U弦长曲率：一种离散曲率计算方法

摘要

Discrete curvature computation of digital curves is widely applied to various tasks of image analysis and computer vision. A computational method of discrete curvature, U-chord curvature, is proposed. For each point in a digital curve, its support region is determined by two points with a given chord distance to the point, and then the U-chord curvature of the point is estimated. A theoretical analysis shows that there is a close relationship between the U-chord curvature and the real curvature of the curve. Compared with the existing computational methods of discrete curvature, the U-chord curvature is more stable under rotation transformations and noise condition. Therefore, it is suitable for image and vision tasks which require a high stability of curvature estimation, such as curve matching. Simulation experiments show the efficiency of the proposed method.%数字曲线的离散曲率计算在图像分析和计算机视觉的各个领域都有广泛应用。文中提出一种离散曲率计算方法---U弦长曲率。数字曲线上的每个点,它的支持领域由距离该点为给定弦长的两点确定,再在这个支持领域内估算当前点的U弦长曲率,理论分析论证U弦长曲率与曲线的真实曲率之间存在一种明确联系。与现有的离散曲率计算方法相比,U弦长曲率具有更强的抗旋转性和抗噪性,适用于完成曲线匹配等对曲率计算稳定性要求高的一类任务。仿真实验结果验证文中方法的有效性。