Fast difference scheme for anisotropic Beltrami smoothing and edge contrast enhancement of gray level and color images
R. Malladi, Igor Ravve · eScholarship (California Digital Library) · 2001
hi this study, we re-arrange the governing equation for Belt.ramidiffusion fiowto the form, where the reaction term and the diffusion tel'm appear explicitly.The reaction term leads to an edge enhance-mEint, and we illustrate this phenomenon by numerical simulations.The Teaction-diffusion form of the Beltrami equation makes it possible to develop the Ullconditionally stable semi-implicitscherrie for image filtering.The method is based on Additive Operator Split, applied ... originally byWeickert for the nonlinear diffusion•fiow.The values of .the edge indicator function are used from the pr:eviousstep in• sca,le; while the pixel values of the next step are used to approximate t.he Beltrami flow.This approach leads to a semi-implicit linearized dif~• fere~ce scheme.The sources of truncation .etrorare examined and.'. : ...... components all vanish or almost vanish.The Beltrami smoothing operator becomes weakly coupled.The principal directions of the edge indicator matrix are normal to the edge and tangent to the edge.Replacing the action of this matrix onthe gradient vector by an action of its eigenvalue, we reduce the color problem to the gray level case and show that the scalar edge indicator function for the color case is exactly the same as that for the gray level image~ Thus, the interprertation of the gray level edge enhancement mechanism caused by reaction term of the smoothing PDE may be applied for color images, and the fast implicit smoothing scheme may be implemented for color images as well.