A new approach is proposed to detect edges based on an artificial neural network (ANN). Some elementary continuous and discontinuous functions interpolated in the polynomial space and their continuity are used as the training sets to train a back propagation neural network containing two hidden layers. The ANN edge detector is used to detect the edges in an image and the locations of discontinuity in the hybrid fifth order Compact-WENO nonlinear (Hybrid) scheme for solving hyperbolic conservation laws with solutions containing both discontinuous and complex fine scale structures. Several classical examples in the image processing show that the ANN edge detector can capture an edge accurately with fewer grid points than the classical multi-resolution analysis. Furthermore, as oppose to the MR analysis, the ANN edge detector is robust with no problem dependent parameter, in addition to being accurate and efficient. The performance of the Hybrid scheme with the ANN edge detector is demonstrated with several one- and two-dimensional benchmark examples in the shallow water equations and Euler equations.

提出了一种基于人工神经网络（ANN）的边缘检测新方法。多项式空间中内插的一些基本连续和不连续函数及其连续性被用作训练集来训练包含两个隐藏层的反向传播神经网络。ANN边缘检测器用于检测图像中的边缘和不连续性的混合五阶Compact-WENO非线性（Hybrid）方案中的不连续位置，以解决包含不连续和复杂精细尺度结构的解决方案的双曲守恒定律。图像处理中的几个经典示例表明，与经典的多分辨率分析相比，ANN边缘检测器可以用更少的网格点准确捕获边缘。此外，与MR分析相反，ANN边缘检测器具有鲁棒性，并且没有问题相关参数，而且准确性高，效率高。通过浅水方程和欧拉方程中的几个一维和二维基准示例，证明了具有ANN边缘检测器的Hybrid方案的性能。