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Anisotropic adapted meshes for image segmentation: application to three-dimensional medical data. (English) Zbl 1451.65186

Summary: This work focuses on a variational approach to image segmentation based on the Ambrosio-Tortorelli functional. We propose an efficient algorithm, which combines the functional minimization with a smart choice of the computational mesh. With this aim, we resort to an anisotropic mesh adaptation procedure driven by an a posteriori recovery-based error analysis. We apply the proposed algorithm to a computed tomography dataset of a fractured pelvis to create a virtual model of the anatomy. The result is verified against a semiautomatic segmentation carried out using the ITK-SNAP tool. Furthermore, a physical replica of the virtual model is produced by means of fused filament fabrication technology to assess the appropriateness of the proposed solution in terms of resolution-quality balance for three-dimensional printing production.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
68U10 Computing methodologies for image processing
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