Abstract
Circle fitting methods are extensively utilized in various industries, particularly in quality control processes and design applications. The effectiveness of these algorithms can be significantly compromised when the point sets to be predicted are noisy. To mitigate this issue, outlier detection and removal algorithms are often applied before the circle fitting procedure. This study introduces the Polar Coordinate-Based Outlier Detection (PCOD) algorithm, which can be effectively employed in circle fitting applications. In the proposed approach, the point set is first transformed into polar coordinates, followed by the calculation of both local and global standard deviations. Outliers are then identified by comparing local mean values with the global standard deviation. The practicality and efficiency of the proposed method are demonstrated by focusing on the high-precision diameter measurement of industrial washer parts. Images from a machine vision system are processed through preprocessing steps, including sub-pixel edge detection. The resulting sub-pixel edge points are then cleaned using the proposed outlier detection and removal algorithm, after which circle fitting is performed. A comparison is made using ten different circle fitting algorithms and five distinct outlier detection methods. The results indicate that the proposed method outperforms the other approaches, delivering the best performance in terms of accuracy within the dataset, thereby demonstrating its potential for enhancing circle fitting applications in industrial environments.
Abstract (translated)
圆拟合方法在多个行业中广泛应用，特别是在质量控制过程和设计应用中。然而，当预测点集存在噪声时，这些算法的效果可能会大打折扣。为解决这一问题，通常会在圆拟合步骤之前使用异常值检测与去除算法。本研究介绍了一种基于极坐标系的异常值检测（PCOD）算法，该算法可以有效用于圆拟合应用中。 在所提出的方法中，首先将点集转换到极坐标系下，然后计算局部和全局标准差。通过比较局部平均值与全局标准差来识别异常值。本研究通过重点关注工业垫圈部件的高精度直径测量，展示了所提方法的实际可行性和效率。使用机器视觉系统获取的图像经过预处理步骤（包括亚像素边缘检测），得到的结果是亚像素边缘点集，并用提议的异常值检测与去除算法进行清洗。随后执行圆拟合操作。 通过对比十种不同的圆拟合算法和五种不同的异常值检测方法，结果表明所提出的方法优于其他方法，在数据集中提供了最高的精度性能，从而展示了其在工业环境中提升圆拟合应用潜力的可能性。
URL
https://arxiv.org/abs/2508.03720
