High-Order Discretization of Backward Anisotropic Diffusion and Application to Image Processing

TL;DR

This paper introduces a high-order discretization method for backward anisotropic diffusion, enhancing image processing tasks like edge detection and denoising with improved accuracy and efficiency.

Contribution

It presents a novel nonlinear operator and discretization technique that accurately captures edges without approximation, improving image reconstruction quality.

Findings

Effective edge detection without approximation

Enhanced image denoising and reconstruction

Low computational cost for high accuracy

Abstract

Anisotropic diffusion is a well recognized tool in digital image processing, including edge detection and denoising. We present here a particular nonlinear time-dependent operator together with an appropriate high-order discretization for the space variable. The iterative procedure emphasizes the contour lines encircling the objects, paving the way to accurate reconstructions at a very low cost. One of the main features of such an approach is the possibility of relying on a rather large set of invariant discontinuous images, whose edges can be determined without introducing any approximation.