized forms of t-conorms and t-norms which include algebraic, Einstein, Hamacher, Frank, and other types of t-conorms and t-norms. From that view point, in this paper the concepts of Archimedean t-conorm and t-norm are introduced to aggregate Pythagorean hesitant fuzzy information. Some new operational laws for Pythagorean hesitant fuzzy numbers based on Archimedean t-conorm and t-norm have been proposed. Using those operational laws, Archimedean t-conorm and t-norm-based Pythagorean hesitant fuzzy weighted averaging operator and weighted geometric operator are developed. Some of their desirable properties have also been investigated. Afterwards, these operators are applied to solve MCDM problems in Pythagorean hesitant fuzzy environment. The developed Archimedean aggregation operators are also applicable in Pythagorean fuzzy contexts also. To demonstrate the validity, practicality, and effectiveness of the proposed method, a practical problem is considered, solved, and compared with other existing method.     

Copy-move forgery detection of duplicated objects using accurate PCET moments and morphological operators

This paper presents a new method for copy-move forgery detection of duplicated objects. A bounding rectangle is drawn around the detected object to form a sub-image. Morphological operator is used to remove the unnecessary small objects. Highly accurate polar complex exponential transform moments are used as features for the detected objects. Euclidian distance and correlation coefficient between the feature vectors are calculated and used for searching the similar objects. A set of 20 forged images with duplicated objects is carefully selected from previously published works. Additional 80 non-forged images are edited by the authors and forged by duplicating different kinds of objects. Numerical simulation is performed where the results show that the proposed method successfully detect different kinds of duplicated objects. The proposed method is much faster than the previously existing methods. Also, it exhibits high robustness to various attacks such as additive white Gaussian noise, JPEG compression, rotation, and scaling.     

ZerNet: Convolutional Neural Networks on Arbitrary Surfaces Via Zernike Local Tangent Space Estimation

In this paper, we propose a novel formulation extending convolutional neural networks (CNN) to arbitrary two-dimensional manifolds using orthogonal basis functions called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific trends and phenomena, where accurate numerical quantification of geometric features is critical. Recently, CNNs have demonstrated a substantial improvement in extracting and codifying geometric features. However, the progress is mostly centred around computer vision and its applications where an inherent grid-like data representation is naturally present. In contrast, many geometry processing problems deal with curved surfaces and the application of CNNs is not trivial due to the lack of canonical grid-like representation, the absence of globally consistent orientation and the incompatible local discretizations. In this paper, we show that the Zernike polynomials allow rigourous yet practical mathematical generalization of CNNs to arbitrary surfaces. We prove that the convolution of two functions can be represented as a simple dot product between Zernike coefficients and the rotation of a convolution kernel is essentially a set of 2 × 2 rotation matrices applied to the coefficients. The key contribution of this work is in such a computationally efficient but rigorous generalization of the major CNN building blocks.     

立体几何褶皱织物的成型与织造

为拓宽立体几何褶皱织物的设计思路,设计具有立体几何效果的褶皱织物,对立体几何褶皱织物的成型原理进行了研究和探讨。提出了在二维织物面料铺设折叠线,形成一定规律的几何图案,并将几何图案按折叠线划分成上凸折叠区、下凹折叠区及非折叠区,在不同折叠区填充不同组织并以弹性纱和非弹性纱交替引纬,以此作为设计立体几何褶皱织物的基础。结果显示:设计好几何图案,选择不同的纬二重组织填充不同折叠区域,选用蚕丝为经纱、涤纶低弹丝与氨纶丝包覆的弹力丝与涤纶全拉丝为纬纱进行织造,所得的织物能形成具有明显立体几何形状的褶皱。     

符合阿贝原则的数控机床几何误差建模

为提高现有数控机床空间误差分析方法的准确度,本文基于阿贝原则对齐次转换矩阵(HTM)几何误差补偿模型进行优化。首先,推导出XYFZ型三轴机床适用的HTM几何误差补偿模型并给出模型正确使用的前提条件;然后,基于阿贝原则分析了三轴机床的空间误差传递机理,指出阿贝误差对机床定位精度的影响,给出理论计算公式并在机床运动轴上进行实验验证;最后,基于阿贝原则和布莱恩原则对现有的HTM几何误差补偿模型进行优化,采用该模型拟合体对角线空间误差,并与实测机床体对角线误差进行对比验证。现有HTM几何补偿模型可将机床空间误差由41.15μm补偿至16.37μm,补偿率为60.22%;优化后的补偿模型可将机床空间误差补偿至5.32μm,补偿率为87.07%,提高了26.85%。实验结果表明,优化后的补偿模型更加合理,进一步改善了空间误差的补偿精度。     

Reduction of sidelobe levels in multicarrier radar signals via the fusion of hill patterns and geometric progression

Multi-carrier waveforms have several advantages over single-carrier waveforms for radar communication. Employing multi-carrier complementary phase-coded (MCPC) waveforms in radar applications has recently attracted significant attention. MCPC radar signals take advantage of orthogonal frequency division multiplexing properties, and several authors have explored the use of MCPC signals and the difficulties associated with their implementation. The sidelobe level and peak-to-mean-envelope-power ratio (PMEPR) are the key issues that must be addressed to improve the performance of radar signals. We propose a scheme that applies pattern-based scaling and geometric progression methods to enhance sidelobe and PMEPR levels in MCPC radar signals. Numerical results demonstrate the improvement of sidelobe and PMEPR levels in the proposed scheme. Additionally, autocorrelations are obtained and analyzed by applying the proposed scheme in extensive simulation experiments.     

基于几何相位的线偏振聚焦超表面器件

设计出基于几何相位的介质超表面实现线偏振光聚焦功能。该设计打破了传统设计中几何相位(Pancharatnam-Berry phase)的手性限制,不再是局限于左旋圆偏振光(LCP)和右旋圆偏振光(RCP)入射。通过有限时域差分仿真来证明这种线偏振聚焦相位调控的特性。该类功能器件可能用于设计新颖的THz元器件、高分辨成像、功能探测等方面。     

基于敏感度分析的机床关键几何误差元素辨识与评定

为了正确识别和判定机床关键几何误差元素对机床精度设计的影响,以PCV-620立式加工中心为研究对象,采用多体系统理论建立机床空间误差模型,从而得到机床几何误差元素与机床精度之间的关联函数。对空间误差模型进行灵敏度分析,获得机床各运动方向的局部灵敏度系数,完成机床关键几何误差元素的初步辨识。以局部灵敏度系数为基础,提出一种与局部灵敏度系数和工作空间中任意位置处的几何误差元素值相关的全局灵敏度系数计算方法,将其作为机床关键几何误差元素的辨识和评定标准,分析得到PCV-620立式加工中心的关键几何误差元素包含3项定位误差、3项垂直度误差和5项直线度误差。