Research On Image Edge Detection Method Based On Partial Differential Equation

Edge is an important part,which is used to describe image features by people.It not only can provide useful information for object recognition,but also important parameters for high level image analysis and comprehension.In the field of machine vision,edge detection is always one of the most basic and popular research.It is the prerequisite for all image analysis and comprehension.Consequently,the research and development of edge detection have a long history.However,there is a core contradiction in the process of image edge detection.That is to say,if we want to protect real edge,the false edge will be introduced.Likewise,if we want to eliminate the false edge,the real edge will be blurred.So far,although the method and theory of edge detection is various and has become increasingly mature,there are many deficiencies.The core contradiction is still not solved perfectly in the image edge detection.Therefore,the improvement according to traditional way or the new method according to the new theory,which is to get more true results closed to real edge,is currently popular research direction.In recent years,in order to achieve image enhancement,image restoration,image segmentation etc.,combining with some characteristic of digital image and constructing the model of partial differential equations is becoming the new research hotspot.Although,the model of partial differential equations involved advanced mathematical theory,complex mathematical formulas,massive algorithm analysis and numerical solution,it put the assessment of the image process result to a new level at the issue of solving core contradiction in the image edge detection.The fusion between the theory of partial differential equations and digital image process is widely used in many fields of science and engineering,such as aerospace,medical imaging,traffic safety,industrial inspection and machine intelligence.This paper has analyzed the image edge detection method based on partial differential equation.Firstly,we introduces the development background and significance of this research and the current situation of the development of image edge detection.We summarize the topic relates to the variation principle and provide the numerical solving method about about variation problem and some examples of variation problem.Secondly,we have introduced the application of the two order PDE in the image edge detection.One is the PDE model according to the evolution theory,which is two order detection model based on the thermal diffusion equation.Then,we describe in detail the thermal equation diffusion model,P-M diffusion model and Catte diffusion model.The other is the PDE model according to the problem of energy function extremum, which is two order detection model based onvariation theory.Then, we describe in detail classical TV model,generalized TV model and adaptive TV model.Furthermore,we analyze and research on the high order PDE model,which can overcome the phenomenon of false edges of the two order PDE model in edge detection.Then,we focus on the classical Y-K model and the Y-K model based on the diffusion coefficient improvement.Finally,we put forward a PDE detection method which is the combination of two order PDE and four order PDE.Then,we provide its Euler-Lagrange equation,the gradient descent method and the numerical discretization method.Experimental results show that this method not only can overcome the false edge of two order model but also restrain edge blur of four order model.Meanwhile,about the issue that the current evaluation index of image edge detection couldn’t appraise the result of edge detection precisely, through in-depth study, this paper put forward four requirements to edge detection and design an objective and comprehensive evaluation index which involve reconstructing similarity index SSIM,edge reliability index BIdx,edge continuity index CIdx and noise evaluation index.This comprehensive index could provide effective numerical evidence for the result of image edge detection and reduce uncertainty and non-universality of traditional evaluation method.