The points on the point clouds that can entirely outline the shape of the model are of critical importance, as they serve as the foundation for numerous point cloud processing tasks and are widely utilized in computer graphics and computer-aided design. This study introduces a novel method, RWoDSN, for extracting such feature points, incorporating considerations of sharp-to-smooth transitions, large-to-small scales, and textural-to-detailed features. We approach feature extraction as a two-stage context-dependent analysis problem. In the first stage, we propose a novel neighborhood descriptor, termed the Disk Sampling Neighborhood (DSN), which, unlike traditional spatially and geometrically invariant approaches, preserves a matrix structure while maintaining normal neighborhood relationships. In the second stage, a random walk is performed on the DSN (RWoDSN), yielding a graph-based DSN that simultaneously accounts for the spatial distribution, topological properties, and geometric characteristics of the local surface surrounding each point. This enables the effective extraction of feature points. Experimental results demonstrate that the proposed RWoDSN method achieves a recall of 0.769-22% higher than the current state-of-the-art-alongside a precision of 0.784. Furthermore, it significantly outperforms several traditional and deep-learning techniques across eight evaluation metrics.