The arithmetic fourier transform and the visual pathway

The Arithmetic Fourier Transform is an algorithm for the computation of Fourier coefficients. In this paper it is extended to the computation of double Fourier coefficients by a repeated sum. We discuss the relevance of the repeated sum algorithm to signal processing by neurons in the visual pathway.     

Learning to See: Making Sense of the Mathematics of Change in Middle School

In this article, we will describe the results of a study of 6th grade students learning about the mathematics of change. The students in this study worked with software environments for the computer and the graphing calculator that included a simulation of a moving elevator, linked to a graph of its velocity vs. time. We will describe how the students and their teacher negotiated the mathematical meanings of these representations, in interaction with the software and other representational tools available in the classroom. The class developed ways of selectively attending to specific features of stacks of centimeter cubes, hand-drawn graphs, and graphs (labeled velocity vs. time) on the computer screen. In addition, the class became adept at imagining the motions that corresponded to various velocity vs. time graphs. In this article, we describe this development as a process of learning to see mathematical representations of motion. The main question this article addresses is: How do students learn to see mathematical representations in ways that are consistent with the discipline of mathematics? This revised version was published online in July 2006 with corrections to the Cover Date.     

基于人眼视觉特性的火炮内膛图像增强方法

为了提高窥膛图像的观测效果,减小背景和噪声对目标图像的模糊度,根据图像特点提出了一种基于人眼视觉特性的图像增强新方法.该方法根据目标图像与背景、噪声图像特性的差异来进行不同的处理,使待测的疵病图像相对增强,目标图像突出,便于人眼观察.     

An Interpretation Architecture for Deep Learning Models with the Application of COVID-19 Diagnosis

The Coronavirus disease 2019 (COVID-19) has become one of the threats to the world. Computed tomography (CT) is an informative tool for the diagnosis of COVID-19 patients. Many deep learning approaches on CT images have been proposed and brought promising performance. However, due to the high complexity and non-transparency of deep models, the explanation of the diagnosis process is challenging, making it hard to evaluate whether such approaches are reliable. In this paper, we propose a visual interpretation architecture for the explanation of the deep learning models and apply the architecture in COVID-19 diagnosis. Our architecture designs a comprehensive interpretation about the deep model from different perspectives, including the training trends, diagnostic performance, learned features, feature extractors, the hidden layers, the support regions for diagnostic decision, and etc. With the interpretation architecture, researchers can make a comparison and explanation about the classification performance, gain insight into what the deep model learned from images, and obtain the supports for diagnostic decisions. Our deep model achieves the diagnostic result of 94.75%, 93.22%, 96.69%, 97.27%, and 91.88% in the criteria of accuracy, sensitivity, specificity, positive predictive value, and negative predictive value, which are 8.30%, 4.32%, 13.33%, 10.25%, and 6.19% higher than that of the compared traditional methods. The visualized features in 2-D and 3-D spaces provide the reasons for the superiority of our deep model. Our interpretation architecture would allow researchers to understand more about how and why deep models work, and can be used as interpretation solutions for any deep learning models based on convolutional neural network. It can also help deep learning methods to take a step forward in the clinical COVID-19 diagnosis field.     

Image quality assessment in multiband DCT domain based on SSIM

The performance of image quality assessment method based on SSIM (structural similarity) is better than the PSNR (peak signal to noise ratio), but the assessment effects of SSIM is poor for seriously blurred image, therefore, the model that combined HVS (human visual sensitivity) and SSIM was established. The basic idea is based on the human eye's sensitivity to different frequency distortion image, the image is two-dimensional discrete cosine transform frequency component into low, mid, high-frequency component, to obtain the frequency component of light, contrast and structural information, using Pearson coefficient for weight and sum processing to the sub-image according to frequency bands of different sensitive degree, finally, get the sharpness of the image. Through nonlinear regression analysis of objective assessment and DMOS, experiments showed that this method was closer to human perception than SSIM and GSSIM for serious blurred distortion image. At the same time, compared to conventional algorithm MAE (mean absolute error), MSE (mean square error) and PSNR, this model was more consistent with human visual characteristics.     

Lightness Change as Perceived in Relation to the Size of Recognized Visual Space of Illumination

According to the concept of the recognized visual space of illumination (RVSI) the lightness of an object surface is perceived in relation to its conceptualized size. To prove this proposition the lightness of gray test patches was judged when they were located at various positions inside an illuminated space composed of two rooms in the depth direction from a subject. No retinal image arrangement was changed in the test patch and its immediate surroundings, but the front room had walls, floors and furniture lower in lightness by the amount of N1.5 than the back room to make the RVSI of the former smaller despite the illuminance in the entire space being the same. The results showed that the apparent lightness of the patches was perceived higher by amount of about 13 in L units for the N4 test patch and about 20 for N6 when the patches were located in the front room, in accordance with the prediction. It was stressed that the experiment of lightness judgment should be conducted in a three dimensional space rather than two dimensional plane as done by several investigators.     

Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

梯度表面能材料上液滴运动特性实验

对水平和30°倾角放置梯度表面能材料表面上液滴运动特性进行了可视化实验,分析了液滴在梯度表面上运动速度的变化规律,以及液滴大小和表面倾角对运动速度变化的影响.实验结果表明:在梯度表面能材料上,液滴能获得较大的宏观运动速度,并可以沿30°倾角放置的梯度表面材料上自下而上的运动;大液滴较小液滴的峰值运动速度大,运动距离更远;液滴在运动过程中出现蠕动的现象.     

基于光谱视觉响应拟合的计算机配色算法

对光谱拟合配色算法进行了讨论,并运用单常数库贝尔卡-芒克理论,导出了基于光谱视觉响应拟合的配色处方基本矩阵方程,以及配色处方修正量公式,提出了相应的计算机配色算法,建立了配色处方的修正迭代步骤。数值实验表明光谱视觉响应拟合法均衡了不同照明体下的色差,且同色异谱程度低于其他光谱拟合法。