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

TL;DR

This paper introduces a parametric active contour method for segmenting and restoring images on 2D surfaces, incorporating topology changes and efficient numerical schemes for practical applications.

Contribution

It extends active contour models to surface images with a parametric approach, including topology change detection and efficient computation methods.

Findings

Effective segmentation and restoration on various surfaces.

Topology changes are accurately detected and handled.

Numerical schemes enable practical implementation.

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.