针对图像灰度各阶导数的离散化表示方法和图像边缘最佳响应方向的确定等关键技术,本文提出基于任意方向图像导数算法的边缘检测技术。该方法根据导数的定义建立数学模型,推导出计算灰度图像任意方向的一阶、二阶导数公式,通过分析待检图像的边缘特性,对图像进行多方向乃至全视角方向的灰度梯度计算和拉普拉斯变换,并输出最佳边缘响应。使用该方法与已有检测算子进行对比实验,证实了该算法的有效性并显示了其在边缘检测效果上的优势。

A new edge detection technique based on derivative algorithm in arbitrary directions is developed. Discrete representation of derivative for grey image and determination of optimal response direction are important to edge detection techniques. The mathematic model of derivative for grey image was represented, and the first derivative and the second derivative algorithms in arbitrary directions were derived from the basic derivative definition. Based on the characteristic analysis of image edge, the grey-level gradients and Laplace transforms in multi-directions or full directions of view were calculated, and the maximums determined the output values for the edge magnitude image. The new algorithm is demonstrated to be valid by detecting the edge of normal image and some advantages of the algorithm are represented over the conventional edge operators.