基于鲁棒回归的圆拟合算法研究

发布时间：2018-02-26 21:21

本文关键词： 圆拟合边缘提取鲁棒回归梯度下降　出处：《国际关系学院》2017年硕士论文　论文类型：学位论文

【摘要】：圆检测是图像处理和模式识别中常见的目标检测问题之一,在机器视觉工业检测领域具有很强的应用价值。此类问题可以概括为设计算法从边缘样本点检测得到目标圆的圆心和半径。圆拟合是圆检测算法的一种,可以归结为数值优化问题。传统圆拟合算法包括几何圆拟合、代数圆拟合,和使用统计特征或圆的性质的拟合算法,它们计算损失误差的目标函数基于最小二乘模型,通过对目标函数进行数值优化得到检测目标。此类方法的缺陷是当部分边缘点偏离大部分待拟合轮廓时,所得到的拟合结果将会较大地偏离理想的目标圆。针对上述缺陷,本文研究提出一种基于鲁棒回归的圆拟合算法,主要研究成果和创新点如下:(1)受光照等环境因素和元器件表面划伤等内在因素影响,拍摄到的元器件表面轮廓较为复杂,本文在已有边缘检测算法基础上,提出一种基于梯度方向的边缘提取算法,为后续的圆拟合打下基础。(2)对比研究传统圆拟合算法,将鲁棒回归理论应用于圆拟合的几何距离误差情形,提出一种基于鲁棒回归的圆拟合算法,解决了实际中圆拟合结果受离群点影响较大的问题。(3)针对目标函数的最优化,研究数值计算中求函数最小值的问题,提出一种基于梯度下降法的算法求解方案,并测试验证了算法的稳定性和收敛性,使其满足工业应用中算法鲁棒性的要求。(4)设计实验确定目标函数参数k的初始化方法,研究黄金分割等步长参数?的计算方法,采取Barzailai和Borwein提出的?计算策略,测试表明,该算法使得正常点平均误差从3.5下降到0.44,迭代次数从21次下降为12次,圆拟合精度和效率明显提升。基于上述研究成果,本文所提出的算法解决了工业应用中目标圆拟合受离群边缘点影响较大而导致检测结果不理想的问题,有效解决了不规则的分叉或离群噪声点对于原有算法的不良影响,满足了精密检测的要求,具有学术和实用的研究意义。
[Abstract]:Circle detection is one of the common target detection problems in image processing and pattern recognition. This kind of problem can be summarized as the design algorithm to detect the center and radius of the target circle from the edge sample point. Circle fitting is one of the circle detection algorithms. Traditional circle fitting algorithms include geometric circle fitting, algebraic circle fitting, and fitting algorithm using statistical characteristics or the properties of circle. Their objective function for calculating loss error is based on the least square model. The defect of this method is that when some edge points deviate from most of the contour to be fitted, the fitting result will deviate from the ideal target circle greatly. In this paper, a circle fitting algorithm based on robust regression is proposed. The main research results and innovations are as follows: 1) affected by environmental factors such as illumination and internal factors such as surface scratches of components, the surface profile of components photographed is more complex. Based on the existing edge detection algorithms, an edge detection algorithm based on gradient direction is proposed in this paper, which lays the foundation for subsequent circle fitting. The robust regression theory is applied to the geometric distance error of circle fitting, and a circle fitting algorithm based on robust regression is proposed, which solves the problem that the result of circle fitting is greatly affected by outliers in practice. In this paper, the problem of finding the minimum value of function in numerical calculation is studied. A solution based on gradient descent method is proposed, and the stability and convergence of the algorithm are tested and verified. Make it meet the requirements of algorithm robustness in industrial applications. 4) Design experiments to determine the initialization method of the objective function parameter k, study the golden section and other step size parameters? The calculation method adopted by Barzailai and Borwein? The calculation strategy and test show that the average error of normal point is reduced from 3.5 to 0.44, the iteration number is reduced from 21 times to 12 times, and the precision and efficiency of circle fitting are improved obviously. The algorithm proposed in this paper solves the problem that the target circle fitting is influenced greatly by outlier edge points in industrial applications, which leads to unsatisfactory detection results, and effectively solves the adverse effects of irregular bifurcation or outliers noise points on the original algorithm. It meets the requirements of precision detection and has academic and practical significance.
【学位授予单位】：国际关系学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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