CN108510543A - A sub-pixel localization method for feature centers of checkerboard images - Google Patents
- ️Fri Sep 07 2018
CN108510543A - A sub-pixel localization method for feature centers of checkerboard images - Google Patents
A sub-pixel localization method for feature centers of checkerboard images Download PDFInfo
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Abstract
本发明公开了一种棋盘格图像特征中心亚像素定位方法，基于双曲正切函数建立关于灰度增益和偏移，灰度跳变边缘方向角和灰度扩散因子的棋盘格特征理论模型，通过模型参数优化和灰度水平调整，使理论模型生成的仿真特征区域与已粗略定位的实际特征区域间达到最高峰值信噪比，并提取理论模型的特征中心参数作为补偿量，实现实际特征中心的亚像素定位。该方法无需设置经验阈值，对特征亮度变化和噪声不敏感，可明显提高棋盘格图像特征中心的定位精度，进而保证相机标定与位姿测量时参数估计的准确性。
The invention discloses a checkerboard image feature center sub-pixel positioning method, based on the hyperbolic tangent function to establish a checkerboard feature theory model about gray scale gain and offset, gray scale jump edge direction angle and gray scale diffusion factor, through Model parameter optimization and gray level adjustment make the peak signal-to-noise ratio between the simulated feature area generated by the theoretical model and the roughly positioned actual feature area reach the highest peak signal-to-noise ratio, and extract the feature center parameter of the theoretical model as the compensation amount to realize the actual feature center. Subpixel positioning. This method does not need to set an empirical threshold, is insensitive to feature brightness changes and noise, and can significantly improve the positioning accuracy of the feature center of the checkerboard image, thereby ensuring the accuracy of parameter estimation during camera calibration and pose measurement.
Description
技术领域technical field
本发明涉及图像处理领域，特别是一种棋盘格图像特征中心亚像素定位方法。The invention relates to the field of image processing, in particular to a sub-pixel positioning method for the feature center of a checkerboard image.
背景技术Background technique
相机标定与位姿测量是机器视觉中的基础和热门问题，其处理过程中通常需要在相机视野内放置靶标，通过靶标上的特征点建立世界坐标系与图像坐标系的映射关系，并求解PnP问题获得相机的内部参数和靶标的位姿参数。现今采用的靶标特征主要有棋盘格和圆。圆特征可通过亚像素边缘提取后再椭圆拟合或利用灰度质心法得到其中心坐标，但椭圆中心非目标圆圆心的真实投影，存在投影误差，在高精度标定和测量优化过程中需要迭代修正。棋盘格图元皆为一次几何图形，该特性决定其角点在仿射变换过程中不存在投影误差，其特征中心的定位过程独立于标定和测量过程，被广泛应用于机器视觉系统。现有棋盘格特征中心亚像素定位算法众多，可以采用边缘交点求取，但是其定位精度对镜头畸变较为敏感，也可基于灰度分析进行求取，常用的有Harris、Susan和Forstner及其改进算子，但其定位精度受噪声和灰度阈值的影响较大。因此，定位算法需要改进。Camera calibration and pose measurement are basic and popular problems in machine vision. During the processing, it is usually necessary to place a target within the camera field of view, establish the mapping relationship between the world coordinate system and the image coordinate system through the feature points on the target, and solve the PnP The problem is to obtain the internal parameters of the camera and the pose parameters of the target. The target features used today are mainly checkerboard and circle. The center coordinates of the circle feature can be obtained by ellipse fitting after sub-pixel edge extraction or the gray-scale centroid method, but the center of the ellipse is not the real projection of the center of the target circle, and there are projection errors, which require iteration in the process of high-precision calibration and measurement optimization fix. The checkerboard primitives are all primary geometric figures. This characteristic determines that there is no projection error in the corner points during the affine transformation process. The positioning process of the feature center is independent of the calibration and measurement process, and is widely used in machine vision systems. There are many sub-pixel positioning algorithms for the center of checkerboard features, which can be obtained by edge intersections, but the positioning accuracy is sensitive to lens distortion, and can also be obtained based on grayscale analysis. Commonly used are Harris, Susan, Forstner and their improvements operator, but its positioning accuracy is greatly affected by noise and gray threshold. Therefore, the localization algorithm needs to be improved.
