针对传统梯度算子中，用于边缘方向检测的计算公式存在的缺点，提出了改进的用于边缘方向检测的计算公式.鉴于用传统梯度算子检测的边缘方向是由反正切函数给出的，而反正切函数所表示的角度范围是 [- π/ 2，π/ 2 ],可是事实上，边缘方向的范围是 [0，2 π].为此，通过对梯度算子中，Prewitt算子的分析，指出传统的边缘算子不能区分两个相差 π的边缘方向，并给出了改进的用于边缘方向检测的计算公式.在传统的梯度算子中，因为用于边缘方向检测的计算公式是不精确的，所以后续图象边缘的细化、短枝消除、缝隙填补和连接等处理就建立在一个不精确的基础之上，从而得到的边缘误差较大.因为在图象低层处理中就引入了误差，所以后续图象高层处理的质量也降低了.计算机仿真实验结果表明，该改进的用于边缘方向检测的计算公式是正确的和有效的.

According to the shortcoming of the classical gradient operator, this paper gives an improved computational formula for edge direction. The edge direction of the classical gradient operator is given by an anti-tangent function, and the angle range which the anti-tangent function can represent is [-π/2,π/2], but the range of edge direction is [0,2π]. This paper analyzes the operator from the gradient operators, and points out that the classical gradient operator can not discrete two edges which have a difference ofπin edge direction, and gives a improved computational formula for edge direction. In the classical gradient operator, because the computational formula for edge direction is not precise, the following image edge thinning, short edge removing, aperture filling and edge linking are constructed on a non-precision foundation, error results being got. Because of the error in low-level image processing, the quality of following high-level image processing is low. The computer-simulated experiments show that, the improved computational formula of edge direction in this paper is correct and effective.