CVT-based 3D image segmentation and quality improvement of tetrahedral/hexahedral meshes using anisotropic Giaquinta-Hildebrandt operator

References

• Arifin AZ, Asano A. 2006. Image segmentation by histogram thresholding using hierarchical cluster analysis. Pattern Recognit Lett. 27:1515–1521.
   Web of Science ®Google Scholar
• Ahmed MN, Yamany SM, Mohamed N, Farag AA, Moriarty T. 2002. A modified fuzzy {\it c}-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans Med Imaging. 21:193–199.
   PubMed Web of Science ®Google Scholar
• Canann SA, Tristano JR, Staten ML. 1998. An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes. 7th International Meshing Roundtable. Dearborn, MI; p. 479–494
   Google Scholar
• Chan TF, Vese LA. 2002. Active contour and segmentation models using geometric PDEs for medical imaging. Geometric methods in bio-medical image processing. Berlin Heidelberg: Springer; p. 63–75.
   Google Scholar
• Cocosco CA, Kollokian V, Kwan RKS, Pike GB, Evans AC. 1997. BrainWeb: online interface to a 3D MRI simulated brain database. NeuroImage. 5:S425.
   Google Scholar
• Du Q, Faber V, Gunzburger M. 1999. Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 41:637–676.
   Web of Science ®Google Scholar
• Du Q, Gunzburger M, Ju L, Wang X. 2006. Centroidal Voronoi tessellation algorithms for image compression, segmentation, and multichannel restoration. J Math Imaging Vision. 24:177–194.
   Web of Science ®Google Scholar
• Foteinos PA, Chrisochoides NP. 2014. High quality real-time image-to-mesh conversion for finite element simulations. J Parallel Distrib Comput. 74:2123–2140.
   Web of Science ®Google Scholar
• Freitag LA. 1997. On combining Laplacian and optimization-based mesh smoothing techniques. Trends in unstructured mesh generation. Vol. 220. AMD; p. 37–44.
   Google Scholar
• Hu K, Zhang Y 2016a. Image segmentation and adaptive superpixel generation based on harmonic edge-weighted centroidal Voronoi tessellation. The special issue of CompIMAGE’14 in Comput Meth. Biomech Biomed Eng: Imaging Visual. 4:46–60.
   Web of Science ®Google Scholar
• Hu K, Zhang Y. 2016b. Centroidal Voronoi tessellation based polycube construction for adaptive all-hexahedral mesh generation. Comput Methods Appl Mech Eng. 305:405–421.
   Web of Science ®Google Scholar
• Hu K, Zhang Y, Xu G. 2016. CVT-based 3D image segmentation for quality tetrahedral meshing. CompIMAGE (Computer Modeling of Objects Presented in Images: Fundamentals, Methods, and Applications); Niagara Falls, (NY). Sep 21–23.
   Google Scholar
• Leng J, Zhang Y, Xu G. 2013. A novel geometric flow approach for quality improvement of multi-component tetrahedral meshes. Comput Aided Des. 45:1182–1197.
   Web of Science ®Google Scholar
• Liao T, Li X, Xu G, Zhang Y. 2016. Secondary Laplace operator and generalized Giaquinta--Hildebrandt operator with applications on surface segmentation and smoothing. A Special Issue of SIAM Conference on Geometric & Physical Modeling 2015. Comput Aided Des. 70: 56–66.
   Google Scholar
• Meyer M, Desbrun M, Schröder P, Barr AH. 2003. Discrete differential-geometry operators for triangulated 2-manifolds. In: Hans-Christian Hege, Konrad Polthier, editors. Visualization and mathematics III. Berlin Heidelberg: Springer.p. 35–57.
   Google Scholar
• Pal NR, Pal SK. 1993. A review on image segmentation techniques. Pattern Recognit. 26:1277–1294.
   Web of Science ®Google Scholar
• Pan Q, Xu G, Xu G, Zhang Y. 2015. Isogeometric analysis based on extended Loop’s subdivision. J Comput Phys. 299:731–746.
   Web of Science ®Google Scholar
• Pappas TN. 1992. An adaptive clustering algorithm for image segmentation. IEEE Trans Sig Proc. 40:901–914.
   Web of Science ®Google Scholar
• Qian J, Zhang Y, Wang W, Lewis AC, Qidwai MAS, Geltmacher AB. 2010. Quality improvement of non-manifold hexahedral meshes for critical feature determination of microstructure materials. Int J Num Methods Eng. 82:1406–1423.
   Web of Science ®Google Scholar
• Ren X, Malik J. 2003. Learning a classification model for segmentation. Ninth IEEE International Conference on Computer Vision. Nice, France; p. 10–17
   Google Scholar
• Sijbers J, Scheunders P, Verhoye M, Van der Linden A, Van Dyck D, Raman E. 1997. Watershed-based segmentation of 3D MR data for volume quantization. Magn Reson Imaging. 15:679–688.
   PubMed Web of Science ®Google Scholar
• Tobias OJ, Seara R. 2002. Image segmentation by histogram thresholding using fuzzy sets. IEEE Trans Image Proc. 11:1457–1465.
   PubMed Web of Science ®Google Scholar
• Tsuda A, Filipovic N, Haberthür D, Dickie R, Matsui Y, Stampanoni M, Schittny JC. 2008. Finite element 3D reconstruction of the pulmonary acinus imaged by synchrotron X-ray tomography. J Appl Physiol. 105:964–976.
   PubMed Web of Science ®Google Scholar
• Wang J, Ju L, Wang X. 2009. An edge-weighted centroidal Voronoi tessellation model for image segmentation. IEEE Trans Image Proc. 18:1844–1858.
   PubMed Web of Science ®Google Scholar
• Wei X, Zhang Y, Hughes T, Scott M. 2015. Truncated hierarchical Catmull-Clark subdivision with local refinement. Comput Methods Appl Mech Eng. 291:1–20.
   Web of Science ®Google Scholar
• Xu G, Zhang Q. 2008. A general framework for surface modeling using geometric partial differential equations. Comput Aided Geometric Des. 25:181–202.
   Web of Science ®Google Scholar
• Zhang Y, Bajaj C, Sohn BS. 2005. 3D finite element meshing from imaging data. Comput Methods Appl Mech Eng. 194:5083–5106.
   PubMed Web of Science ®Google Scholar
• Zhang Y, Bajaj C, Xu G. 2009. Surface smoothing and quality improvement of quadrilateral/hexahedral meshes with geometric flow. Commun Num Methods Eng. 25:1–18.
   Google Scholar
• Zhang Y, Hughes Y, Bajaj C. 2010. An automatic 3D mesh generation method for domains with multiple materials. Comput Methods Appl Mech Eng. 199:405–415.
   PubMed Web of Science ®Google Scholar
• Zhang Y, Qian J. 2012. Resolving topology ambiguity for multiple-material domains. Comput Methods Appl Mech Eng. 247:166–178.
   Web of Science ®Google Scholar
• Zhang Y, Bajaj C. 2006. Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Comput Methods Appl Mech Eng. 195:942–960.
   PubMed Web of Science ®Google Scholar