发明内容Contents of the invention
本发明所要解决的技术问题是，针对现有技术不足，提供一种棋盘格图像特征中心亚像素定位方法，提高棋盘格图像特征中心的定位精度。The technical problem to be solved by the present invention is to provide a sub-pixel positioning method for the feature center of a checkerboard image to improve the positioning accuracy of the feature center of the checkerboard image.
为解决上述技术问题，本发明所采用的技术方案是：一种棋盘格图像特征中心亚像素定位方法，其特征在于，包括以下步骤：In order to solve the above-mentioned technical problems, the technical solution adopted in the present invention is: a sub-pixel positioning method for the feature center of a checkerboard image, which is characterized in that it comprises the following steps:
1)对于像素级定位的棋盘格特征中心[ur,vr]，在其邻域以12～18像素为窗半径截取矩形区域Dr；1) For the pixel-level checkerboard feature center [u r , v r ], intercept a rectangular area D r in its neighborhood with a window radius of 12-18 pixels;
2)在局部图像坐标系o-uv下建立关于灰度增益λ，灰度偏移κ，灰度跳变边缘方向角α和β，灰度扩散因子ρ的棋盘格特征理论模型为：2) Under the local image coordinate system o-uv, establish a checkerboard feature theory model about gray gain λ, gray shift κ, gray jump edge direction angles α and β, and gray diffusion factor ρ as follows:
3)优化步骤1)中的各参数，使Dt(u,v)与Dr间达到最高峰值信噪比；3) Optimizing the parameters in step 1) to achieve the highest peak signal-to-noise ratio between D t (u, v) and D r ;
4)提取步骤2)中优化后的理论模型特征中心参数[u,v]，将棋盘格特征中心调整为[ur－u,vr－v]，完成亚像素定位。4) Extract the optimized theoretical model feature center parameters [u, v] in step 2), and adjust the checkerboard feature center to [u r -u, v r -v] to complete sub-pixel positioning.
步骤1)中，基于OpenCV的棋盘格特征粗定位函数进行特征中心的像素级定位。In step 1), the pixel-level positioning of the feature center is performed based on the rough positioning function of the checkerboard feature of OpenCV.
步骤3)的具体实现过程为：The specific implementation process of step 3) is:
1)初始化u，v，λ，κ，α，β和ρ；1) Initialize u, v, λ, κ, α, β and ρ;
2)根据当前初值生成所述理论模型Dt(u,v)；2) generating the theoretical model D t (u, v) according to the current initial value;
3)计算当前初值下Dt(u,v)关于各参数的一阶导数；3) Calculate the first derivative of D t (u, v) with respect to each parameter under the current initial value;
4)计算所述矩形区域Dr与Dt(u,v)中对应像素的灰度差；4) Calculating the gray level difference of corresponding pixels in the rectangular area D r and D t (u, v);
5)基于所述一阶导数数据和灰度差，采用线性最小二乘求得各参数的修正值，修正各参数；5) based on the first-order derivative data and the gray level difference, the correction value of each parameter is obtained by linear least squares, and each parameter is corrected;
6)考察u和v的修正值，若二者的绝对值都小于0.001，终止迭代，否则跳转至步骤2)，继续迭代；6) Investigate the correction values of u and v, if the absolute values of both are less than 0.001, terminate the iteration, otherwise jump to step 2) and continue the iteration;
7)考察迭代次数，当迭代次数大于20时终止迭代。7) Investigate the number of iterations, and terminate the iteration when the number of iterations is greater than 20.
参数中u和v的初值设为0，α和β的初值基于OpenCV的直线提取函数获得，λ的初值设置为Dr中最大与最小灰度值之差，κ的初值设置为Dr中最大与最小灰度值之和，ρ的初值设置为0.5。The initial values of u and v in the parameters are set to 0, the initial values of α and β are obtained based on the straight line extraction function of OpenCV, the initial value of λ is set to the difference between the maximum and minimum gray value in D r , and the initial value of κ is set to The sum of the maximum and minimum gray values in D r , the initial value of ρ is set to 0.5.
