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In this article, a new method for segmentation and restoration of images ontwo-dimensional surfaces is given. Active contour models for image segmentationare extended to images on surfaces. The evolving curves on the surfaces aremathematically described using a parametric approach. For image restoration, adiffusion equation with Neumann boundary conditions is solved in apostprocessing step in the individual regions. Numerical schemes are presentedwhich allow to efficiently compute segmentations and denoised versions ofimages on surfaces. Also topology changes of the evolving curves are detectedand performed using a fast sub-routine. Finally, several experiments arepresented where the developed methods are applied on different artificial andreal images defined on different surfaces.

Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes