Local image features are routinely used in state-of-the-art methods to solve many computer vision problems like image retrieval, classification, or 3D registration. As the applications become more complex, the research for better visual features is still active. In this paper we present a feature detector that exploits the inherent geometry of sampled image edges using α-shapes. We propose a novel edge sampling scheme that exploits local shape and investigate different triangulations of sampled points. We also introduce a novel approach to represent the anisotropy in a triangulation along with different feature selection methods. Our detector provides a small number of distinctive features that is ideal for large scale applications, while achieving competitive performance in a series of matching and retrieval experiments.