A new differential operator is proposed for edge detection based on Taylor expansion to calculate intensity difference of the image along horizontal and vertical orientations. Compared with classical first-order or second-order differential operators, its gradient magnitude calculation is more accurate, thus improving the situation in which few weak edges are detected and their approximation to the image is poor. Then, a threshold is calculated based on Otsu method from the gradient magnitude histogram, thus a new adaptive differential operator is obtained. Simulation results show that the new operator can automatically detect edges. Moreover, compared with the classical ones, it finds more weak edges especially for those images with low contrast, and has good approximation for curves and can be applied to those images with rich details such as face image. In addition, the advantages of new operator are also confirmed when it is applied to Canny detector, thus the edge detection accuracy and the efficiency are improved.%提出一种新的微分算子用于边缘提取,基于泰勒展开分别计算图像水平和竖直方向的灰度差分,相比传统一阶或二阶微分算子,其梯度值结果更精确,弥补了传统算子微弱边缘提取少且与原图逼近度较差的缺陷.然后基于大津法思想对图像梯度幅值直方图计算分割阈值,从而得到一种新的能自适应提取边缘的微分算子.仿真结果表明,新算子不仅能够对不同图像自适应提取边缘,并且相比传统微分算子,它能提取更多微弱边缘,尤其对灰度对比度较低的图像.同时对曲线部分具有较好的逼近效果,适用于人脸等线条细节比较丰富的图像.将新算子应用到Canny算子中能获取更精确的结果.
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