Convolutional solutions of partial difference equations

A significant part of the theory of one-dimensional linear shift-invariant systems is based on the concept of weighting function (or impulse response): the output is the convolution of the weighting function with the input. This paper introduces the concept of linear translation-invariant systems and uses this notion in studying impulse response, z-transforms, and transfer functions for multidimensional systems.     

A combination of differential equations and convolution in understanding the spread of an epidemic

Nonlinear dynamical method of projecting the transmission of an epidemic is accurate if the input parameters and initial value variables are reliable. Here, such a model is proposed for predicting an epidemic. A method to supplement two variables and two parameters for this proposed model is demonstrated through a robust statistical approach. The method described here worked well in case of three continuous distributions. Model predictions could be lower estimates due to under-reporting of disease cases. Anad hoc procedure with a technical note is provided in the appendix An earlier version of this paper was presented at the annual conference of the Indian Society for Mathematical Modelling & Computer Simulation, Bangalore, November 14–15, 2002     

Multi-Scale Dilated Convolutional Neural Network for Hyperspectral Image Classification

基于多尺度空洞卷积神经网络的高光谱图像分类

郑姗姗¹,刘文¹,单锐¹,赵静一²,江国乾³,张智⁴

（1. 燕山大学理学院,河北 秦皇岛 066004;2. 燕山大学机械工程学院,河北 秦皇岛 066004;3. 燕山大学电气工程学院,河北 秦皇岛 066004;4. 北京航天研究所,北京 100094）

创新点说明：

1）将图像分割方法——空洞卷积用于卷积神经网络进行高光谱图像分类,提取更加广泛、抽象的图像特征。

2）构建基于多尺度空洞卷积神经网络的高光谱图像分类方法。搭建多尺度聚合结构,在每个通道中使用快捷连接和空洞卷积结构,有效提取图像特征,避免信息丢失。

研究目的：

针对图像信息丢失问题,得到高精度的高光谱图像分类方法。

研究方法：

在Indian Pines和Pavia University数据集上,与4个已有的高光谱图像分类方法进行对比实验,比较OA, AA和Kappa值。

研究结果：

多尺度空洞卷积神经网络在Indian Pines和Pavia University数据集上OA值分别达到了99.58%,99.92%。AA值分别达到了99.57%,99.90%。Kappa分别达到了99.52%,99.89%。

结论：

1）在卷积神经网络中引入空洞卷积,可以有效避免图像信息丢失。

2）多尺度空洞卷积神经网络能提取更佳的判别性特征,实现高分类性能。

关键词：多尺度聚合;空洞卷积;高光谱图像分类;快捷连接

     

基于多任务卷积神经网络的虹膜图像质量评估方法

为了自动、准确、高效地评估采集图像的质量,设计了一个名为MTIQA的卷积神经网络。该网络能够输出与主观评价指标保持较高一致性的客观评估结果。MTIQA采用多任务学习策略,包含网络训练质量评估和失真类型分类两个任务,将两个任务的损失融合并构成新的损失函数。为了评估算法所得到的客观指标的可靠性,建立了名为SIR2019的单眼虹膜质量评估数据集,并召集志愿者进行主观实验以得到主观评价指标。在SIR2019和CASIA-Iris-Distance-Lamp数据集上的实验结果表明,该网络在虹膜图像质量评估上具有较好的可行性、准确性和鲁棒性。     

基于模糊梯度卷积核的在线棒材断面中心识别

针对传动带上严重堆叠、形状尺寸不规则的棒材,提出基于模糊梯度卷积核的在线棒材断面中心识别方法.以标准圆边缘为中心环,结合棒材断面边缘点偏离中心环的程度定义一个模糊梯度卷积核;通过模糊梯度卷积核与实时棒材断面梯度图像的卷积操作,实现棒材断面中心的增强;依次执行候选点选取、局部峰值抑制、距离检测步骤确定中心位置.实验结果表明,该方法能有效抑制棒材中心增强过程中易产生的峰值扩散现象,减少误识别和漏识别;平均计算时间为8.3 ms,满足系统实时性要求.     

Continuous Self‐Collision Detection for Deformable Surfaces Interacting with Solid Models

In this paper, we propose a new continuous self‐collision detection (CSCD) method for a deformable surface that interacts with a simple solid model. The method is developed based on the radial‐view‐based culling method. Our method is suitable for the deformable surface that has large contact region with the solid model. The deformable surface may consist of small round‐shaped holes. At the pre‐processing stage, the holes of the deformable surface are filled with ghost triangles so as to make the mesh of the deformable surface watertight. An observer primitive (i.e. a point or a line segment) is computed so that it lies inside the solid model. At the runtime stage, the orientations of triangles with respect to the observer primitive are evaluated. The collision status of the deformable surface is then determined. We evaluated our method for several animations including virtual garments. Experimental results show that our method improves the process of CSCD.     

Robust Treatment of Degenerate Elements in Interactive Corotational FEM Simulations

We address the problem of robust and efficient treatment of element collapse and inversion in corotational FEM simulations of deformable objects in two and three dimensions, and show that existing degeneration treatment methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new method that avoids such flaws, yields faster and smoother degeneration recovery and extends the range of well‐behaved degenerate configurations without adding significant complexity or computational cost to standard explicit and quasi‐implicit solvers.     

一类分数阶微分方程组的L^p稳定性

讨论了一类分数阶微分方程组的L^p稳定性,给出了分数阶微分方程组在有限时间情况下L^p稳定的充分条件,其主要是利用了一类特殊卷积的性质．     

面向交通流量预测的多头注意力时空卷积图网络模型

为了充分获取交通流量数据中隐藏的复杂动态时空相关性,提高交通流量预测精度,提出一种多头注意力时空卷积图网络模型MASCGN。首先,采用多头注意力机制为路网中的交通传感器节点自动分配注意力权重,实现对不同邻居节点的权值自适应匹配,充分获取空间相关性;其次,采用带有门控和注意力机制的时空卷积网络充分提取时间序列相关性,并使用残差块结构实现时空卷积层之间的连接,使得模型更具有泛化能力;最后,分别提取周相关、日相关、邻近时间的序列数据,输入三个并行的时空组件以挖掘周、日、邻近三个时间窗口间的时间周期相关性,并通过全连接层获取最终的交通流量预测结果。利用高速公路交通数据集PEMSO4、PEMSO8进行了15 min、30 min、45 min和60 min的交通流量预测实验。实验结果表明MASCGN模型与现有基线模型相比,在未来短期和长期的交通流量预测任务上都具有更优的建模能力。