Abstract: A method of ellipse detection and location based on Principal Components Analysis（PCA） and Heteroscedastic Errors-in-Variable（HEIV） is proposed. According to the fact that major axis of an ellipse is the direction of principal components, the data points are projected on the coordinate frame of principal axis using PCA. A new evaluation method for elliptical profile error is proposed, and the ellipse objects are recognized according to the elliptical profile error of the data points after translation. An ellipse fitting method based to the HEIV model is applied to realizing the precision locating of the ellipse objects. The method simplifies the process of ellipse detection by translating arbitrary ellipse to standard one, and improves the location precision in view of the heteroscedastic performance of data points. The location precision is less than 0.04 pixel when the noise variance is 0.05.

Key words: machine vision, ellipse recognition, Principal Components Analysis（PCA）, profile error, Heteroscedastic Errors-in-Variable（HEIV）

摘要： 提出结合主元变换与异方差变量含误差模型的椭圆识别与定位方法。根据椭圆长轴对应于椭圆主元方向的特点，利用主元变换法将目标边缘数据变换到主元坐标系，给出新的椭圆轮廓度误差评定方法，将变换后数据点集的椭圆轮廓度误差作为椭圆识别的依据，采用基于异方差变量含误差模型的拟合算法获取椭圆的中心坐标。该方法将任意椭圆转化为标准型椭圆，简化了识别过程，考虑到椭圆数据点的异方差特性，提高了椭圆的定位精度，在噪声方差为0.05情况下，定位精度小于0.04 pixel。

关键词: 机器视觉, 椭圆识别, 主元分析, 轮廓度误差, 异方差变量含误差