Abstract—Second-order curvature driven diffusion methods such as mean curvature driven diffusion and Gauss curvature driven diffusion were introduced in the literature for image denoising. However, the second-order Partial Differential Equations modify smooth areas in images into piece-wise constant areas resulting in a staircase effect. Moreover, important information present in images such as textures is often lost in the course of evolution. In this paper, we propose a fourth-order diffusion equation, which uses a function of Gauss curvature as the conductance term to control the magnitude of diffusion. The fourth-order PDE helps to preserve the planar approximation by approximating the observed image with a piecewise planar image. This provides a more natural look to the filtered image. The Gauss curvature based conductance term preserves curvy edges, ramps and corners, with non-zero curvature value. The visual and quantitative results of the method are presented and compared with some of the existing PDE based denoising methods.

Index Terms—Fourth-order PDE, gauss curvature, denoising, edge preserving.

The authors are with National Institute of Technology, Karnataka, and Mangalore, INDIA-575025 (e-mail: jidesh@nitk.ac.in, sgeorge@nitk.ac.in).

Cite: P. Jidesh and Santhosh George, "Fourth-order Gauss Curvature Driven Diffusion for Image Denoising," International Journal of Computer and Electrical Engineering vol. 4, no. 3, pp. 350-354, 2012.