The scale of edges

Although the scale of isotropic visual elements such as blobs and interest points, e.g. SIFT[12], has been well studied and adopted in various applications, how to determine the scale of anisotropic elements such as edges is still an open problem. In this paper, we study the scale of edges, and try to answer two questions: 1) what is the scale of edges, and 2) how to calculate it. From the points of human cognition and physical interpretation, we illustrate the existence of the scale of edges and provide a quantitative definition. Then, an automatic edge scale selection approach is proposed. Finally, a cognitive experiment is conducted to validate the rationality of the detected scales. Moreover, the importance of identifying the scale of edges is also shown in applications such as boundary detection and hierarchical edge parsing.