Image Denoising Using Mean Curvature of Image Surface

Abstract

We propose a new variational model for image denoising, which employs the L 1-norm of the mean curvature of the image surface (x, f (x)) of a given image f : Ω → R. Besides eliminating noise and preserving edges of objects efficiently, our model can keep corners of objects and greyscale intensity contrasts of images and also remove the staircase effect. In this paper, we analytically study the proposed model and justify why our model can preserve object corners and image contrasts. We apply the proposed model to the denoising of curves and plane images, and also compare the results with those obtained by using the classical Rudin-Osher-Fatemi model [Phys. D, 60 (1992), pp. 259-268].

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

“…One approach suggested by Zhu and Chan [Zhu12] is to treat an image v : Ω → R as a surface in Ω × R and utilize the surface mean curvature information in the regularization term. More specifically, the surface in question is defined by the equation…”

“…As noted in [Zhu12], this model has the ability to remove noise without the undesirable drawbacks associated with the ROF model. However, the non-convex and non-smooth nature of the objective function (5) makes the problem very difficult to solve.…”

Introduction to variational image-processing models and applications

“…Below we give the derivation for its EL equation, as such details are absent in [4,13,28]. To mimick the above TV equation, set ∂u/∂n| = 0 and there should be another condition to be defined.…”

Generalized Gradient on Vector Bundle – Application to Image Denoising

“…Since then, this model has been extended in several ways (see e.g. [4], [10], [15], [16], [17], [18], [24] for local methods based on a modification of the regularizing term, and [9], [11] for nonlocal methods). In this paper, we construct a new regularizing term by the introduction of a generalization of the gradient operator.…”