Edge extraction has attracted a lot of attention in computer vision. The accuracy of extracting edges in point clouds can be a significant asset for a variety of engineering scenarios. To address these issues, we propose a segmentation-based multi-scale edge extraction technique. In this approach, different regions of a point cloud are segmented by a global analysis according to the geodesic distance. Afterwards, a multi-scale operator is defined according to local neighborhoods. Thereupon, by applying this operator at multiple scales of the point cloud, the persistence of features is determined. We illustrate the proposed method by computing a feature weight that measures the likelihood of a point to be an edge, then detects the edge points based on that value at both global and local scales. Moreover, we evaluate quantitatively and qualitatively our method. Experimental results show that the proposed approach achieves a superior accuracy. Furthermore, we demonstrate the robustness of our approach in noisier real-world datasets.