Abstract: This paper mainly solves the problem of measuring the small crack in industrial CT（Computer Tomography） images.Ridgelet transform is developed from wavelet transform.The idea of ridgelet transform is that turns line singularity into point singularity according to radon transform，and then deals with point singularities using wavelet in radon domain.Therefore，it is appropriate that ridgelet transform can detect the defects in images such as cracks，which have line singularities，and it can suppress the point noises in images.In this paper，image is firstly projected，one-dimensional wavelet transform is next applied to projections，then do approach on the crack，reduce the scope of crack.Finally the edge of the crack can be obtained.But the measured width of cracks is larger than true width because of the influence of point pervasion in CT images.The width shrinkage and scale calibration are used in this paper.An industrial CT testing image is used to do experiment.The result of the measurement can reach sub-pixel accuracy.The ridgelet transform，edge approach and width shrinkage are used for measuring the small crack in industrial CT image.This presented method can also be applied to other measurements.

Key words: image processing, ridgelet transform, sub-pixel, crack measure, industrial Computer Tomography（CT）

摘要： 工业部件内部小间隙裂纹测量是公认的技术难题，研究工件断面CT图像中小间隙裂纹的测量方法，使之达到亚像素精度。脊波变换是近年在小波变换基础上发展起来的新的分析方法，脊波变换对于图像中的线状奇异性（如边缘、裂纹等）较敏感，且它对图像中的点状噪声有抑制作用。在利用脊波变换检测工业CT图像中工件裂纹边缘的基础上，对小间隙裂纹的平均宽度进行亚像素测量。而工业CT图像成像时存在的点扩散效应，使测得裂纹宽度较真实的要宽些。因此采用宽度收缩的方法获得裂纹平均宽度并进行尺寸标定。实际工业CT图像的实验结果表明，该方法的测量精度能够达到亚像素级精度，可应用于工业CT图像中的小间隙裂纹测量，也可应用于其他类型图像。

关键词: 图像处理, 脊波变换, 亚像素, 裂纹测量, 工业CT