与现有技术相比，本发明所具有的有益效果为：本发明无需设置经验阈值，对镜头畸变、特征亮度变化和噪声不敏感，可明显提高棋盘格图像特征中心的定位精度，进而保证相机标定与位姿测量时参数估计的准确性。Compared with the prior art, the present invention has the beneficial effects that: the present invention does not need to set an empirical threshold, is insensitive to lens distortion, characteristic brightness changes and noise, and can significantly improve the positioning accuracy of the feature center of the checkerboard image, thereby ensuring that the camera Accuracy of parameter estimation during calibration and pose measurement.
附图说明Description of drawings
图1为棋盘格特征理论模型定义原理图；Fig. 1 is a schematic diagram of the definition of the theoretical model of the checkerboard feature;
图2为图1所示实施例的数据处理流程图；Fig. 2 is the data processing flowchart of the embodiment shown in Fig. 1;
图3为图1所示实施例的参数优化流程图。Fig. 3 is a flow chart of parameter optimization in the embodiment shown in Fig. 1 .
具体实施方式Detailed ways
本发明具体实现过程如下：The concrete realization process of the present invention is as follows:
a、对于一副棋盘格靶标图像，采用OpenCV的棋盘格特征粗定位函数对特征中心进行像素级定位；a. For a checkerboard target image, use OpenCV's checkerboard feature coarse positioning function to perform pixel-level positioning on the feature center;
b、在步骤a所确定的特征中心邻域截取窗半径为15像素矩形区域；b. The interception window radius in the neighborhood of the feature center determined in step a is a rectangular area of 15 pixels;
c、以灰度增益，灰度偏移，灰度跳变边缘方向角，灰度扩散因子和像素坐标为参数，基于双曲正切函数定义棋盘格特征的理论模型；c. With gray gain, gray offset, gray jump edge direction angle, gray diffusion factor and pixel coordinates as parameters, a theoretical model of checkerboard features is defined based on hyperbolic tangent function;
d、对步骤c所定义的理论模型进行参数优化，使其生成的特征区域与步骤b中的矩形区域间达到最高峰值信噪比；d. Optimizing the parameters of the theoretical model defined in step c to achieve the highest peak signal-to-noise ratio between the generated feature region and the rectangular region in step b;
e、提取理论模型的特征中心参数作为补偿量，对步骤a所确定的特征中心进行补偿，实现亚像素定位。e. Extracting the feature center parameter of the theoretical model as a compensation amount, and compensating the feature center determined in step a to realize sub-pixel positioning.
如图1所示，在局部图像坐标系o-uv下选择宽度为2d+1的矩形区域(窗半径d＝15)用于定义理论棋盘格特征模型。两条过o点的直线l1，l2用于确定灰度跳变边缘方向角α和β：As shown in Figure 1, a rectangular area with a width of 2d+1 (window radius d=15) is selected under the local image coordinate system o-uv to define a theoretical checkerboard feature model. Two straight lines l 1 and l 2 passing through point o are used to determine the direction angles α and β of the gray-scale transition edge:
区域中高亮度点灰度为1，低亮度点灰度为-1的理论棋盘格特征模型Di基于单位阶跃函数H(t)定义：The theoretical checkerboard feature model D i in which the gray level of high brightness points in the area is 1 and the gray level of low brightness points is -1 is defined based on the unit step function H(t):
Di(u,v)＝[2H(usinα-vcosα)-1][2H(usinβ-vcosβ)-1]。D i (u,v)=[2H(usinα-vcosα)-1][2H(usinβ-vcosβ)-1].
