A new nonlinear tracking differentiator and its application in edge detection

Edge detection has traditionally been a fundamental problem in digital image processing. Although many different detection approaches have already been proposed, there still exists a contradiction between noise suppression, edge protection and algorithm complexity. So it is still a challenging problem and continues to be an active research area. In this paper, we explore new solutions in nonlinear field by introducing the idea of optimal control into edge detection. Firstly, a new discrete-time nonlinear Tracking Differentiator is derived by phase plane analysis, which has a better noise suppression ability and a smaller amount of calculation compared with some influential algorithms. Then, the new tracking differentiator is applied to 2-dimensional space to obtain the gray gradient of an image. Subsequently, the edges can be extracted by applying hysteresis thresholding to the gray gradient obtained. The experimental results show our method can outperform the conventional Canny algorithm. This paper provides a new idea for edge detection technology.