This study presents a novel methodology to extract feature lines from unorganized point clouds. In this study, the extraction of feature lines from point clouds is divided into two stages: region segmentation and feature detection. In the region segmentation stage, the social particle swarm optimization fuzzy C-means clustering algorithm is introduced to cluster the point cloud data; further, each partition is obtained with a clear boundary, which is beneficial to extract the boundary features. In the feature detection stage, local surface reconstruction that is based on the radial basis function is conducted for each partition. Additionally, the curvature values of the sampling points are calculated according to the established local implicit surface; further, local feature weights that are based on the mean curvature are proposed. The feature points can be identified based on the local feature weights using the curvature extremum method. Finally, the feature lines can be generated by establishing the minimum spanning tree of the feature points. Different point cloud models are selected to perform the feature line extraction experiments. The experimental results exhibit that the proposed method can extract significant and sharp features from the point cloud models along with the curve features with intensity variations.