CN112710632A - Method and system for detecting high and low refractive indexes of glass beads - Google Patents
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Abstract
本发明涉及一种玻璃微珠高低折射率检测方法及系统,所述检测方法包括:对采集的高折射率图像依次进行畸变矫正、对比度增强、傅里叶变换、轮廓优化提取和最小二乘法拟合圆处理;对采集的低折射率图像依次进行畸变矫正、灰度增强、对比度增强、阈值分割、形态学处理、轮廓优化和最小二乘法拟合圆处理;根据上述处理得到轮廓圆的半径以及圆中心坐标值,进而计算出高折射率图像和低折射率图像中的折射率。本发明的优点在于:不仅能够同时对玻璃微珠的高折射率和低折射率进行同时检测,而且通过图像分析处理的方法极大地提高了检测效率以及检测准确率。
The invention relates to a method and system for detecting the high and low refractive indices of glass microbeads. The detection method comprises: sequentially performing distortion correction, contrast enhancement, Fourier transform, contour optimization extraction and least squares fitting on a collected high refractive index image Circle-closing processing; perform distortion correction, grayscale enhancement, contrast enhancement, threshold segmentation, morphological processing, contour optimization and least squares fitting circle processing on the collected low-refractive index images in turn; according to the above processing, the radius of the contour circle and The coordinate value of the center of the circle, and then calculate the refractive index in the high-refractive index image and the low-refractive index image. The advantages of the present invention are: not only can the high refractive index and low refractive index of the glass microbeads be simultaneously detected, but also the detection efficiency and detection accuracy are greatly improved by the method of image analysis and processing.
Description
技术领域technical field
本发明涉及玻璃微珠折射率检测领域,尤其涉及一种玻璃微珠高低折射率检测方法及系统。The invention relates to the field of refractive index detection of glass microbeads, in particular to a method and system for detecting high and low refractive indices of glass microbeads.
背景技术Background technique
玻璃微珠是一种硅酸盐材料,具有良好的化学稳定性、机械强度和电绝缘性,其独特的特性是对光具有回归反射特性,被广泛应用于公路、铁路、港口、海洋运输、矿山、坑道、消防和城建等领域作为各种标志、警示牌、车辆拍照和救生用品等;随着我国公路建设的快速发展,与道路逆反射材料配合使用的玻璃微珠的用量迅速增加,在广告标志、反光膜、反光油墨、反光标线等交通安全产品和设施中发挥着越来越重要的作用。Glass beads are a kind of silicate material with good chemical stability, mechanical strength and electrical insulation. Its unique feature is that it has retro-reflection characteristics to light, and is widely used in highways, railways, ports, marine transportation, Mines, tunnels, fire protection and urban construction are used as various signs, warning signs, vehicle photography and life-saving supplies, etc. With the rapid development of highway construction in my country, the amount of glass microspheres used in conjunction with road retroreflective materials has increased rapidly. Advertising signs, reflective films, reflective inks, reflective lines and other traffic safety products and facilities play an increasingly important role.
目前测量玻璃微珠折射率的方法主要有成像法、一次彩虹法和二次彩虹法等;而目前上面上的测量技术,基于成像法存在光路调整复杂,自动定量化测量过程实现困难,透过率低,成像效果差等缺点;基于一次彩虹法只能测量低折射率的玻璃微珠,基于二次彩虹法只能测量高折射率的玻璃微珠,不能实现高低折射率的同时测量,存在功能单一的缺点,而且现有都是通过调节光路来实现对玻璃微珠折射率的测量,但是一般情况下光路调节麻烦且复杂,需要采用带环形标尺测量,且调节精度不高,可操作性差。At present, the methods for measuring the refractive index of glass microspheres mainly include imaging method, primary rainbow method and secondary rainbow method, etc. At present, the above measurement technology, based on the imaging method, has complicated optical path adjustment, and it is difficult to realize the automatic quantitative measurement process. Low refractive index and poor imaging effect; based on the primary rainbow method, only glass beads with low refractive index can be measured, and based on the secondary rainbow method, only glass beads with high refractive index can be measured, and simultaneous measurement of high and low refractive index cannot be achieved. The disadvantage of single function, and the current measurement of the refractive index of glass beads is achieved by adjusting the optical path, but in general, the adjustment of the optical path is troublesome and complicated, and it needs to be measured with a ring scale, and the adjustment accuracy is not high, and the operability is poor. .
发明内容SUMMARY OF THE INVENTION
本发明的目的在于克服现有技术的缺点,提供了一种玻璃微珠高低折射率检测方法及系统,解决了现有对玻璃微珠折射率检测方式中存在的不足。The purpose of the present invention is to overcome the shortcomings of the prior art, and to provide a method and system for detecting the high and low refractive index of glass microbeads, which solves the deficiencies in the existing methods for detecting the refractive index of glass microbeads.
