Resolving closely spaced corners using second order Gaussian directional derivatives

Corner detection is a fundamental step in many computer vision tasks, including image matching and 3D reconstruction. However, closely spaced corners are difficult to distinguish because inappropriate smoothing scales may cause the filtered responses of neighboring structures to overlap, leading to missed or inaccurately localized corners. In this study, we analyze the responses of second-order Gaussian directional derivative (SOGDD) filters to three representative geometric models, namely the END-type, STAIR-type, and L-type models. For each model, we derive its SOGDD representation and establish scale-selection conditions under which the response at a true corner remains stronger than that at the intermediate edge point. Based on this analysis, we propose a detector designed to preserve discriminative directional intensity variations and resolve closely spaced corners. A dedicated adjacent-corner benchmark directly evaluates the minimum resolvable inter-corner distance, separation rate, localization error, and false detections. Additional experiments on localization accuracy, affine-transformation robustness, image matching, 3D reconstruction, and computational efficiency demonstrate the effectiveness and limitations of the proposed method.