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.

Segmentation of patient-specific vascular segments of interest from medical images is an important topic for numerous applications. Despite the great importance of having semi-automatic segmentation methods in this field, the process of image segmentation is still based on several operator-dependent steps which make large-scale segmentation a non trivial and time consuming task. In this work we present a semi-automatic segmentation method to reconstruct vascular structures from three-dimensional medical images. We start from the minimization of the Region Scalable Fitting Energy using the Split-Bregman method and we modify the resulting algorithm adding a connected component extraction of the solution starting from a point that identifies the vascular structure of interest. In this way, we add a constraint to the algorithm focusing it only on the vascular structure we want to reconstruct and avoiding the attachment with the nearby objects. Finally, we describe a strategy to minimize the number of involved parameters in order to limit the user effort. The results obtained on two different images (a Magnetic Resonance and a Computed Tomography) demonstrate that our method outperforms the original method in segmenting the vascular region of interest without the inclusion of nearby objects in the result.