本发明的目的通过以下技术方案来实现:一种玻璃微珠高低折射率检测方法,所述检测方法包括:The object of the present invention is achieved through the following technical solutions: a method for detecting the high and low refractive index of glass microbeads, the detection method comprises:
对采集的高折射率图像依次进行畸变矫正、对比度增强、傅里叶变换、轮廓优化提取和最小二乘法拟合圆处理;对采集的低折射率图像依次进行畸变矫正、灰度增强、对比度增强、阈值分割、形态学处理、轮廓优化和最小二乘法拟合圆处理;Distortion correction, contrast enhancement, Fourier transform, contour optimization extraction and least square fitting circle processing are performed on the collected high refractive index images in sequence; distortion correction, grayscale enhancement, and contrast enhancement are performed on the collected low refractive index images in sequence. , threshold segmentation, morphological processing, contour optimization and least squares fitting circle processing;
根据上述处理得到轮廓圆的半径以及圆中心坐标值,进而计算出高折射率图像和低折射率图像中的折射率。According to the above process, the radius of the contour circle and the coordinate value of the center of the circle are obtained, and then the refractive indices in the high-refractive index image and the low-refractive index image are calculated.
所述畸变矫正处理包括:The distortion correction processing includes:
将输入的高折射率图像或者低折射率图像在图像像素坐标系中的中心坐标设置为图像物理坐标系的原点,根据图像中每个像素在图像物理坐标系中的尺寸,得到图像像素坐标系和图像物理坐标系的转换矩阵,进而得到高折射率图像或者低折射率图像的图像物理坐标系 ;Put the input high refractive index image or low refractive index image in the image pixel coordinate system The center coordinate in the image is set as the origin of the image physical coordinate system. According to the size of each pixel in the image in the image physical coordinate system, the conversion matrix of the image pixel coordinate system and the image physical coordinate system is obtained, and then the high refractive index image or the low refractive index image is obtained. Image Physical Coordinate System for Refractive Index Images ;
将图像物理坐标系 转换为相机坐标系 ,再将相机坐标系 转换为世界坐标系 ;Convert the image to the physical coordinate system Convert to camera coordinate system , and then the camera coordinate system Convert to world coordinate system ;
进而得到摄像机内参矩阵、透视射影矩阵和尺度因子,根据摄像机内参矩阵、透视射影矩阵和尺度因子对输入的高折射率图像和低折射率图像进行矫正后图像 。Then, the camera internal parameter matrix, perspective projective matrix and scale factor are obtained, and the input high refractive index image and low refractive index image are corrected according to the camera internal parameter matrix, perspective projective matrix and scale factor. .
所述灰度增强处理包括:对经过畸变矫正,灰度为r的输入图像 通过灰度增强公式: 处理后得到灰度为s的输出图像 ,实现输入图像灰度的线性扩展或压缩,将该步骤的作为输出图像 下一步骤的输入图像 。The grayscale enhancement processing includes: correcting the distortion of the input image with a grayscale of r Through the grayscale enhancement formula: After processing, the output image with grayscale s is obtained , to achieve linear expansion or compression of the grayscale of the input image, and use this step as the output image Input image for the next step .
所述对比度增强处理包括:对输入图像 进行低通滤波,根据得到的灰度值和原始值进行计算得到结果值: ,得到输出图像,实现对图像的高频区域进行强调,使图像更加清晰,将该步骤的作为输出图像下一步骤的输入图像 。The contrast enhancement processing includes: processing the input image Perform low-pass filtering, and calculate the resulting value according to the obtained gray value and the original value: , get the output image , to emphasize the high-frequency area of the image to make the image clearer, and use this step as the output image Input image for the next step .
所述阈值分割处理包括:选取输入图像 灰度值满足在灰度区间[MinGray,MaxGray]的像素,将所有满足的像素点作为一个区域返回;The threshold segmentation process includes: selecting an input image If the gray value satisfies the pixels in the gray interval [MinGray, MaxGray], return all the satisfied pixels as a region;
所述形态学处理包括:将所述阈值分割处理后得出来的区域依次进行膨胀和腐蚀处理,或者依次进行腐蚀和膨胀处理滤掉图像中的干扰信息。The morphological processing includes: sequentially performing dilation and erosion processing on the region obtained after the threshold segmentation processing, or sequentially performing erosion and dilation processing to filter out interference information in the image.
所述傅里叶变换处理包括:The Fourier transform process includes:
傅里叶正变换:把经过对比度增强后的图像进行傅里叶变换将时域图像转换为频域图像;Fourier transform: Fourier transform is performed on the contrast-enhanced image to convert the time domain image into a frequency domain image;
高斯卷积:将经过傅里叶变换的图像与卷积核模板进行卷积,对于图像上的一个点,让卷积核模板的原点与该点重合,然后将卷积核模板上的点与图像上对应的点相乘,并将各点的积相加,得到该点的卷积值,再对图像上的每个点都这样处理后得到卷积图像;Gaussian convolution: Convolve the Fourier-transformed image with the convolution kernel template. For a point on the image, let the origin of the convolution kernel template coincide with the point, and then convolve the point on the convolution kernel template with the convolution kernel template. Multiply the corresponding points on the image, and add the products of each point to obtain the convolution value of the point, and then process each point on the image in this way to obtain the convolution image;
傅里叶逆变换:将卷积图像进行傅里叶逆变换将频域图像转换为时域图像。Inverse Fourier Transform: Inverse Fourier transform the convolutional image to convert the frequency domain image to the time domain image.
