Foundations and applications of nonlinear anisotropic diffusion filtering

of anisotropic diffusion equations is investigated which are useful for image processing. These filters calculate a family {u(t)\t greater than or equal to 0} of processed versions of an image f is an element of L(infinity)(Omega) was the solution of partial derivative(t)u=div(D del u) on Omega x(0, infinity), u(x, 0)=f(x) on Omega, (D del u, n)=0 on partial derivative Omega x(0, infinity). In order to adapt the positive definite diffusion tensor D to the local image structure, it is chosen to be a function of the structure tensor K-rho*((del K-sigma*u)(T)), where K-rho denotes a Gaussian with standard deviation rho. Under smoothness and uniform positive definiteness requirements for D one can establish existence, uniqueness and regularity results. The solution depends continuously on the initial image and satisfies an extremum principle. ii large class of Lyapunov functionals ensures that the image becomes smoother with respect to numerous aspects. Examples are discussed which illustrate that anisotropic diffusion filtering can be easily adapted to specific demands such as smoothing with simultaneous edge enhancement, or enhancement of flow-like coherent structures.