考虑实际情况下视觉系统成像时的点扩散效应，采用标准差为σ的二维高斯卷积核对Di进行灰度扩散，将其响应Df定义为：Considering the point diffusion effect of visual system imaging in actual situations, a two-dimensional Gaussian convolution kernel with a standard deviation of σ is used to perform grayscale diffusion on D i , and its response D f is defined as:
Df无法直接通过卷积得到准确的解析表达，基于高斯卷积核的旋转不变性和可分离性，采用高斯误差函数erf(t)得到其主分量表达式：D f cannot be directly obtained through convolution to obtain an accurate analytical expression. Based on the rotation invariance and separability of the Gaussian convolution kernel, the Gaussian error function erf(t) is used to obtain its principal component expression:
取a＝6164/5123，采用双曲正切函数tanh(at)用于erf(t)的近似闭式表达。实际采集的数字图像灰度范围为0～255，与Df不在同一水平，需引入增益和偏移修正。最终的棋盘格特征理论模型Dt的参数包括灰度增益λ，灰度偏移κ，灰度跳变边缘方向角α及β，灰度扩散因子和坐标[u,v]，基于双曲正切函数近似表达：Take a=6164/5123, and use the hyperbolic tangent function tanh(at) for the approximate closed expression of erf(t). The gray scale range of the actual collected digital image is 0-255, which is not at the same level as Df , so gain and offset correction need to be introduced. The parameters of the final checkerboard characteristic theoretical model D t include gray gain λ, gray shift κ, gray jump edge direction angles α and β, and gray diffusion factor And the coordinates [u,v], based on the approximate expression of the hyperbolic tangent function:
根据图2所示，本发明实例如下：According to shown in Fig. 2, example of the present invention is as follows:
步骤S201、基于OpenCV的棋盘格特征粗定位函数对图像中的棋盘格特征中心进行像素级定位，得到坐标[ur,vr]；Step S201, perform pixel-level positioning on the center of the checkerboard feature in the image based on the coarse positioning function of the checkerboard feature of OpenCV, and obtain the coordinates [u r , v r ];
步骤S202、以S201所述坐标[ur,vr]为中心，15像素为窗半径截取矩形区域Dr；Step S202, taking the coordinates [u r , v r ] described in S201 as the center and 15 pixels as the window radius to intercept the rectangular area D r ;
步骤S203、以图1所定义的图案作为理论棋盘格特征Dt；Step S203, using the pattern defined in Figure 1 as the theoretical checkerboard feature D t ;
步骤S204、优化Dt所包含的灰度增益λ，灰度偏移κ，灰度跳变边缘方向角α及β，灰度扩散因子和坐标[u,v]，使Dt与Dr间达到最高峰值信噪比，目标函数为：Step S204, optimize the gray scale gain λ, gray scale shift κ, gray scale jump edge direction angle α and β, and gray scale diffusion factor contained in D t And the coordinates [u, v], so that the highest peak signal-to-noise ratio is achieved between D t and D r , the objective function is:
步骤S205、提取S204中优化后的[u,v]，将棋盘格特征中心调整为[ur－u,vr－v]，完成亚像素定位。Step S205, extracting the optimized [u, v] in S204, adjusting the checkerboard feature center to [u r -u, v r -v] to complete sub-pixel positioning.
根据图3所示，本发明实例S204中的参数优化采用Gauss-Newton算法，步骤如下：According to shown in Figure 3, the parameter optimization in the example S204 of the present invention adopts Gauss-Newton algorithm, and the steps are as follows:
步骤S301、对S204所述参数赋初值，u和v的初值设为0，α和β的初值基于OpenCV的直线提取函数对S202所述Dr进行灰度跳变边缘提取获得，λ的初值设置为Dr中最大与最小灰度值之差，κ的初值设置为Dr中最大与最小灰度值之和，ρ的初值设置为0.5Step S301, assign initial values to the parameters described in S204, the initial values of u and v are set to 0, the initial values of α and β are obtained based on the straight line extraction function of OpenCV, and the gray-scale transition edge extraction of D r described in S202 is obtained, λ The initial value of κ is set to the difference between the maximum and minimum gray value in D r , the initial value of κ is set to the sum of the maximum and minimum gray value in D r , and the initial value of ρ is set to 0.5
步骤S302、根据当前参数值生成理论棋盘格特征数据Dt；Step S302, generating theoretical checkerboard feature data D t according to the current parameter value;
