Although many existing vision measurement systems have achieved high performances, they are object-specific and have limitations in flexibility. Toward intelligent vision measurement that can be conveniently reused for novel objects, this article focuses on the image geometric feature extraction with one-shot learning ability. We propose a contour primitive of interest (CPI) extraction network with dual metric (CPieNet-DM), which can obtain a designated CPI in a query image of a novel object under the guidance of only one annotated support image. First, the dual-metric learning mechanism is proposed, which not only utilizes inter-image similarity as guidance but also leverages the intra-image coherency of CPI pixels to facilitate the inference. Second, a neural network is designed to infer the CPI map based on the dual metric, which also predicts the CPI's geometric parameters. Moreover, the dual context aggregator is plugged in to provide the awareness of both images’ contexts. Third, the network training is jointly supervised by the multiple tasks of dual-metric learning, geometric parameters regression, and CPI extraction. The online hard example mining is utilized to improve the training outcome. The effectiveness of the proposed methods is validated with a series of experiments.