所述轮廓优化提取处理包括:The contour optimization extraction process includes:
通过理论圆度值对图像中的轮廓进行筛选,并计算筛选出的轮廓的面积和周长;Screen the contours in the image by the theoretical roundness value, and calculate the area and perimeter of the screened contours;
通过面积和周长计算出圆形轮廓的实际圆度值,并将实际圆度值与理论圆度值进行比较,如果实际圆度值在理论圆度值的误差范围内,则判断筛选出的轮廓为圆形轮廓,如果实际圆度值不再理论圆度值的误差范围内,则重新进行筛选提取。Calculate the actual roundness value of the circular contour through the area and perimeter, and compare the actual roundness value with the theoretical roundness value. If the actual roundness value is within the error range of the theoretical roundness value, judge the selected The contour is a circular contour. If the actual roundness value is no longer within the error range of the theoretical roundness value, re-screen and extract.
所述最小二乘法拟合圆处理包括:The least squares fitting circle processing includes:
根据圆曲线的方程 和,设样本集中的一点到圆心的距离为,则;According to the equation of the circular curve and , let a point in the sample set The distance to the center of the circle is ,but ;
求出点 到圆边缘的距离的平方与半径平方的差为:;find the point The difference between the square of the distance to the edge of the circle and the square of the radius is: ;
令 为 的平方和, , 大于0,因此函数存在大于或等于0的极小值, 为对a,b,c求偏导,令偏导等于0,得到极值点:,,;make for the sum of squares, , is greater than 0, so the function has a minimum value greater than or equal to 0, In order to find the partial derivative with respect to a, b, and c, set the partial derivative equal to 0, and get the extreme point: , , ;
计算求出a,b,c的值,进而得到A,B和R的拟合值。Calculate the values of a, b, c, and then get the fitted values of A, B and R.
一种基于玻璃微珠高低折射率检测方法的检测系统,它包括:A detection system based on the high and low refractive index detection method of glass microbeads, comprising:
图像采集模块:对高低折射率图像进行采集并将采集到的图像传递给图像处理模块;Image acquisition module: acquires high and low refractive index images and transmits the acquired images to the image processing module;
图像处理模块:对输入的高低折射率图像进行畸变矫正、灰度增强、对比度增强、阈值分割、形态学处理、傅里叶变换、轮廓优化和最小二乘法拟合圆处理后将处理结果传输到数据处理模块;Image processing module: perform distortion correction, grayscale enhancement, contrast enhancement, threshold segmentation, morphological processing, Fourier transform, contour optimization and least square fitting circle processing on the input high and low refractive index images, and then transmit the processing results to data processing module;
数据处理模块:对数据进行分析处理根据圆半径和成像距离计算得到折射率,最后输出并保存数据信息。Data processing module: analyze and process the data to calculate the refractive index according to the radius of the circle and the imaging distance, and finally output and save the data information.
所述图像处理模块包括高折射率图像处理单元和低折射率图像处理单元;The image processing module includes a high refractive index image processing unit and a low refractive index image processing unit;
所述高折射率图像处理单元依次通过畸变矫正、对比度增强、傅里叶变换、轮廓优化提取和最小二乘法拟合圆处理输入的高折射率图像,得到圆形轮廓的半径和成像距离;The high-refractive-index image processing unit sequentially processes the input high-refractive index image through distortion correction, contrast enhancement, Fourier transform, contour optimization extraction, and least-squares fitting circle to obtain the radius of the circular contour and the imaging distance;
所述低折射率图像处理单元依次通过畸变矫正、灰度增强、对比度增强、阈值分割、形态学处理、轮廓优化提取和最小二乘法拟合圆处理输入的低折射率图像,得到圆形轮廓的半径和成像距离。The low-refractive-index image processing unit sequentially processes the input low-refractive index image through distortion correction, grayscale enhancement, contrast enhancement, threshold segmentation, morphological processing, contour optimization extraction, and least squares fitting circle to obtain a circular contour. Radius and imaging distance.
本发明具有以下优点:一种玻璃微珠高低折射率检测方法及系统,不仅能够同时对玻璃微珠的高折射率和低折射率进行同时检测,而且通过图像分析处理的方法极大地提高了检测效率以及检测准确率。The invention has the following advantages: a method and system for detecting the high and low refractive indices of glass microbeads can not only simultaneously detect the high and low refractive indices of glass microbeads, but also greatly improve the detection rate through the method of image analysis and processing. efficiency and detection accuracy.
附图说明Description of drawings
图1 为本发明方法的流程示意图;Fig. 1 is the schematic flow chart of the method of the present invention;
图2 为图像像素坐标系至图像物理坐标系示意图1;Figure 2 is a schematic diagram 1 of the image pixel coordinate system to the image physical coordinate system;
图3 为图像像素坐标系至图像物理坐标系示意图2;Figure 3 is a schematic diagram 2 of the image pixel coordinate system to the image physical coordinate system;
图4 为相机坐标系至图像物理坐标系示意图;Figure 4 is a schematic diagram of the camera coordinate system to the image physical coordinate system;
图5 为世界坐标系至相机坐标系示意图。Figure 5 is a schematic diagram of the world coordinate system to the camera coordinate system.
