针对齿轮视觉测量过程中因齿廓表面受到污染导致齿廓图像边缘出现光学失真, 从而影响齿廓偏差、齿距偏差测量精度问题, 提出一种基于视觉测量的齿廓图像边缘失真迭代逼近——临近度判别算法(IAPD).建立渐开线齿廓图像边缘过渡带内像素点法向偏距与像素点极径的映射关系, 将复杂的二维图像边缘信号转化为容易处理的一维信号; 利用小波去噪算法对信号进行处理, 提取齿廓边缘的失真特征; 采用变阈值迭代逼近算法分离出齿廓倾斜偏差; 采用K-邻近度分类方法自动判别齿廓图像边缘失真的起止位置, 为齿距、齿廓偏差测量时进行齿廓图像边缘失真修正提供定位依据.为验证本算法的可靠性, 根据相邻同名齿廓真实边缘的相似性, 对失真齿廓和无失真齿廓图像提取亚像素边缘, 并进行相似性比较, 实现基于相似性比较的齿廓图像边缘失真判别算法, 以此对IAPD算法的失真区域判别精度进行校验.实验结果表明：本文提出的齿廓图像边缘失真判别算法能够快速自动识别图像失真区域, 失真区域边界的径向定位精度可以达到2.5个像素(50 μm), 能够满足图像边缘失真修正补偿的定位精度要求, 可以实现齿轮测量的实时计算.

The problem of optical distortion caused by the contamination of the toothed gear profile surface was studied which affects the accuracy of measurement on the toothed gear profile deviation and the pitch deviation. Iterative Approximation-Proximity Discrimination algorithm(IAPD) using visual measurement is proposed to determine the image edge distortion of the toothed gear profile. The algorithm constructs the mapping relationship between the normal pixel offset in the edge transition zone of the involute profile image and the polar diameter of the pixel. This mapping converts the complex two-dimensional image edge signal into a one-dimensional signal, which is easier to process. The wavelet denoising algorithm was used to process the signal to extract the distortion features of the toothed gear profile edge, and the variable threshold iterative fitting algorithm was used to separate the toothed gear profile tilt deviation. According to the reasonable range of the normal toothed gear profile error, K-proximity classification method is adopted. The starting and ending position of the edge distortion of the toothed gear profile image is determined, and the positioning basis is provided for correcting the edge distortion of the toothed gear profile image during the measurement of the pitch and the toothed gear profile deviation. In order to verify the reliability of the IAPD algorithm, according to the similarity of the real edges of adjacent ipsilateral tooth profiles, the sub-pixel edges are extracted from the distortion tooth profile and the distortion-free tooth profile image, and similarity comparison is performed to realize the profile edge similarity comparison algorithm of distortion region recognition. The algorithm is used to verify the distortion region discrimination accuracy of the IAPD algorithm. The experimental results show that the toothed gear profile image edge distortion detecting algorithm can identify the image distortion region with good accuracy. The accuracy of radial range of the distortion region can reach 2.5 pixels(50 μm), which can meet the requirement of the image edge distortion correction. In addition, the algorithm is easy to understand and highly effective, which is easy to deploy and can meet the requirements of real-time calculation during gear measurement.