Crest lines for surface segmentation and flattening

We present a method for extracting feature curves called crest lines from a triangulated surface. Then, we calculate the geodesic Voronoi diagram of crest lines to segment the surface into several regions. Afterward, barycentric surface flattening using theory from graph embeddings is implemented and, using the geodesic Voronoi diagram, we develop a faster surface flattening algorithm.

[1]  Michael S. Floater,et al.  Mean value coordinates , 2003, Comput. Aided Geom. Des..

[2]  Nicholas Ayache,et al.  Automatic Retrieval of Anatomical Structures in 3D Medical Images , 1995, CVRMed.

[3]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[4]  Franz-Erich Wolter,et al.  Geodesic Voronoi diagrams on parametric surfaces , 1997, Proceedings Computer Graphics International.

[5]  Georgios Stylianou,et al.  Shape Feature Extraction , 2003 .

[6]  Michael S. Floater,et al.  Parametrization and smooth approximation of surface triangulations , 1997, Comput. Aided Geom. Des..

[7]  Jerry L. Prince,et al.  Using a statistical shape model to extract sulcal curves on the outer cortex of the human brain , 2002, IEEE Transactions on Medical Imaging.

[8]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[9]  Ron Kikinis,et al.  On the Laplace-Beltrami operator and brain surface flattening , 1999, IEEE Transactions on Medical Imaging.

[10]  André Guéziec,et al.  Large deformable splines, crest lines and matching , 1993, 1993 (4th) International Conference on Computer Vision.

[11]  Pascal Fua,et al.  Using crest lines to guide surface reconstruction from stereo , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[12]  Georgios Stylianou.  A Feature Based Method for Rigid Registration of Anatomical Surfaces , 2004 .

[13]  J A Sethian,et al.  Computing geodesic paths on manifolds. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[15]  Guillermo Sapiro,et al.  Conformal Surface Parameterization for Texture Mapping , 1999 .

[16]  W. T. Tutte.  Convex Representations of Graphs , 1960 .

[17]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[18]  Alexis Gourdon,et al.  The 3D Marching Lines Algorithm , 1996, CVGIP Graph. Model. Image Process..

[19]  Mark Meyer,et al.  Intrinsic Parameterizations of Surface Meshes , 2002, Comput. Graph. Forum.

[20]  Bernd Hamann,et al.  Curvature Approximation for Triangulated Surfaces , 1993, Geometric Modelling.

[21]  Gabriele Lohmann,et al.  Extracting line representations of sulcal and gyral patterns in MR images of the human brain , 1998, IEEE Transactions on Medical Imaging.

[22]  Olivier Monga,et al.  Thin Nets and Crest Lines: Application to Satellite Data and Medical Images , 1997, Comput. Vis. Image Underst..

[23]  Leif Kobbelt,et al.  Extraction of feature lines on triangulated surfaces using morphological operators , 2000 .

[24]  Bruno Lévy,et al.  Least squares conformal maps for automatic texture atlas generation , 2002, ACM Trans. Graph..

[25]  Sven Kreiborg,et al.  4D Shape-Preserving Modeling of Bone Growth , 1998, MICCAI.

[26]  G. Farin.  Curves and Surfaces for Cagd: A Practical Guide , 2001 .

[27]  Nicholas Ayache,et al.  Smoothing and Matching of 3-D Space Curves , 1992, ECCV.

[28]  Michael I. Miller,et al.  Dynamic Programming Generation of Curves on Brain Surfaces , 1998, IEEE Trans. Pattern Anal. Mach. Intell..