具体实施方式Detailed ways
为使本申请实施例的目的、技术方案和优点更加清楚,下面将结合本申请实施例中附图,对本申请实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅仅是本申请一部分实施例,而不是全部的实施例。通常在此处附图中描述和示出的本申请实施例的组件可以以各种不同的配置来布置和设计。因此,以下结合附图中提供的本申请的实施例的详细描述并非旨在限制要求保护的本申请的保护范围,而是仅仅表示本申请的选定实施例。基于本申请的实施例,本领域技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例,都属于本申请保护的范围。下面结合附图对本发明做进一步的描述。In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only It is a part of the embodiments of the present application, but not all of the embodiments. The components of the embodiments of the present application generally described and illustrated in the drawings herein may be arranged and designed in a variety of different configurations. Accordingly, the following detailed description of the embodiments of the present application provided in conjunction with the accompanying drawings is not intended to limit the scope of protection of the present application as claimed, but merely represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application. The present invention will be further described below with reference to the accompanying drawings.
需要说明的是,本发明中f(x,y)表示输入图像,g(x,y)表示输出图像,每一步中的f(x,y)和g(x,y)表示不同的图像,即某一个处理步骤中的输出图像g(x,y)到下一个处理步骤后就表示下一个处理步骤中的输入图像f(x,y)。It should be noted that in the present invention, f(x, y) represents the input image, g(x, y) represents the output image, and f(x, y) and g(x, y) in each step represent different images, That is, after the output image g(x, y) in a certain processing step goes to the next processing step, it represents the input image f(x, y) in the next processing step.
实施例1Example 1
如图1所示,本发明涉及一种玻璃微珠高低折射率检测方法,其主要包括以下内容:As shown in Figure 1, the present invention relates to a method for detecting the high and low refractive index of glass microbeads, which mainly includes the following contents:
程序启动并初始化,软件启动后,会自动初始化,加载配置文件,检测相机连接状态,进入等待检测状态;The program starts and initializes. After the software starts, it will automatically initialize, load the configuration file, detect the connection status of the camera, and enter the waiting state;
手动调整玻璃微珠样品的位置,待图像达到最佳采图效果后,开启高折射率相机图像采集或者低折射率相机图像采集;高折射率相机和低折射率相机采用单独相机、单独线程,可实现实时图像读取、处理、传输、显示;Manually adjust the position of the glass microbead sample. After the image reaches the best image acquisition effect, start the image acquisition of the high-refractive index camera or the low-refractive index camera; the high-refractive index camera and the low-refractive index camera use a separate camera and separate thread. Real-time image reading, processing, transmission and display can be realized;
图像采集成功后,进入图像处理模块,经过一系列的算法处理,获取我们想要的信息,最后提取圆半径;其中,高折射率图像处理模块主要用到的算法有畸变矫正、对比度增强、傅里叶变换、轮廓优化提取和最小二乘法拟合圆;低折射率图像处理模块主要用到的算法有畸变矫正、灰度增强、对比度增强、阈值分割、形态学处理、轮廓优化提取和最小二乘法拟合圆。此模块通过特有的算法对图像进行一系列的处理,并将计算结果传递给数据处理模块;After the image acquisition is successful, enter the image processing module, through a series of algorithm processing, obtain the information we want, and finally extract the radius of the circle; among them, the algorithms mainly used in the high refractive index image processing module are distortion correction, contrast enhancement, Liye transform, contour optimization extraction and least squares fitting circle; the algorithms mainly used in the low refractive index image processing module are distortion correction, grayscale enhancement, contrast enhancement, threshold segmentation, morphological processing, contour optimization extraction and least squares Multiply fit circle. This module performs a series of processing on the image through a unique algorithm, and transmits the calculation result to the data processing module;
通过数据处理模块,根据圆半径和成像距离,计算得到折射率,最后输出数据,测量结束。Through the data processing module, the refractive index is calculated according to the circle radius and the imaging distance, and finally the data is output, and the measurement is over.
进一步地,畸变矫正:相机的成像过程实质上是坐标系的转换。首先空间中的点由“世界坐标系”转换到“像机坐标系”,然后再将其投影到成像平面(图像物理坐标系) ,最后再将成像平面上的数据转换到图像像素坐标系。但是由于透镜制造精度以及组装工艺的偏差会引入畸变,导致原始图像的失真。镜头的畸变分为径向畸变和切向畸变两类。Further, distortion correction: the imaging process of the camera is essentially the transformation of the coordinate system. First, the points in the space are converted from the "world coordinate system" to the "camera coordinate system", then they are projected to the imaging plane (image physical coordinate system), and finally the data on the imaging plane is converted to the image pixel coordinate system. However, due to the lens manufacturing precision and the deviation of the assembly process, distortion will be introduced, resulting in the distortion of the original image. The distortion of the lens is divided into two categories: radial distortion and tangential distortion.
