For intelligent vision measurement, the geometric image feature extraction is an essential issue. Contour primitive of interest (CPI) means a regular-shaped contour feature lying on a target object, which is widely used for geometric calculation in vision measurement and servoing. To realize that the CPI extraction model can be flexibly applied to different novel objects, the one-shot learning based CPI extraction can be implemented with deep convolutional neural network, by using only one annotated support image to guide the CPI extraction process. In this paper, we propose a multi-stage contour primitives of interest extraction network (MS-CPieNet), which uses the multi-stage strategy to improve the discrimination ability of CPI and complex background. Second, the spatial nonlocal attention module is utilized to enhance the deep features, by globally fusing the image features with both short and long ranges. Moreover, the dense 4-direction classification is designed to obtain the normal direction of the contour, and the directions can be further used for the contour thinning post-process. The effectiveness of the proposed methods is validated by the experiments with the OCP and ROCM datasets. A 2-D measurement experiments are conducted to demonstrate the convenient application of the proposed MS-CPieNet.