Corner detection is important in image analysis and understanding, but most existing corner detectors are sensitive to image quality, lens radial distortion, and illumination. In this paper, we propose a corner detector for robust corner detection in continuous space. We use the open string theory to construct the continuous representation of an image. Defining a corner as the intersection of two or more curve edges or straight line edges, we design a corner response function for corner determination. In detail, for each integer point, we construct multiple grayscale-parallelograms by any two directed line segments of that point, and the corner response function is based on these grayscale-parallelograms. Finally, a point with a high response value is detected as a corner. Experimental results on conventional images, wide-angle images, and fisheye images show that the proposed method obtains state-of-the-art performance on conventional images and achieves superior performance on wide-angle images and fisheye images, even under weak lighting and low-quality conditions.