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

摘要

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