径向畸变:是沿着透镜半径方向分布的畸变,产生原因是光线在远离透镜中心的地方比靠近中心的地方更加弯曲。成像仪光轴中心的畸变为0,沿着镜头半径方向向边缘移动,畸变越来越严重。畸变的数学模型可以用主点(principle point)周围的泰勒级数展开式的前几项进行描述,通常使用前两项,即k1和k2,对于畸变很大的镜头,如鱼眼镜头,可以增加使用第三项k3来进行描述,成像仪上某点根据其在径向方向上的分布位置,调节公式为:Radial Distortion: Distortion distributed along the radius of the lens, caused by the fact that light is more curved farther from the center of the lens than near the center. The distortion in the center of the optical axis of the imager is 0, and it moves to the edge along the radius of the lens, and the distortion becomes more and more serious. The mathematical model of distortion can be described by the first few terms of the Taylor series expansion around the principal point. Usually, the first two terms are used, namely k1 and k2. For lenses with large distortion, such as fisheye lenses, you can The third item k3 is added to describe. According to the distribution position of a point on the imager in the radial direction, the adjustment formula is:
其中: in:
式里(x0,y0)是畸变点在成像仪上的原始位置,(x,y)是畸变较真后新的位置;In the formula (x0, y0) is the original position of the distortion point on the imager, (x, y) is the new position after the distortion is true;
切向畸变:是由于透镜本身与相机传感器平面(成像平面)或图像平面不平行而产生的,这种情况多是由于透镜被粘贴到镜头模组上的安装偏差导致。畸变模型可以用两个额外的参数p1和p2来描述:Tangential distortion: It is caused by the lens itself being not parallel to the camera sensor plane (imaging plane) or the image plane. This situation is mostly caused by the installation deviation of the lens being pasted on the lens module. The distortion model can be described by two additional parameters p1 and p2:
其中 , , 为径向畸变参数, , 为切向畸变参数。综上,我们需要5个参数( , , , , )来描述镜头畸变,本发明通过相机标定来消除相机畸变,即畸变矫正。in , , is the radial distortion parameter, , is the tangential distortion parameter. To sum up, we need 5 parameters ( , , , , ) to describe lens distortion, the present invention eliminates camera distortion through camera calibration, that is, distortion correction.
相机标定的目的就是要获得相机的内参(畸变参数)和外参,得到二维平面像素坐标和三维世界坐标的关系。四个坐标系:摄像机坐标系 、 图像物理坐标系、图像像素坐标系 和 世界坐标系(参考坐标系) 。The purpose of camera calibration is to obtain the internal parameters (distortion parameters) and external parameters of the camera, and obtain the relationship between the two-dimensional plane pixel coordinates and the three-dimensional world coordinates. Four coordinate systems: camera coordinate system, image physical coordinate system, image pixel coordinate system, and world coordinate system (reference coordinate system).
图像坐标系:是一个以像素为单位的坐标系,它的原点在左上方,每个像素点的位置是以像素为单位来表示的,所以这样的坐标系叫图像像素坐标系(u,v),u和v分别表示像素在数字图像中的列数和行数,但是并没有用物理单位表示像素的位置,因此还需建立以物理单位表示的图像坐标系,叫图像物理坐标系(x,y),该坐标系是以光轴与图像平面的交点为原点,该点一般位于图像中心,但是由于制造原因,很多情况下会偏移。以毫米为单位。两个坐标轴分别与图像像素坐标系平行。即:像素坐标(u,v),物理坐标(x,y)。Image coordinate system: It is a coordinate system in pixels, its origin is at the upper left, and the position of each pixel is expressed in pixels, so such a coordinate system is called an image pixel coordinate system (u, v ), u and v respectively represent the number of columns and rows of pixels in the digital image, but the position of pixels is not represented by physical units, so it is necessary to establish an image coordinate system represented by physical units, called the image physical coordinate system (x , y), the coordinate system is based on the intersection of the optical axis and the image plane as the origin, which is generally located in the center of the image, but due to manufacturing reasons, it will be offset in many cases. in millimeters. The two coordinate axes are respectively parallel to the image pixel coordinate system. Namely: pixel coordinates (u, v), physical coordinates (x, y).
如图2所示,若图像物理坐标系的原点在图像像素坐标系中的坐标为(u0,v0),每个像素在图像物理坐标系中的尺寸为dx,dy,则两个坐标系的关系为:As shown in Figure 2, if the coordinates of the origin of the image physical coordinate system in the image pixel coordinate system are (u0, v0), and the size of each pixel in the image physical coordinate system is dx, dy, then the two coordinate systems are The relationship is:
矩阵形式为:The matrix form is:
但是一般情况下,两轴互相不垂直:But in general, the two axes are not perpendicular to each other:
如图3所示,此时有:As shown in Figure 3, at this time there are:
写成矩阵形式为:Written in matrix form as:
如图4所示,相机坐标系(Xc,Yc,Zc)至图像坐标系(x,y);As shown in Figure 4, the camera coordinate system (Xc, Yc, Zc) to the image coordinate system (x, y);
根据相似三角形原理可得:According to the similar triangle principle, we can get:
如图5所示,世界坐标系(Xw,Yw,Zw)至相机坐标系(Xc,Yc,Zc);As shown in Figure 5, the world coordinate system (Xw, Yw, Zw) to the camera coordinate system (Xc, Yc, Zc);
将上式合并得到:Combining the above equations, we get:
其中, 表示摄像机内参矩阵, 表示透视摄影矩阵,s = Zc 表示尺度因子。in, represents the camera intrinsic parameter matrix, represents the fluoroscopy matrix, and s = Zc represents the scale factor.
