构造了反映轮廓曲线局部几何特征的梯度相关矩阵(GCM)，并基于Lagrange乘子优化方法和Γ角点模型分析和证明了GCM的特征值与特征向量的特性，解释了相应的几何意义。将GCM的行列式定义为角点的响应函数，提出了相应的角点检测算法。最后，通过大量实验证明了GCM方法具有较好的检测性能，以及对各种几何变换和噪声的鲁棒性。

Gradient correlation matrixes representing local geometrical features of planar contour is constructed, and properties of eigenvalues and eigenvectors of GCM are analyzed and proved based on Lagrange multiplier optimal method and Γ corner model Thus, the corresponding geometrical meaning is obtained The determinant of GCM is defined as corner response function and the corresponding corner detection algorithm is presented Finally, a number of experiments demonstrate that the proposed algorithm has a good detection performance and robustness to the various geometrical transformations and noise