High-quality feature matching is a critical prerequisite in a wide range of applications. Most contemporary methods concentrate on detecting keypoints or line features for matching, which have achieved adequate results. However, in some low-texture environments where these features are both lacking, previously used approaches may result in an insufficient number of matches. Besides, in repeated-texture environments, feature matching is also a challenging task. As a matter of fact, there exist numerous irregular curves that can be detected in all kinds of images, including low-texture and repeated-texture scenes, which inspires us to move a step further and dig into the research of curves. In this paper, we propose an accurate method to match invariant features from irregular curves. Our method consists of two stages, the first of which is to match the curves as accurately as possible by an elaborate three-step matching strategy. The second is to extract the matching features with the presented self-adaptive curve fitting approach. Experiments have shown that the matching performances of our features in ordinary scenes are comparable to previous keypoints. Particularly, our features can outperform the keypoints in low-texture and repeated-texture scenes.