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Image denoising using mean curvature of image surface. (English) Zbl 1258.94021

Summary: 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 \(f:\Omega\rightarrow\mathbb{R}\). 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 [L. I. Rudin et al., Physica D 60, No. 1–4, 259–268 (1992; Zbl 0780.49028)].

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
53A05 Surfaces in Euclidean and related spaces
65K10 Numerical optimization and variational techniques
68U10 Computing methodologies for image processing

Citations:

Zbl 0780.49028
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