Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion to Preserve Singularities and Delete Isolated Points in Image Smoothing

Abstract

Existing Nonlinear Anisotropic Diffusion (NAD) methods in image smoothing cannot obtain satisfied results near singularities and isolated points because of the discretization errors. In this paper, we propose a new scheme, named Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion (ELONAD), which allows us to provide a unified framework for points in flat regions, edge points and corners, even can delete isolated points and spurs. ELONAD extends two diffusion directions of classical NAD to eight or more enclosed directions. Thus it not only performs NAD according to modules of enclosed directions which can reduce the influence of traction errors greatly, but also distinguishes isolated points and small spurs from corners which must be preserved. Smoothing results for test patterns and real images using different discretization schemes are also given to test and verify our discussions.