Image processing with rational operators: noise smoothing and anisotropic diffusion

A brief overview is given in this paper of the possible applications of rational operators in the image processing area. In this family of operators, each output sample can be calculated as a nonlinear function of the input variables, which is expressed as the ratio of two polynomials. This approach is able to yield good results at limited computational costs in the fields of contrast enhancement, interpolation, and edge-preserving noise smoothing. This paper focuses on the noise smoothing ability of rational operators, presenting some relationships with the anisotropic diffusion method.