“Seamless surface mappings”
Conference:
Type(s):
Title:
- Seamless surface mappings
Session/Category Title: Parameterization & Mapping
Presenter(s)/Author(s):
Moderator(s):
Abstract:
We introduce a method for computing seamless bijective mappings between two surface-meshes that interpolates a given set of correspondences.A common approach for computing a map between surfaces is to cut the surfaces to disks, flatten them to the plane, and extract the mapping from the flattenings by composing one flattening with the inverse of the other. So far, a significant drawback in this class of techniques is that the choice of cuts introduces a bias in the computation of the map that often causes visible artifacts and wrong correspondences.In this paper we develop a surface mapping technique that is indifferent to the particular cut choice. This is achieved by a novel type of surface flattenings that encodes this cut-invariance, and when optimized with a suitable energy functional results in a seamless surface-to-surface map.We show the algorithm enables producing high-quality seamless bijective maps for pairs of surfaces with a wide range of shape variability and from a small number of prescribed correspondences. We also used this framework to produce three-way, consistent and seamless mappings for triplets of surfaces.
References:
1. Aigerman, N., Poranne, R., and Lipman, Y. 2014. Lifted bijections for low distortion surface mappings. ACM Trans. Graph. 33, 4 (July), 69:1–69:12. Google ScholarDigital Library
2. Andersen, E. D., and Andersen, K. D. 1999. The MOSEK interior point optimization for linear programming: an implementation of the homogeneous algorithm. Kluwer Academic Publishers, 197–232.Google Scholar
3. Bogo, F., Romero, J., Loper, M., and Black, M. J. 2014. FAUST: Dataset and evaluation for 3D mesh registration. In Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), IEEE, Piscataway, NJ, USA. Google ScholarDigital Library
4. Bommes, D., Zimmer, H., and Kobbelt, L. 2009. Mixed-integer quadrangulation. ACM Trans. Graph. 28, 3 (July), 77:1–77:10. Google ScholarDigital Library
5. Bommes, D., Lévy, B., Pietroni, N., Puppo, E., Silva, C., Tarini, M., and Zorin, D. 2013. Quad-Mesh Generation and Processing: A Survey. Computer Graphics Forum 32, 6, 51–76. Google ScholarDigital Library
6. Bradley, D., Popa, T., Sheffer, A., Heidrich, W., and Boubekeur, T. 2008. Markerless garment capture. ACM Trans. Graph. 27, 3 (Aug.), 99:1–99:9. Google ScholarDigital Library
7. Bronstein, A. M., Bronstein, M. M., and Kimmel, R. 2006. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc. National Academy of Sciences (PNAS).Google Scholar
8. Floater, M. S. 2003. Mean value coordinates. Computer Aided Geometric Design 20, 1, 19–27. Google ScholarDigital Library
9. Giorgi, D., Biasotti, S., and Paraboschi, L. 2007. SHREC: SHape REtrieval Contest: Watertight models track. http://watertight.ge.imati.cnr.it/.Google Scholar
10. Hormann, K., Lévy, B., and Sheffer, A. 2007. Mesh parameterization: Theory and practice video files associated with this course are available from the citation page. In ACM SIGGRAPH 2007 Courses, ACM, New York, NY, USA, SIGGRAPH ’07. Google ScholarDigital Library
11. Huang, Q.-X., and Guibas, L. 2013. Consistent shape maps via semidefinite programming. In Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing, Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, SGP ’13, 177–186. Google ScholarDigital Library
12. Jain, V., Zhang, H., and van Kaick, O. 2007. Non-rigid spectral correspondence of triangle meshes. International Journal on Shape Modeling 13, 1, 101–124.Google ScholarCross Ref
13. Kälberer, F., Nieser, M., and Polthier, K. 2007. Quadcover – surface parameterization using branched coverings. 375–384.Google Scholar
14. Knöppel, F., Crane, K., Pinkall, U., and Schröder, P. 2013. Globally optimal direction fields. ACM Trans. Graph. 32, 4. Google ScholarDigital Library
15. Kraevoy, V., and Sheffer, A. 2004. Cross-parameterization and compatible remeshing of 3d models. ACM Trans. Graph. 23, 3 (Aug.), 861–869. Google ScholarDigital Library
16. Lee, A. W. F., Dobkin, D., Sweldens, W., and Schröder, P. 1999. Multiresolution mesh morphing. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, SIGGRAPH ’99, 343–350. Google ScholarDigital Library
