Recursive Separable Schemes for Nonlinear Diffusion Filters

摘要: Poor efficiency is a typical problem of nonlinear diffusion filtering, when the simple and popular explicit (Euler-forward) scheme used: for stability reasons very small time step sizes are necessary. In order to overcome this shortcoming, novel type semi-implicit schemes studied, so-called additive operator splitting (AOS) methods. They share advantages (semi-)implicit by combining simplicity with absolute stability. reliable, since they satisfy recently established criteria discrete scale-spaces. Their due fact that can be separated into one-dimensional processes, which fast recursive algorithm linear complexity available. AOS reveal good rotational invariance symmetric respect all axes. Examples demonstrate that, under accuracy requirements, at least ten times more efficient than schemes.