Graph-based Image Sharpening Filter Applied to Image Denoising

The present paper focuses on a new class of mesh filter for grayscale images, called grid smoothing filter. The framework presented considers an image as a sampling grid associated to a set of gray levels. Furthermore, the sampling grid is seen as mesh composed by vertices and edges, the number of vertices being equal to the number of pixels in the image. Embedding the mesh in a 2D Euclidian space, each vertex has two spatial coordinates and one attribute, the value of the gray level. Starting from the classical formulation of Laplacian mesh filtering, a novel objective function is introduced. The minimization of the objective function leads to new spatial coordinates for the vertices in the mesh. A reconstruction mechanism is then applied to the non-uniform mesh to reconstruct a grayscale image. Whereas the Laplacian mesh filter aims at smoothing an image, the grid smoothing tends at sharpening the edges of the image. The grid smoothing framework is applied to image enhancement in this paper.