灰度增强:表示对输入图像灰度做线性扩张或压缩,映射函数为一个直线方程,输入图像为f(x,y),灰度为r,输出图像为g(x,y),灰度为s;其表达式如下:Factor、k为参数因子;Grayscale enhancement: Indicates that the grayscale of the input image is linearly expanded or compressed. The mapping function is a linear equation, the input image is f(x,y), the grayscale is r, the output image is g(x,y), and the grayscale is s; its expression is as follows: Factor, k are parameter factors;
对比度增强:主要强调图像的高频区域(边缘和角落),使得到的图像更加清晰。先对图像g(x,y)进行低通滤波(mean_image),根据得到的灰度值(mean)和原始值(orig)进行计算得到结果值(res),其表达式如下:Factor为参数因子Contrast Enhancement: Emphasizes the high frequency areas (edges and corners) of the image, making the resulting image clearer. First perform low-pass filtering (mean_image) on the image g(x,y), and calculate the result value (res) according to the obtained gray value (mean) and original value (orig), and its expression is as follows: Factor is the parameter factor
阈值分割:输入图像f(x,y)中选取灰度值满足在灰度区间[MinGray,MaxGray]的像素,将所有满足的点作为一个区域返回,其表达式如下:Threshold segmentation: select the pixels whose gray value satisfies the gray value interval [MinGray, MaxGray] in the input image f(x, y), and return all satisfying points as an area, and the expression is as follows:
其中,MinGray表示最优灰度值范围的最小灰度值,MaxGray表示最优灰度值范围的最大灰度值,如我们需要灰度值为100左右像素,就可以将灰度区间设置为[90,110]。Among them, MinGray represents the minimum gray value of the optimal gray value range, and MaxGray represents the maximum gray value of the optimal gray value range. If we need a gray value of about 100 pixels, we can set the gray interval to [ 90,110].
形态学处理:数学形态学是由一组形态学的代数运算子组成的,它的基本运算有4个:膨胀、腐蚀、开操作和闭操作,主要作用是保持图像的基本特征并除去不相干的结构;通过对阈值分割后得出来的区域进行形态学处理,可以滤除掉一些干扰信息Morphological processing: Mathematical morphology is composed of a group of morphological algebraic operators. It has four basic operations: dilation, erosion, opening operation and closing operation. The main function is to maintain the basic characteristics of the image and remove irrelevant structure; some interference information can be filtered out by morphological processing of the region obtained after threshold segmentation
膨胀(Dilate):是将与物体接触的所有背景点合并到该物体中,使边界向外部扩张的过程。可以用来填补物体中的空洞。膨胀可以看做是腐蚀的对偶运算,其定义是:把结构元素B平移a后得到Ba,若Ba击中X,我们记下这个a点。所有满足上述条件的a点组成的集合称做X被B膨胀的结果。Dilate: It is the process of merging all the background points in contact with the object into the object to expand the boundary to the outside. Can be used to fill holes in objects. Dilation can be regarded as a dual operation of erosion, and its definition is: Ba is obtained by translating the structuring element B by a. If Ba hits X, we record the point a. The set of all points a satisfying the above conditions is called the result of X being inflated by B.
腐蚀(Erode):是一种消除边界点的方法,使边界向内收缩的过程。可以消除小且毫无意义的物体。X用S腐蚀的结果是所有使S平移x后仍在X中的x的集合。换句话说,用S来腐蚀X得到的集合是S完全包括在X中时S的原点位置的集合,用公式表示为:Erode: It is a method of eliminating boundary points and shrinking the boundary inward. Small and meaningless objects can be eliminated. The result of X being eroded by S is the set of all x's that are still in X after S has been translated by x. In other words, the set obtained by corroding X with S is the set of the origin position of S when S is completely included in X, expressed by the formula:
开操作(Close):先膨胀后腐蚀称为闭(close),即 CLOSE(X)=E(D(X))。一般来说,闭运算能够填平小湖(即小孔),弥合小裂缝,而总的位置和形状不变。Open operation (Close): first expansion and then corrosion is called close (close), that is, CLOSE(X)=E(D(X)). In general, the closing operation can fill in small lakes (ie, small holes) and close small cracks, while the overall position and shape remain unchanged.
