No Access
POSTURE INVARIANT CORRESPONDENCE OF INCOMPLETE TRIANGULAR MANIFOLDS
https://doi.org/10.1142/S0218654307000981Cited by:13 (Source: Crossref)
Abstract
We present an approach to find dense point-to-point correspondences between two deformed surfaces corresponding to different postures of the same non-rigid object in a fully automatic way. The approach requires no prior knowledge about the shapes being registered or the initial alignment of the shapes. We consider surfaces that are represented by possibly incomplete triangular meshes. We model the deformations of an object as isometries. To solve the correspondence problem, our approach maps the intrinsic geometries of the surfaces into a low-dimensional Euclidean space via multi-dimensional scaling. This results in posture-invariant shapes that can be registered using rigid correspondence algorithms.
References
- ACM Transactions on Graphics 22(3), 587 (2003), DOI: 10.1145/882262.882311. Crossref, Google Scholar
-
Dragomir Anguelov , The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces , Neural Information Processing Systems ( 2004 ) . Google Scholar - ACM Transactions on Graphics 24(3), 408 (2005), DOI: 10.1145/1073204.1073207. Crossref, Google Scholar
- ACM Transactions on Graphics 26(3), (2007), DOI: 10.1145/1276377.1276467. Google Scholar
-
Ingwer Borg and Patrick Groenen , Modern Multidimensional Scaling Theory and Applications ( Springer , 1997 ) . Crossref, Google Scholar - National Academy of Sciences 103(5), 1168 (2006), DOI: 10.1073/pnas.0508601103. Crossref, Google Scholar
- IEEE Transactions of Visualization and Computer Graphics 13(5), 902 (2007). Crossref, Google Scholar
- Numerical Linear Algebra with Applications 13(2–3), 149 (2006), DOI: 10.1002/nla.475. Crossref, Google Scholar
- SIAM Journal on Computing 17(4), 830 (1988), DOI: 10.1137/0217052. Crossref, Google Scholar
-
Trevor Cox and Michael Cox , Multidimensional Scaling , 2nd edn. ( Chapman & Hall CRC , 2001 ) . Google Scholar -
Ian Dryden and Kanti Mardia , Statistical Shape Analysis ( Wiley , 2002 ) . Google Scholar - IEEE Transactions on Pattern Analysis and Machine Intelligence 25(10), 1285 (2003), DOI: 10.1109/TPAMI.2003.1233902. Crossref, Google Scholar
- IEEE Transactions on Image Processing 6(9), 1305 (1997), DOI: 10.1109/83.623193. Crossref, Google Scholar
- Biometrika 53, 325 (1966). Crossref, Google Scholar
Piotr Indyk , Dimensionality reduction techniques for proximity problems, Symposium on Discrete Algorithms (2000) pp. 371–378. Google Scholar- , Handbook of Discrete and Computational Geometry , 2nd edn. , eds.
Jacob E. Goodman and Joseph O'Rourke ( CRC Press , 2004 ) . Google Scholar - Computer-Aided Design 39(5), 398 (2007), DOI: 10.1016/j.cad.2007.02.009. Crossref, Google Scholar
- International Journal on Shape Modeling (2006). Google Scholar
- National Academy of Sciences 95, 8431 (1998), DOI: 10.1073/pnas.95.15.8431. Crossref, Google Scholar
- ACM Transactions on Graphics 22(3), 326 (2003), DOI: 10.1145/882262.882271. Crossref, Google Scholar
-
Xinju Li and Igor Guskov , Multi-scale features for approximate alignment of point-based surfaces , Proceedings of 3rd ACM Siggraph/Eurographics Symposium on Geometry Processing ( 2005 ) . Google Scholar - Mathematical Programming 45, 503 (1989), DOI: 10.1007/BF01589116. Crossref, Google Scholar
- Information and Computation 106(2), 286 (1993), DOI: 10.1006/inco.1993.1057. Crossref, Google Scholar
- Journal of the Society of Industrial and Applied Mathematics 5(1), 32 (1957). Crossref, Google Scholar
-
Brian Flannery , Saul Teukolsky and William Vetterling , Numerical Recipes in C: the Art of Scientific Computing ( Cambridge University Press , 1993 ) . Google Scholar Kathleen Robinette , Hans Daanen and Eric Paquet , The caesar project: A 3-d surface anthropometry survey, 3-D Digital Imaging and Modeling (1999) pp. 180–186, DOI: 10.1109/IM.1999.805368. Google Scholar- ACM Transactions on Graphics 23, 870 (2004), DOI: 10.1145/1015706.1015812. Crossref, Google Scholar
- Computer Graphics Forum 23(3), 381 (2004), DOI: 10.1111/j.1467-8659.2004.00769.x. Crossref, Google Scholar
Zouhour Ben Azouz , Approximations of geodesic distances for incomplete triangular manifolds, Proceedings of the 19th Canadian Conference on Computational Geometry (2007) pp. 177–180. Google Scholar
