A GENERAL FRAMEWORK FOR GEOMETRY-DRIVEN EVOLUTION-EQUATIONS

This paper presents a general framework to generate multi-scale repres entations of image data. The process is considered as an initial value problem with an acquired image as initial condition and a geometrical invariant as ''driving force'' of an evolutionary process. The geomet rical invariants are extracted using the family of Gaussian derivative operators. These operators naturally deal with scale as a free parame ter and solve the ill-posedness problem of differentiation. Stability requirements for numerical approximation of evolution schemes using Ga ussian derivative operators are derived and establish an intuitive con nection between the allowed time-step and scale. This approach has bee n used to generalize and implement a variety of nonlinear diffusion sc hemes. Results on test images and medical images are shown.