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Figure 2: 3D triangulation of a human heart. The left figure shows the surface of the original mesh with artifacts,while theright shows the correspondingsmoothedversionwhere theartifactsarereduced. 6. Discussionandoutlook Theproposedmethodallows for improvementof thevisual surfacequality in3Dtetrahedralmeshes. However, the procedure does not always succeed in removing all artifacts as can be observed par- ticularly when there is an area lying dominantly above its surrounding surface like a plateau. The reason for this might be that only the surface, and thus, the outermost tetrahedra are changed, while the layerbelowremainsunchanged. Theconstraints that avoid the lossofmeshqualityaredisadvan- tageous in this regard, since the second layer prevents the outer layer from sinking. Therefore, the plateau might remain dominant above its surrounding. A possible solution is not only to change the outermost layer, but also a few layers inside as well. However, this would, of course, increase com- putational costs. Another possibility would be to modify the constraints to avoid such a problem, in particular,alsoconsidernon-convexbounds. Indeed, thiswouldallowformoreflexibility inchoosing the constraints, however, at thecostof losing theadvantageouspropertiesgaineddue toconvexity. References [1] Amir Beck and Marc Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse prob- lems. SIAM journalon imaging sciences, 2(1):183–202,2009. [2] M. Botsch, L. Kobbelt, M. Pauly, L. Alliez, and B. Le´vy. Polygon mesh processing. CRC press, Taylor andFrancis, 2010. [3] M.Botsch,M.Pauly,L.Kobbelt,P.Alliez,B.Le´vy,S.Bischoff,andC.Rossl. Geometricmodelingbased onpolygonalmeshes. In ACMSIGGRAPHCourse Notes, 2007. [4] S. Bo¨rm and C.Mehl. Numerical Methods forEigenvalueProblems. WalterdeGruyter, 2012. [5] A. Chambolle and T. Pock. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal ofMathematical ImagingandVision, 40(1):120–145,2010. [6] A. Crozier, C. M. Augustin, A. Neic, A. J. Prassl, M. Holler, T. E. Fastl, A. Hennenmuth, K. Bredies, T. Kuehne,M.J.Bishop,S.A.Niederer, andG.Plank. Image-basedpersonalizationofcardiacanatomyfor coupled electromechanical modeling. AnnalsofBiomedicalEngineering, 44(1):58–70,2016. [7] I. Ekeland. Convexanalysis and variationalproblems. SIAM,1999. [8] L. Freitag and C. Ollivier-Gooch. Tetrahedral mesh improvement using swapping and smoothing. Inter- national Journal for Numerical Methods inEngineering, 40(21):3979–4002,1997. [9] B. M. Klingne and J. R. Shewchuk. Aggressive tetrahedral mesh improvement. In Proceedings of the 16th International MeshingRoundtable, pages3–23.Springer, 2008. 7 69