闭操作(Open):开和闭是对偶运算。先腐蚀后膨胀称为开(open),即 OPEN(X)=D(E(X))。作用:消除小物体,在纤细点出分离物体,位置和形状总是不变的。Close operation (Open): Open and close are dual operations. Erosion first and then expansion is called open, that is, OPEN(X)=D(E(X)). Function: Eliminate small objects, separate objects at the slender point, and the position and shape are always unchanged.
傅里叶变换:图像的频率是表征图像中灰度变化剧烈程度的指标。频域图像的每一点都来自于整个原图像,频谱图上的各点与图像上各点并不存在一一对应的关系在进行图像处理时,很多时候需要获得图像中灰度变化剧烈的地方,或者灰度变化相对缓慢的区域,灰度变化剧烈的地方就是那些灰度值变化大的地方,或梯度大的地方,该地方频率高;灰度变化缓慢的地方,就是梯度小的地方,频率低;傅立叶变换(FT, Fourier Transform)的作用是将一个信号由空间域或时间域变换到频域。其实就是把数据由横坐标时间、纵坐标采样值的波形图格式,转换为横坐标频率、纵坐标振幅(或相位)的频谱格式。傅里叶逆变换就是把频域还原为空间域或时间域。Fourier Transform: The frequency of an image is an indicator that characterizes the intensity of grayscale changes in the image. Each point of the frequency domain image comes from the entire original image, and there is no one-to-one correspondence between the points on the spectrogram and the points on the image. When performing image processing, it is often necessary to obtain places where the grayscale changes drastically in the image. , or the area where the grayscale changes relatively slowly, the places where the grayscale changes sharply are those places where the grayscale value changes greatly, or the place where the gradient is large, the frequency is high; the place where the grayscale changes slowly is the place where the gradient is small, The frequency is low; the function of Fourier Transform (FT, Fourier Transform) is to transform a signal from the space domain or time domain to the frequency domain. In fact, it is to convert the data from the waveform format of the abscissa time and the ordinate sample value to the spectrum format of the abscissa frequency and the ordinate amplitude (or phase). The inverse Fourier transform is to restore the frequency domain to the space domain or time domain.
进一步地,把经过对比度增强后的图像进行傅里叶变换,再对傅里叶图像进行高斯卷积,最后再把傅里叶图像还原为空间域图像,可以很明显地看出一些原先不易察觉的特征得到了增强,对接下来轮廓优化提取有很大的帮助;Further, the Fourier transform of the contrast-enhanced image is performed, and then Gaussian convolution is performed on the Fourier image, and finally the Fourier image is restored to a spatial domain image. The features have been enhanced, which is of great help to the next contour optimization extraction;
傅里叶变换公式:Fourier transform formula:
高斯卷积:用一个模板(卷积核)和一幅图像进行卷积,对于图像上的一个点,让模板的原点和该点重合,然后模板上的点和图像上对应的点相乘,然后各点的积相加,就得到了该点的卷积值,对图像上的每个点都这样处理最后得到卷积图像。卷积是一种积分运算,用来求两个曲线重叠区域面积。把一个点的像素值用它周围的点的像素值的加权平均代替,可以看作加权求和,可以用来消除噪声、特征增强。Gaussian convolution: Convolve with a template (convolution kernel) and an image. For a point on the image, let the origin of the template coincide with the point, and then multiply the point on the template with the corresponding point on the image, Then the product of each point is added to obtain the convolution value of the point, and each point on the image is processed in this way to finally obtain the convolution image. Convolution is an integral operation used to find the area of the overlapping area of two curves. The pixel value of a point is replaced by the weighted average of the pixel values of its surrounding points, which can be regarded as a weighted summation, which can be used to eliminate noise and feature enhancement.
卷积公式:Convolution formula:
其中 为输出图像(傅里叶变换步骤中的输出图像), 为输入图像,为模板(卷积核),一般卷积核选用二维高斯分布函数:in is the output image (the output image in the Fourier transform step), for the input image, For the template (convolution kernel), the general convolution kernel uses a two-dimensional Gaussian distribution function:
傅里叶逆变换公式:Inverse Fourier transform formula:
其中,f(x,y)图像矩阵,x/y图像的行列。Among them, f(x,y) image matrix, the row and column of the x/y image.
轮廓优化提取:通过圆度对轮廓进行筛选的过程。对于一个圆型轮廓,其半径为r,面积为S,周长为L则有:Contour optimization extraction: The process of screening contours by roundness. For a circular contour with radius r, area S, and perimeter L, we have:
从上面公式可以看出当轮廓为标准圆时C为一个定值(理论值),而通过前面算法处理得出来的轮廓往往有很多轮廓,包括圆形轮廓和非圆形轮廓,而其中只有圆形才是我们所需要的,所以计算出轮廓的面积和周长再通过上述公式就能筛选出需要的圆形轮廓。当计算出的实际圆度值在理论圆度值±10%的误差范围内时,表示筛选出的轮廓为圆形轮廓。It can be seen from the above formula that C is a fixed value (theoretical value) when the contour is a standard circle, and the contour processed by the previous algorithm often has many contours, including circular contours and non-circular contours, of which only circles are The shape is what we need, so after calculating the area and perimeter of the contour, the required circular contour can be filtered out through the above formula. When the calculated actual roundness value is within the error range of ±10% of the theoretical roundness value, it means that the screened contour is a circular contour.
