Image Processing and Analysis Based on Partial Differential Equation Method

Abstract

This paper analyzes the characteristics of image processing method based on nonlinear evolution equations, expounds the advantages, mechanism and theoretical basis of nonlinear evolution equations model in image processing algorithm, and uses the method of partial differential equation for image denoising and edge sharpening (Deblurring), image resolution enhancement, image shaping and image measurement. I. INTRODUCTION Digital image processing is the mathematical processing of converted digital images of simulation image sampling and quantization by use of digital computer technology and other hardware in order to improve the practicability of the image and achieve some expected results. In information society, digital image processing, no matter in theory or in practice, has a huge potential: the image is an important source for people to obtain information from the objective world; Image information processing is an important means of expanding human vision; Image processing technology has important significance to national industrial, economic and social development. Along with the development of image processing hardware and software, image processing disciplines increasingly need the intervention and boost of modern mathematical tools. Mathematics provides not only image information representation and coding style and language, but also provides direct foundation and core algorithm for image information processing, processing and utilization. Originally it was from physics and mechanics' nonlinear partial differential equations, which has opened up a new field in image processing and computer vision in recent years. A large number of literature and academic conference based on nonlinear partial differential equation research has received widespread attention and has made great success. The thought of using partial differential equations in image processing can be traced back to D. Gabor and A.K.Jain's work. However, the field's substantial founding work was due to J.J.Koenderink and A. Pwitkin's independent study: they introduced scale space theory, namely image multi-scale expression, which laid foundation for the application of partial differential equations in image processing.