Benninghoff, Heike and Garcke, Harald (2017) Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes. JOURNAL OF SCIENTIFIC COMPUTING, 72 (3). pp. 1333-1367. ISSN 0885-7474, 1573-7691
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GEOMETRIC EVOLUTION-EQUATIONS; CONTOUR MODELS; DATABASE CONSORTIUM; CURVE EVOLUTION; MUMFORD; COLOR; SHAPE; APPROXIMATION; RESTORATION; ENHANCEMENT; Image segmentation; Finite element approximation; Parametric method; Three-dimensional images; Active surfaces; Topology changes |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:15 |
| Last Modified: | 13 Feb 2019 13:50 |
| URI: | https://pred.uni-regensburg.de/id/eprint/1327 |
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