切点是表征图像中平面曲线局部形状变化的重要点特征，现有的研究鲜有涉及。构建了表征平面曲线局部几何特征的梯度相关矩阵（GCMs），通过GCMs行列式检测到了角点，但无法检测典型切点模型。由于GCM行列式仅在直线段上的点处取零，可将平面曲线分段为平面子直线段和子曲线段，结合方向函数，检测位于子直线段与子曲线段之间、或子曲线段上的切点。利用精确度（ACU）与定位误差（LE）准则测试算法，给出实验仿真结果，证明算法有效，具有较好的稳健性。

Tangent vertices are important feature points characterizing the local shape changes of planar curves in the image, but there are few researches aiming at them. Gradient correlation matrices (GCMs) are constructed which encode the geometric features of these curves. Corners are detected by the determinants of the GCMs, but this method is invalid to detect tangent vertices of typical tangent models. The determinants of the GCMs are found to be zero merely at points on straight-line segments so that planar curves can be divided into sub-straight-line segments and sub-curve-line segments. Combining the function of direction orientation, tangent vertices are located between the sub-straight-line segments and the sub-curve-line segments, or on the sub-curve-line segments. The accuracy and location error criteria are utilized to test the algorithm and experimental results are shown. These results demonstrate that the algorithm of this paper can detect tangent vertices efficiently and is robust to noise.