Depending on the application, local feature detectors should comply to properties that are often contradictory, e.g. distinctiveness vs robustness. Providing a good balance is a standing problem in the field. In this direction, we propose a novel approach for local feature detection starting from sampled edges and based on shape stability measures across the weighted alpha-filtration, a computational geometry construction that captures the shape of a non-uniform set of points. Detected features are blob-like and include non-extremal regions as well as regions determined by cavities of boundary shape. The detector provides distinctive regions, while achieving high robustness in terms of repeatability and matching score, as well as competitive performance in a large scale image retrieval application.