PDE based image processing theory and computation

  • Vijayakrishna Rowthu
  • B.V. Rathish Kumar

Abstract

This article is aimed at emphasizing a complete mathematical framework to the concept of image processing (IP) based on Variational Partial Differential Equations (PDE) models. After discussing few problems of IP like denoising, inpainting, segmentation, deblurring etc. along with their PDE models in various function spaces, some computations carried over on biomedical data will be presented in support of the robustness of PDE/Variational based methods compared to the Statistical
tools of IP. An attempt has been made successfully in depicting a cartoon type image segmentation capability of Cahn-Hilliard equation which now opens up yet another approach in object recognition. Some highlights on few of the issues related to PDE models lacking theoretical justification such as wellposedness and also related IP problems which need to be addressed are provided.

Published
2014-05-25
Section
Articles