最小二乘法拟合圆:最小二乘法(least squares analysis)是一种数学优化技术,它通过最小化误差的平方和找到一组数据的最佳函数匹配。最小二乘法是用最简的方法求得一些绝对不可知的真值,而令误差平方之和为最小来寻找一组数据的最佳匹配函数的计算方法,最小二乘法通常用于曲线拟合 (least squares fitting) 。最小二乘圆拟合方法是一种基于统计的检测方法,可实现亚像素级别的精确拟合定位。Least Squares Fitting Circles: Least squares analysis is a mathematical optimization technique that finds the best functional fit for a set of data by minimizing the sum of squared errors. The least squares method is a calculation method that uses the simplest method to find some absolutely unknowable true values, and minimizes the sum of squared errors to find the best matching function for a set of data. The least squares method is usually used for curve fitting. (least squares fitting). The least squares circle fitting method is a statistical-based detection method that can achieve accurate fitting localization at the sub-pixel level.
圆的公式:The formula for the circle:
, ,
其中A、B为圆中心坐标,R为半径where A and B are the coordinates of the center of the circle, and R is the radius
令 , , make , ,
可得出圆曲线的另外一个方程:Another equation for the circular curve can be derived:
只要求出a,b,c,就能得出圆的半径参数:The radius parameter of the circle can be obtained by only asking for a, b, and c:
设样本集(此处样本集为提取到的轮廓上所有点的集合)中一点到圆心的距离为 :Set a point in the sample set (here the sample set is the set of all points on the extracted contour) The distance to the center of the circle is :
点 到圆边缘的距离的平方与半径平方的差为:point The difference between the square of the distance to the edge of the circle and the square of the radius is:
令 为 的平方和make for sum of squares
大于0,因此函数存在大于或等于0的极小值, 为对a,b,c求偏导,令偏导等于0,得到极值点: is greater than 0, so the function has a minimum value greater than or equal to 0, In order to find the partial derivative with respect to a, b, and c, set the partial derivative equal to 0, and get the extreme point:
解此方程组就能得出a,b,c的值,再通过上面公式就能得出A,B,R的拟合值。The values of a, b, and c can be obtained by solving this system of equations, and then the fitted values of A, B, and R can be obtained through the above formula.
实施例2Example 2
本发明还涉及一种玻璃微珠高低折射率检测系统,其包括初始化模块、图像采集模块、图像处理模块以及数据处理模块。The invention also relates to a glass microbead high and low refractive index detection system, which comprises an initialization module, an image acquisition module, an image processing module and a data processing module.
进一步地,初始化模块:加载系统参数、配置文件、初始化相机;Further, the initialization module: load system parameters, configuration files, and initialize the camera;
图像采集模块:对高低折射率图像进行采集并将采集到的图像传递给图像处理模块;Image acquisition module: acquires high and low refractive index images and transmits the acquired images to the image processing module;
图像处理模块:分为高折射率图像处理模块和低折射率处理模块,分别采用不同的算法,高折射率图像处理模块主要用到的算法有畸变矫正、对比度增强、傅里叶变换、轮廓优化提取和最小二乘法拟合圆;低折射率图像处理模块主要用到的算法有畸变矫正、灰度增强、对比度增强、阈值分割、形态学处理、轮廓优化提取和最小二乘法拟合圆。此模块通过特有的算法对图像进行一系列的处理,并将计算结果传递给数据处理模块;Image processing module: It is divided into a high-refractive index image processing module and a low-refractive index processing module, which use different algorithms respectively. The main algorithms used in the high-refractive index image processing module are distortion correction, contrast enhancement, Fourier transform, and contour optimization. Extraction and least squares fitting circle; the algorithms mainly used in the low refractive index image processing module are distortion correction, grayscale enhancement, contrast enhancement, threshold segmentation, morphological processing, contour optimization extraction and least squares fitting circle. This module performs a series of processing on the image through a unique algorithm, and transmits the calculation result to the data processing module;
数据处理模块:对数据进行分析和处理,最后输出并保存数据。Data processing module: analyze and process the data, and finally output and save the data.
以上所述仅是本发明的优选实施方式,应当理解本发明并非局限于本文所披露的形式,不应看作是对其他实施例的排除,而可用于各种其他组合、修改和环境,并能够在本文所述构想范围内,通过上述教导或相关领域的技术或知识进行改动。而本领域人员所进行的改动和变化不脱离本发明的精神和范围,则都应在本发明所附权利要求的保护范围内。The foregoing are only preferred embodiments of the present invention, and it should be understood that the present invention is not limited to the forms disclosed herein, and should not be construed as an exclusion of other embodiments, but may be used in various other combinations, modifications, and environments, and Modifications can be made within the scope of the concepts described herein, from the above teachings or from skill or knowledge in the relevant field. However, modifications and changes made by those skilled in the art do not depart from the spirit and scope of the present invention, and should all fall within the protection scope of the appended claims of the present invention.
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