Abstract: A corner detection algorithm based on the multi-scale multiplication of the determinant of the covariance matrix is proposed.The covariance matrix is explored upon the local support region of the planar curve.The analysis of the eigenvalue and the eigenvector of the covariance matrix proves that the determinant of the covariance matrix has the strongest response at corners by using V corner model.In order to effectively incorporate the characteristics of different scales，multi-scale multiplication is used，which not only promotes the magnitude of the response at corners，but also suppresses the peaks of the non-corners and noises.Experimental results show that the proposed method is well localized，robust to noise and have good characteristic of rotation and scale invariance by comparison with the classical corner detectors.

Key words: corner detection, multi-scale product, covariance matrices, region of support

摘要： 研究平面轮廓局部支撑域上的协方差矩阵，通过对图像协方差矩阵的特征值和特征向量的分析，以V角点模型为例，证明了协方差矩阵行列式在角点位置有唯一的极值响应。同时，为了有效地融合各个尺度信息，采用多尺度乘积方法来增强角点响应的幅度，抑制非角点或噪声的幅度。基于此，提出以多尺度乘积的协方差矩阵行列式作为角点响应函数的角点检测算法。实验结果表明：通过比较经典的角点检测算法，算法具有很好的定位、抗噪及旋转和尺度不变性。

关键词: 角点检测, 多尺度乘积, 协方差矩阵, 轮廓支撑域