Journal of Mathematical Imaging and Vision

, Volume 55, Issue 1, pp 105–124

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

• Heike Benninghoff
• Harald Garcke
Article

## Abstract

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.

## Keywords

Image segmentation Images on surfaces Evolving curves on surfaces Active contours Parametric method Mumford–Shah Chan–Vese Topology changes Triple junctions Image restoration Finite element approximation

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