数学分析中部分求解函数极限的问题,实质上就是求解函数列积分的极限。分段拟合法作为一种研究函数极限的关键方法,同样在研究函数列问题中发挥着重要作用。本文将借助分段拟合的思想,讨论研究limn→∞∫abfn(x)g(x)dx这类极限问题以及...数学分析中部分求解函数极限的问题,实质上就是求解函数列积分的极限。分段拟合法作为一种研究函数极限的关键方法,同样在研究函数列问题中发挥着重要作用。本文将借助分段拟合的思想,讨论研究limn→∞∫abfn(x)g(x)dx这类极限问题以及迭代函数列的相关问题。In mathematical analysis, partially solving the function limit problem is essentially solving the limit of the sequence of functions integral. As a key method to study the limit of function, piecewise fitting method also plays an important role in the study of function sequence. In this paper, we will discuss the limit problem of limn→∞∫abfn(x)g(x)dxand the related problems of iterative function sequence by means of the idea of piecewise fitting.展开更多
双指针式仪表盘广泛应用于建筑、材料、化工等工业生产过程中。相比于单指针式仪表盘,双指针式仪表盘存在指针易重叠和双指针读数变化呈现一定联系等特点。为了提高现有双指针式仪表盘读数识别算法的准确性,本研究提出了一种基于图像分...双指针式仪表盘广泛应用于建筑、材料、化工等工业生产过程中。相比于单指针式仪表盘,双指针式仪表盘存在指针易重叠和双指针读数变化呈现一定联系等特点。为了提高现有双指针式仪表盘读数识别算法的准确性,本研究提出了一种基于图像分割及质心拟合法的读数识别新方法。首先,利用YOLOv8网络从背景图像中分离出大指针表盘和小指针表盘。其次,利用Fast-SCNN将大指针和小指针进行语义分割,并将分割区域的轮廓点集伸展为二维平面以得到质心。最后,通过质心和表盘中心坐标拟合成一条直线,采用该线段与参考线的角度变换来实现初步读数。大小指针的读数采用交叉判断来进行校正,相加之后得到最终的读数。实际工业场景下的实验结果验证了该方法的可行性。Dual pointer instrument meters are widely used in construction, materials, chemical, and other industrial production processes. Compared with single-pointer meters, dual pointer meters have the characteristics of easy overlapping of pointers and a certain correlation between the readings of dual-pointers. To improve the accuracy of the existing dual pointer instrument meters reading recognition algorithm, this study proposes a new reading recognition method based on image segmentation and the center of mass fitting method. First, the YOLOv8 network is used to separate the large pointer dials and small pointer dials from the background image. Next, the large and small pointers are semantically segmented using Fast-SCNN, and the set of contour points in the segmented region is stretched into a two-dimensional plane to obtain the center of mass. Finally, a straight line is fitted to the center of mass and the dial center coordinates, and the angular transformation between this line segment and the reference line is used to achieve the preliminary readings. The readings of the small and large pointers are corrected by cross-judging and summed up to get the final readings. Experiment results in real industrial scenarios verify the feasibility of this method.展开更多
文摘数学分析中部分求解函数极限的问题,实质上就是求解函数列积分的极限。分段拟合法作为一种研究函数极限的关键方法,同样在研究函数列问题中发挥着重要作用。本文将借助分段拟合的思想,讨论研究limn→∞∫abfn(x)g(x)dx这类极限问题以及迭代函数列的相关问题。In mathematical analysis, partially solving the function limit problem is essentially solving the limit of the sequence of functions integral. As a key method to study the limit of function, piecewise fitting method also plays an important role in the study of function sequence. In this paper, we will discuss the limit problem of limn→∞∫abfn(x)g(x)dxand the related problems of iterative function sequence by means of the idea of piecewise fitting.
文摘双指针式仪表盘广泛应用于建筑、材料、化工等工业生产过程中。相比于单指针式仪表盘,双指针式仪表盘存在指针易重叠和双指针读数变化呈现一定联系等特点。为了提高现有双指针式仪表盘读数识别算法的准确性,本研究提出了一种基于图像分割及质心拟合法的读数识别新方法。首先,利用YOLOv8网络从背景图像中分离出大指针表盘和小指针表盘。其次,利用Fast-SCNN将大指针和小指针进行语义分割,并将分割区域的轮廓点集伸展为二维平面以得到质心。最后,通过质心和表盘中心坐标拟合成一条直线,采用该线段与参考线的角度变换来实现初步读数。大小指针的读数采用交叉判断来进行校正,相加之后得到最终的读数。实际工业场景下的实验结果验证了该方法的可行性。Dual pointer instrument meters are widely used in construction, materials, chemical, and other industrial production processes. Compared with single-pointer meters, dual pointer meters have the characteristics of easy overlapping of pointers and a certain correlation between the readings of dual-pointers. To improve the accuracy of the existing dual pointer instrument meters reading recognition algorithm, this study proposes a new reading recognition method based on image segmentation and the center of mass fitting method. First, the YOLOv8 network is used to separate the large pointer dials and small pointer dials from the background image. Next, the large and small pointers are semantically segmented using Fast-SCNN, and the set of contour points in the segmented region is stretched into a two-dimensional plane to obtain the center of mass. Finally, a straight line is fitted to the center of mass and the dial center coordinates, and the angular transformation between this line segment and the reference line is used to achieve the preliminary readings. The readings of the small and large pointers are corrected by cross-judging and summed up to get the final readings. Experiment results in real industrial scenarios verify the feasibility of this method.
