圆形标志投影偏心差补偿算法

目的 圆形标志目前正广泛地应用于各类视觉测量系统，其圆心定位精度决定了测量系统的测量精度。当相机主光轴与标志表面不平行时，圆被映射为椭圆，圆心位置计算产生偏差。光轴与标志表面夹角较大或标志较大等情况下会产生较大的偏心差进而严重影响系统测量精度。为此，提出一种基于三同心圆圆形标志的投影偏心差补偿算法。方法 算法基于三同心圆的圆形标志设计，根据3组椭圆拟合中心坐标解算偏心差模型进行计算补偿。结果 针对圆形标志偏心差问题，同心圆补偿算法取得良好效果，有效提升了圆形标志定位精度。仿真结果表明，在拍摄角度、拍摄距离、圆形标志大小不同的情况下，偏心差在像素量级，补偿后偏心差在10^-11像素量级。实物实验结果表明，若设计有直径分别为6 cm，12 cm，18 cm的三同心圆标志，经解算补偿结果较以往两同心圆算法精度提高一倍，偏心差值减小80%，测量误差在0.1 mm左右。结论 本文提出了一种新的偏心差补偿算法，利用三同心圆标志增加约束解算偏心差。与以往偏心差补偿算法相比，此方法精度更高，且无需预先平差解算相机与目标的距离、拍摄角等参数，仅需要知道标志圆形半径比例及椭圆中心坐标即可计算补偿，具有很高的实用性，可用于改善基于非编码标志点的深度像匹配、基于圆形标志点的全自动相机标定方法、视觉导航定位等应用中。

Eccentricity error compensation for circular targets

Objective Currently,circular target is widely used in a multitude of vision measurement systems in which center positioning accuracy determines the accuracy of the measuring system.The projection of a circular feature is generally an ellipse and not a true circle because the main optical axis of a camera is not parallel with the feature surface.When the angle between the main optical axis of a camera and the feature surface is large,the eccentricity error will affect the accuracy of the measurement system extremely.Most of the research on eccentricity errors in the last two decades has examined quite a few methods and conducted experiments to derive the mechanism of eccentricity and attempted to correct the errors.Incidentally,the past studies used geometric parameters to calculate the eccentricity errors,which increased the complexity of the process.This paper introduces a new method for correcting the eccentricity error with the help of the three concentric circle targets.Method Most algorithms for eccentricity errors usually involve several geometric parameters,and calibration and bundle adjustment are always required to obtain these parameters.These algorithms increase the computational complexity and reduce the rate of convergence.Our method designs three concentric circles as the target,which has common center coordinates in the object plane and different centers in the image plane,which are on a line.The moment invariants of Zernike moment are used for the edge detection of the pixel level to obtain the precise positioning of the sub-pixel level edge.The center of the ellipse is determined with the least-square ellipse fitting.To achieve better results,the images of the concentric circle targets should include at least 20 pixels to ensure sufficient effective edge points.The ellipse center is easily calculated with the sub-pixel level edge,then we can use the three groups of ellipse centers to calculate the eccentricity error model.The three concentric circles in the error equation have the same six parameters.Thus,the corresponding parameters can be set into blocks as new variables,which in turn can be reduced to three unknown parameters.The error equations can be sufficiently solved with the help of the three concentric circles.Through the formulas derived in this study,the eccentricity errors can be solved completely.Obtaining geometrical parameters should be avoided and the nonlinear model should be solved.Result A possible solution for the correction of this systematic eccentricity error is proposed in this paper.The method can effectively improve the positioning accuracy of the circular target center.Simulation experiment results by using MATLAB show that the eccentricity errors can be compensated from the pixel level to the 10^-11-pixel level when the targets are photos taken in different angles,distances,and sizes of the targets.This study designs a target that has three concentric circles and diameters of 6,12,and 18 cm.To calculate the true center of the circles,a circle with a size of 2 mm is designed in the central area of the target.During image processing,we use the improved gray barycenter localization algorithm to calculate the center of the small circle.By comparison,its radius is extremely small,and the simulation experiment shows that its eccentric error is only 0.02 pixels,which can be ignored compared with the three concentric circles used in the experiment and regarded as the true value in the experiment.Experiment results show that the measurement errors can be controlled at 0.1 mm.Relative to the concentric circles method,the accuracy is two times than that of before and the eccentricity error is decreased by approximately 80%.Conclusion This paper presents a new eccentricity compensation method for calculating eccentricity error by using three concentric circle targets to add constraint.Unlike in previous eccentricity error correction methods,additional parameters should be estimated to correct the eccentricity error.Consequently,the computation complexity increases and convergence speed decreases.Prior knowledge about the geometric parameters of the measurement system (target and camera) are not needed;rather,the proportional relationship of the circles and ellipse center coordinates are the only information required.The experiment results show the efficiency of the proposed method for eccentricity error compensation.The algorithm can improve the location efficiency of circular targets.Consequently,the algorithm can enhance the effect on depth image matching that is based on non-coding markers,the precision of the automatic camera calibration method that is based on circular markers,and the robustness of the navigation and positional system.