Crack segmentation plays an important role in industrial CT image processing. However, interference in CT images, such as noise and artifacts, can adversely affect the accuracy and precision of crack segmentation. To improve crack segmentation precision in CT image processing, this paper analyzes the characteristics of cracks in CT images, and proposes a method for CT image crack recognition and segmentation that combines a Hessian matrix with a support vector machine. Firstly, a linear filter based on a Hessian matrix is used to extract the linear structures from a CT image and enhance the contrast of these linear structures. Moreover, to represent the texture features of these linear structure images, the method directly extracts textural feature information using a Grey Level Co-occurrence Matrix, which reflects the spatial distribution of grayscale. In addition, a crack identification classifier is trained by a Support Vector Machine (SVM), which is based on a Radial Basis Function (RBF) kernel. Furthermore, the crack identification classifier is used to locate the block area positions of cracks in CT images. Finally, the binary segmentation results for cracks are obtained by Otsu threshold segmentation. The experiments demonstrate that this proposed method can improve the anti-jamming resistance of the algorithm by shielding the non-interest region in the image, and the recognition accuracy reaches 94.5%. This algorithm has practical engineering application value as it has high recognition accuracy and high segmentation accuracy.