Boundary-based corner detection has been widely applied in spline curve fitting, automated optical inspection, image segmentation, object recognition, etc. In order to obtain good results, users usually need to adjust the length of region of support to resist zigzags due to quantization and random noise on digital boundaries. To automatically determine the length of region of support for corner detection, Teh-Chin and Guru-Dinesh presented adaptive approaches based on some local properties of boundary points. However, these local-property based approaches are sensitive to noise. In this paper, we propose a new approach to find the optimum length of region of support for corner detection based on a statistic discriminant criterion. Since our approach is based on the global perspective of all boundary points, rather than the local properties of some points, the experiments show that the determined length of region of support increases as the noise intensity strengthens. In addition, the detected corners based on the optimum length of region of support are consistent with human experts' judgment, even for noisy boundaries.