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

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.