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Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes

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Abstract

In this paper, we introduce a novel parametric finite element method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford–Shah and the Chan–Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images.

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Notes

  1. The author acknowledges the National Cancer Institute and the Foundation for the National Institutes of Health, and their critical role in the creation of the free publicly available LIDC/IDRI Database.

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Acknowledgements

The authors would like to thank Prof. Dr. Christian Stroszczynski, Department of Radiology of University Hospital Regensburg, for providing computed tomography images which have been used in Figs. 18, 19, 20, 21 and 22.

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  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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Benninghoff, H., Garcke, H. Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes. J Sci Comput 72, 1333–1367 (2017). https://doi.org/10.1007/s10915-017-0401-3

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