IEEE TRANSACTIONS ON IMAGE PROCESSING VOL NO PP MARCH Ecient and Reliable Schemes for Nonlinear Diusion Filtering

Abstract Nonlinear diusion ltering is usually per formed with explicit schemes They are only stable for very small time steps which leads to poor eciency and limits their practical use Based on a recent discrete nonlin ear diusion scalespace framework we present semiimplicit schemes which are stable for all time steps These novel schemes use an additive operator splitting AOS which guarantees equal treatment of all coordinate axes They can be implemented easily in arbitrary dimensions have good rotational invariance and reveal a computational complex ity and memory requirement which is linear in the number of pixels Examples demonstrate that under typical accu racy requirements AOS schemes are at least ten times more ecient than the widelyused explicit schemes KeywordsNonlinear diusion recursive lters absolut