In this article, a new method for segmentation and restoration of images on
two-dimensional surfaces is given. Active contour models for image segmentation
are extended to images on surfaces. The evolving curves on the surfaces are
mathematically described using a parametric approach. For image restoration, a
diffusion equation with Neumann boundary conditions is solved in a
postprocessing step in the individual regions. Numerical schemes are presented
which allow to efficiently compute segmentations and denoised versions of
images on surfaces. Also topology changes of the evolving curves are detected
and performed using a fast sub-routine. Finally, several experiments are
presented where the developed methods are applied on different artificial and
real images defined on different surfaces
