Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression

TL;DR

This paper introduces a novel fourth-order anisotropic diffusion method for image inpainting and compression, extending second-order edge-enhancing diffusion to improve reconstruction accuracy with a flexible, unifying framework.

Contribution

It generalizes second-order EED to a fourth-order approach using a new diffusion tensor, offering enhanced flexibility and improved image reconstruction performance.

Findings

Outperforms second-order EED in image reconstruction accuracy

Provides a unifying framework for anisotropic fourth-order diffusion methods

Achieves efficient implementation with a semi-iterative scheme

Abstract

Edge-enhancing diffusion (EED) can reconstruct a close approximation of an original image from a small subset of its pixels. This makes it an attractive foundation for PDE based image compression. In this work, we generalize second-order EED to a fourth-order counterpart. It involves a fourth-order diffusion tensor that is constructed from the regularized image gradient in a similar way as in traditional second-order EED, permitting diffusion along edges, while applying a non-linear diffusivity function across them. We show that our fourth-order diffusion tensor formalism provides a unifying framework for all previous anisotropic fourth-order diffusion based methods, and that it provides additional flexibility. We achieve an efficient implementation using a fast semi-iterative scheme. Experimental results on natural and medical images suggest that our novel fourth-order method produces more accurate reconstructions compared to the existing second-order EED.