A general framework for geometry-driven evolution equations

This paper presents a general framework to generate multi-scale representations 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 geometrical invariants are extracted using the family of Gaussian derivative operators. These operators naturally deal with scale as a free parameter and solve the ill-posedness problem of differentiation. Stability requirements for numerical approximation of evolution schemes using Gaussian derivative operators are derived and establish an intuitive connection between the allowed time-step and scale. This approach has been used to generalize and implement a variety of nonlinear diffusion schemes. Results on test images and medical images are shown.