17. Lévy, B., Petitjean, S., Ray, N., and Maillot, J. 2002. Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph. 21, 3 (July), 362–371. Google ScholarDigital Library
18. Lin, J. L., Chuang, J. H., Lin, C. C., and Chen, C. C. 2003. Consistent parametrization by quinary subdivision for remeshing and mesh metamorphosis. In Proceedings of the 1st International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia, ACM, New York, NY, USA, GRAPHITE ’03, 151–158. Google ScholarDigital Library
19. Lipman, Y. 2012. Bounded distortion mapping spaces for triangular meshes. ACM Trans. Graph. 31, 4 (July), 108:1–108:13. Google ScholarDigital Library
20. Löfberg, J. 2004. Yalmip : A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference.Google ScholarCross Ref
21. Mémoli, F., and Sapiro, G. 2005. A theoretical and computational framework for isometry invariant recognition of point cloud data. Foundations of Computational Mathematics 5, 3, 313–347. Google ScholarDigital Library
22. Michikawa, T., Kanai, T., Fujita, M., and Chiyokura, H. 2001. Multiresolution interpolation meshes. In Computer Graphics and Applications, 2001. Proceedings. Ninth Pacific Conference on, 60–69. Google ScholarDigital Library
23. Myles, A., and Zorin, D. 2012. Global parametrization by incremental flattening. ACM Trans. Graph. 31, 4 (July), 109:1–109:11. Google ScholarDigital Library
24. Myles, A., and Zorin, D. 2013. Controlled-distortion constrained global parametrization. ACM Trans. Graph. 32, 4 (July), 105:1–105:14. Google ScholarDigital Library
25. Nguyen, A., Ben-Chen, M., Welnicka, K., Ye, Y., and Guibas, L. 2011. An optimization approach to improving collections of shape maps. Computer Graphics Forum 30, 5, 1481–1491.Google ScholarCross Ref
26. Ovsjanikov, M., Mérigot, Q., Mémoli, F., and Guibas, L. 2010. One point isometric matching with the heat kernel. In Computer Graphics Forum (Proc. of SGP).Google Scholar
27. Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A., and Guibas, L. 2012. Functional maps: A flexible representation of maps between shapes. ACM Trans. Graph. 31, 4 (July), 30:1–30:11. Google ScholarDigital Library
28. Panozzo, D., Baran, I., Diamanti, O., and Sorkine-Hornung, O. 2013. Weighted averages on surfaces. ACM Trans. Graph. 32, 4 (July), 60:1–60:12. Google ScholarDigital Library
29. Praun, E., Sweldens, W., and Schröder, P. 2001. Consistent mesh parameterizations. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, 179–184. Google ScholarDigital Library
30. Ray, N., Li, W. C., Lévy, B., Sheffer, A., and Alliez, P. 2006. Periodic global parameterization. ACM Trans. Graph. 25, 4 (Oct.), 1460–1485. Google ScholarDigital Library
31. Ray, N., Vallet, B., Li, W. C., and Lévy, B. 2008. N-symmetry direction field design. ACM Trans. Graph. 27, 2 (May), 10:1–10:13. Google ScholarDigital Library
32. Schreiner, J., Asirvatham, A., Praun, E., and Hoppe, H. 2004. Inter-surface mapping. ACM Trans. Graph. 23, 3 (Aug.), 870–877. Google ScholarDigital Library
33. Sheffer, A., Praun, E., and Rose, K. 2006. Mesh parameterization methods and their applications. Found. Trends. Comput. Graph. Vis. 2, 2 (Jan.), 105–171. Google ScholarDigital Library
34. Steiner, D., and Fischer, A. 2005. Planar parameterization for closed manifold genus-g meshes using any type of positive weights. Journal of Computing and Information Science in Engineering 5, 2, 118–125.Google ScholarCross Ref
35. Tong, Y., Alliez, P., Cohen-Steiner, D., and Desbrun, M. 2006. Designing quadrangulations with discrete harmonic forms. In Proceedings of the Fourth Eurographics Symposium on Geometry Processing, Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, SGP ’06, 201–210. Google ScholarDigital Library
36. Tsui, A., Fenton, D., Vuong, P., Hass, J., Koehl, P., Amenta, N., Coeurjolly, D., DeCarli, C., and Carmichael, O. 2013. Globally optimal cortical surface matching with exact landmark correspondence. In Proceedings of the 23rd International Conference on Information Processing in Medical Imaging, Springer-Verlag, Berlin, Heidelberg, IPMI’13, 487–498. Google ScholarDigital Library
37. van Kaick, O., Zhang, H., Hamarneh, G., and Cohen-Or, D. 2011. A survey on shape correspondence. Computer Graphics Forum 30, 6, 1681–1707.Google ScholarCross Ref