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

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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.

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Notes

  1. https://graphics.stanford.edu/data/3Dscanrep/.

    Fig. 2
    figure 2

    Illustration of how triangles are assigned to a region. 1st sub-figure image and initial curve. 2nd sub-figure small band after \(n_0=4\) steps. 3rd sub-figure regions colored with mean brightness value after assignment of all triangles. The surface data are from the Stanford Computer Graphics Laboratory, cf. [31]

    Full size image

  2. http://faces.cs.unibas.ch/bfm/main.php?nav=1-0&id=basel_face_model.

  3. http://neo.sci.gsfc.nasa.gov/

  4. Imagery by Jesse Allen, NASA Earth Observatory, based on FLASHFlux data. FLASHFlux data are produced using CERES observations convolved with MODIS measurements from both the Terra and Aqua satellite. Data provided by the FLASHFlux team, NASA Langley Research Center.

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Authors and Affiliations

  1. Deutsches Zentrum für Luft- und Raumfahrt (DLR), 82234, Weßling, Germany

    Heike Benninghoff

  2. Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    Harald Garcke

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  1. Heike Benninghoff
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  2. Harald Garcke
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Correspondence to Heike Benninghoff.

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Benninghoff, H., Garcke, H. Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes. J Math Imaging Vis 55, 105–124 (2016). https://doi.org/10.1007/s10851-015-0616-6

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