Euler Lagrange based Solution for Image Processing

Abstract

Image processing is one of the rapidly growing technologies with operations that can be applied to image data which may be in the form of a 2D, 3D or 4D signals. It has created tremendous opportunities for mathematical modeling, analysis, and computation. A novel approach in image processing has been developed, known as PDE (Partial Differential Equations) based image processing. The PDE approach is very promising for solving many problems in image processing because it provides new and more intuitive mathematical models, gives better approximations to the Euclidean geometry of the problem, and is supported by efficient discrete numerical algorithms based on difference approximations. In this paper, we have discussed how Euler Lagrange Equation plays a significant role in solving PDE based image processing problems. The typical image processing problems such as denoising and inpainting can be solved using EL equation. The ROF and Tikhnov models of denoising and Total Variation based inpainting has been implemented and a comparative study is done with the conventional methods. We have considered various well-known objective quality evaluation metrics used in image processing in this comparison. The results show that PDE based image processing techniques outperforms the conventional approaches.