Corner detection is a critical component of many image analysis and image understanding tasks, such as object recognition and image matching. Our research indicates that existing corner detection algorithms cannot properly depict the difference between edges and corners and this results in wrong corner detections. In this paper, the capability of second-order generalized (isotropic and anisotropic) Gaussian directional derivative filters to suppress Gaussian noise is evaluated. The second-order generalized Gaussian directional derivative representations of step edge, L-type corner, Y- or T-type corner, X-type corner, and star-type corner are investigated and obtained. A number of properties for edges and corners are discovered which enable us to propose a new image corner detection method. Finally, the criteria on detection accuracy and average repeatability under affine image transformation, JPEG compression, and noise degradation, and the criteria on region repeatability are used to evaluate the proposed detector against nine state-of-the-art methods. The experimental results show that our proposed detector outperforms all the other tested detectors.