步骤S303、根据当前参数值并参考S204所述目标函数计算位置序列i，j所对应的一阶导数数据：Step S303, calculate the first-order derivative data corresponding to the position sequence i, j according to the current parameter value and referring to the objective function described in S204:
其中 in
步骤S304、基于S204所述目标函数，计算Dr与Dt间对应位置序列的灰度差数据：Step S304, based on the objective function described in S204, calculate the grayscale difference data of the corresponding position sequence between Dr and Dt :
di,j＝Dr(i+ur,j+vr)-Dt(i+u,j+v)；d i,j =D r (i+u r ,j+v r )-D t (i+u,j+v);
步骤S305、整理S303所述一阶导数数据和S304所述灰度差数据生成矩阵A和向量B:Step S305, arrange the first-order derivative data described in S303 and the gray scale difference data described in S304 to generate matrix A and vector B:
其中 in
采用线性最小二乘优化方法，求解参数[u v α β λ κ ρ]对应的的修正值[δu δvδα δβ δλ δκ δρ]:Using the linear least squares optimization method, solve the correction value [δ u δ v δ α δ β δ λ δ κ δ ρ ] corresponding to the parameter [uv α β λ κ ρ ]:
[δu δv δα δβ δλ δκ δρ]T＝(ATA)-1ATB，[δ u δ v δ α δ β δ λ δ κ δ ρ ] T = (A T A) -1 A T B,
将参数进行修正：Modify the parameters:
[u v α β λ κ ρ]←[u+δu v+δv α+δα β+δβ λ+δλ κ+δκ ρ+δρ]；[uv α β λ κ ρ]←[u+δ u v+δ v α+δ α β+δ β λ+δ λ κ+δ κ ρ+δ ρ ];
步骤S306、考察S305所述修正值δu和δv，若|δu|<0.001且|δv|<0.001，终止迭代，否则跳转至步骤S302，继续迭代；Step S306, examine the correction values δ u and δ v described in S305, if |δ u |<0.001 and |δ v |<0.001, terminate the iteration, otherwise jump to step S302 and continue the iteration;
步骤S307、考察迭代次数，若大于20，终止迭代。Step S307, check the number of iterations, if it is greater than 20, terminate the iteration.
重复采用本发明实例所述方法对32幅棋盘格图像进行特征中心亚像素定位，实验装置包含32级可调亮度的LED环形光源，焦距为16mm的镜头，分辨率为2592×1944的工业相机和单元格尺寸为33mm、特征阵列为6×6棋盘格靶标，图像采集过程中保证相机与靶标间的相对位姿固定不变，调整光源亮度，每级亮度采集一副图像。本发明实例所述方法与OpenCV的棋盘格特征亚像素定位函数及“《光学精密工程》,2015,23(12):3480-3489”所述基于直线检测的定位方法相比，定位结果更加准确，见下表：The method described in the example of the present invention was repeatedly used to locate the sub-pixels in the feature center of 32 checkerboard images. The experimental device included a 32-level LED ring light source with adjustable brightness, a lens with a focal length of 16mm, an industrial camera with a resolution of 2592×1944, and The cell size is 33mm, and the feature array is a 6×6 checkerboard target. During the image acquisition process, the relative pose between the camera and the target is kept constant. The brightness of the light source is adjusted, and an image is collected for each level of brightness. The method described in the example of the present invention is compared with the positioning method based on line detection described in the checkerboard feature sub-pixel positioning function of OpenCV and "" Optical Precision Engineering ", 2015,23(12):3480-3489", and the positioning result is more accurate , see the table below:
本发明实例Example of the invention OpenCVOpenCV 直线检测Line detection u向最大偏差(像素)u direction maximum deviation (pixel) 0.1770.177 0.3010.301 0.2620.262 v向最大偏差(像素)v to the maximum deviation (pixels) 0.1920.192 0.3630.363 0.2950.295 u向均方根偏差(像素)Root mean square deviation in u direction (pixel) 0.1260.126 0.2570.257 0.1880.188 v向均方根偏差(像素)v to root mean square deviation (pixel) 0.1180.118 0.2300.230 0.2040.204
在硬件配置为Intel Core i7-6700处理器、16GB内存、1TB硬盘和Intel HDGraphics530显卡，操作系统为WIN7 64位，编程环境为VS2010的上位机上采用上述三种方法进行32幅图像的特征亚像素定位耗时测试，测试结果显示本发明实例所述方法的定位效率具有优势，见下表：The above three methods were used to locate the characteristic sub-pixels of the 32 images on the host computer with the hardware configuration of Intel Core i7-6700 processor, 16GB memory, 1TB hard disk and Intel HDGraphics530 graphics card, the operating system was WIN7 64-bit, and the programming environment was VS2010 Time-consuming test, the test results show that the positioning efficiency of the method described in the examples of the present invention has advantages, see the following table:
本发明实例Example of the invention OpenCVOpenCV 直线检测Line detection 耗时(秒)Time-consuming (seconds) 2.082.08 2.262.26 4.134.13
Claims (4)
1.一种棋盘格图像特征中心亚像素定位方法，其特征在于，包括以下步骤：1. a checkerboard image feature center sub-pixel location method, is characterized in that, comprises the following steps: 1)对于像素级定位的棋盘格特征中心[ur,vr]，在其邻域以12～18像素为窗半径截取矩形区域Dr；1) For the pixel-level checkerboard feature center [u r , v r ], intercept a rectangular area D r in its neighborhood with a window radius of 12-18 pixels; 2)在局部图像坐标系o-uv下建立关于灰度增益λ，灰度偏移κ，灰度跳变边缘方向角α和β，灰度扩散因子ρ的棋盘格特征理论模型为：2) Under the local image coordinate system o-uv, establish a checkerboard feature theory model about gray gain λ, gray shift κ, gray jump edge direction angles α and β, and gray diffusion factor ρ as follows: 3)优化步骤1)中的各参数，使Dt(u,v)与Dr间达到最高峰值信噪比；3) Optimizing the parameters in step 1) to achieve the highest peak signal-to-noise ratio between D t (u, v) and D r ; 4)提取步骤2)中优化后的理论模型特征中心参数[u,v]，将棋盘格特征中心调整为[ur－u,vr－v]，完成亚像素定位。4) Extract the optimized theoretical model feature center parameters [u, v] in step 2), and adjust the checkerboard feature center to [u r -u, v r -v] to complete sub-pixel positioning. 2.根据权利要求1所述的棋盘格图像特征中心亚像素定位方法，其特征在于，步骤1)中，基于OpenCV的棋盘格特征粗定位函数进行特征中心的像素级定位。2. the checkerboard image feature center sub-pixel location method according to claim 1, is characterized in that, in step 1), the pixel-level location of feature center is carried out based on the coarse location function of checkerboard feature of OpenCV. 3.根据权利要求1所述的棋盘格图像特征中心亚像素定位方法，其特征在于，步骤3)的具体实现过程为：3. the checkerboard image feature center sub-pixel location method according to claim 1, is characterized in that, the concrete realization process of step 3) is: 1)初始化u，v，λ，κ，α，β和ρ；1) Initialize u, v, λ, κ, α, β and ρ; 2)根据当前初值生成所述理论模型Dt(u,v)；2) generating the theoretical model D t (u, v) according to the current initial value; 3)计算当前初值下Dt(u,v)关于各参数的一阶导数；3) Calculate the first derivative of D t (u, v) with respect to each parameter under the current initial value; 4)计算所述矩形区域Dr与Dt(u,v)中对应像素的灰度差；4) Calculating the gray level difference of corresponding pixels in the rectangular area D r and D t (u, v); 5)基于所述一阶导数数据和灰度差，采用线性最小二乘求得各参数的修正值，修正各参数；5) based on the first-order derivative data and the gray level difference, the correction value of each parameter is obtained by linear least squares, and each parameter is corrected; 6)考察u和v的修正值，若二者的绝对值都小于0.001，终止迭代，否则跳转至步骤2)，继续迭代；6) Investigate the correction values of u and v, if the absolute values of both are less than 0.001, terminate the iteration, otherwise jump to step 2) and continue the iteration; 7)考察迭代次数，当迭代次数大于20时终止迭代。7) Investigate the number of iterations, and terminate the iteration when the number of iterations is greater than 20. 4.根据权利要求3所述的棋盘格图像特征中心亚像素定位方法，其特征在于，参数中u和v的初值设为0，α和β的初值基于OpenCV的直线提取函数获得，λ的初值设置为Dr中最大与最小灰度值之差，κ的初值设置为Dr中最大与最小灰度值之和，ρ的初值设置为0.5。4. the sub-pixel positioning method of the checkerboard image feature center according to claim 3 is characterized in that, the initial value of u and v in the parameter is set to 0, and the initial value of α and β obtains based on the straight line extraction function of OpenCV, λ The initial value of κ is set to the difference between the maximum and minimum gray value in D r , the initial value of κ is set to the sum of the maximum and minimum gray value in D r , and the initial value of ρ is set to 0.5.
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