A computational model of bounded developable surfaces with application to image-based three-dimensional reconstruction

Computer Animation and Virtual Worlds

Volumn 24, Issue 5, 2013, Pages 459-476

  Perriollat, Mathieu ^a   Bartoli, Adrien ^b  

^a VI Technology   (France)

^b UNIVERSITÉ CLERMONT AUVERGNE   (France)

Author keywords

3D reconstruction; capture; developable; structure from motion; surface

Indexed keywords

3D MODELING; AUGMENTED REALITY; DEFORMATION; IMAGE RECONSTRUCTION; SURFACES;

3-D RECONSTRUCTION ALGORITHMS; 3D RECONSTRUCTION; CAPTURE; DEVELOPABLE; SMOOTH SURFACE MODELING; STRUCTURE FROM MOTION; THREE-DIMENSIONAL (3-D) RECONSTRUCTION; THREE-DIMENSIONAL RECONSTRUCTION;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 84886100474     PISSN: 15464261     EISSN: 1546427X     Source Type: Journal    
DOI: 10.1002/cav.1478     Document Type: Article

References (45)

1. Billinghurst M, Kato H, Poupyrev I,. The magicbook: A transitional AR interface. Computers & Graphics 2001; 25: 745-753.
2. Perriollat M, Bartoli A,. A quasi-minimal model for paper-like surfaces, In IEEE Towards Benchmarking Automated Calibration, Orientation and Surface Reconstruction from Images, Minneapolis, Minnesota, USA, 2007.
3. Hartley R, Zisserman A,. Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge, UK, 2004. ISBN: 0521540518.
4. Chen H-Y, Lee I-K, Leopoldseder S, Pottmann H, Randrup T, Wallner J,. On surface approximation using developable surfaces. Graphical Models and Image Processing 1999; 61: 110-124.
5. Peternell M,. Developable surface fitting to point clouds. Computer Aided Geometric Design 2004; 21: 785-803.
6. Courteille F, Crouzil A, Durou J-D, Gurdjos P,. Towards shape from shading under realistic photographic conditions, In Proceedings of the International Conference on Pattern recognition, Cambridge, England, UK, 2004.
7. Houle PA, Sethna JP,. Acoustic emission from crumpling paper. Physical Review E 1996; 54: 278-283.
8. Struik D,. Lectures on Classical Differential Geometry. Addison-Wesley Press, Boston, USA, 1961.
9. Glaeser G, Gruber F,. Developable surfaces in contemporary architecture. Journal of Mathematics and the Arts 2007; 01: 59-71.
10. Liu Y, Pottmann H, Wallner J, Yang Y-L, Wang W,. Geometric modeling with conical meshes and developable surfaces, In Proceedings of SIGGRAPH, Boston, USA, 2006.
11. Aumann G,. Interpolation with developable bézier patches. Computer Aided Geometric Design 1991; 8: 409-420.
12. Lang J, Röschel O,. Developable (1, n)-bézier surfaces. Computer Aided Geometric Design 1992; 9: 291-298.
13. Chu C-H, Séquin CH,. Developable bézier patches: Properties and design. Computer-Aided Design 2002; 34: 511-522.
14. Aumann G,. A simple algorithm for designing developable Bézier surfaces. Computer Aided Geometric Design 2003; 20: 601-619.
15. Aumann G,. Degree elevation and developable bézier surfaces. Computer Aided Geometric Design 2004; 21: 661-670.
16. Fernández-Jambrina L,. B-spline control nets for developable surfaces. Computer Aided Geometric Design 2007; 24: 189-199.
17. Bo P, Wang W,. Geodesic-controlled developable surfaces for modeling paper bending, In Proceedings of the Eurographics, Prague, Czech Republic, 2007.
18. Leopoldseder S, Pottmann H,. Approximation of developable surfaces with cone spline surfaces. Computer-Aided Design 1998; 30: 571-582.
19. Sun M, Fiume E,. A technique for constructing developable surfaces, In Proceedings of Graphics Interface, Toronto, Ontario, Canada, May 1996; 176-185.
20. Hilbert D, Cohn-Vossen S,. Geometry and the Imagination. University of Illinois at Urbana-Champaign, New York, Chelsea, 1952.
21. Pottmann H, Wallner J,. Approximation algorithms for developable surfaces. Computer Aided Geometric Design 1999; 16: 539-556.
22. Pottmann H, Wallner J,. Computational line geometry. Springer, Amsterdam, 2001.
23. Kergosien Y, Gotoda H, Kunii T,. Bending and creasing virtual paper. IEEE Computer Graphics & Applications 1994; 14: 40-48.
24. Gumerov NA, Zandifar A, Duraiswami R, Davis LS,. Structure of applicable surfaces from single views, In Proceedings of the European Conference on Computer Vision, volume III, Prague, Czech Republic, 2004; 482-496.
25. Liang J, DeMenthon D, Doermann D,. Flattening curved documents in images, In Proceedings of the International Conference on Computer Vision and Pattern Recognition, volume 2, San Diego, CA, USA, 2005; 338-345.
26. Brown MS, Sun M, Yang R, Yun L, Seales WB,. Restoring 2D content from distorted documents. IEEE Transactions on Pattern Analysis and Machine Intelligence 2007; 29: 1904-1916.
27. Pressley A,. Elementary Differential Geometry. Springer, Amsterdam, 2005.
28. Do Carmo M,. Differential Geometry of Curves and Surfaces. Prentice-hall, London, 1976.
29. Wang C, Tang K,. Developable triangulations of a strip. Computer-Aided Design & Applications 2005; 2: 233-242.
30. de Boor C,. A Practical Guide to Splines. Springer, Amsterdam, 2001.
31. Lowe DG,. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision 2004; 60: 91-110.
32. Pollefeys M, Gool LV, Vergauwen M, Verbiest F, Cornelis K, Tops J, Koch R,. Visual modeling with a hand-held camera. International Journal of Computer Vision 2004; 59: 207-232.
33. Demartines P, Hérault J,. Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets. IEEE Transactions on Neural Networks 1997; 8: 148-154.
34. Tenenbaum JB, Silva VD, Langford JC,. A global geometric framework for nonlinear dimensionality reduction. Science 2000; 290: 2319-2323.
35. Weinberger KQ, Saul LK,. Unsupervised learning of image manifolds by semidefinite programming. International Journal of Computer Vision 2005; 70: 77-90.
36. Roweis S, Saul L,. Nonlinear dimensionality reduction by locally linear embedding. Science 2000; 290 (5500): 2323-2326. http://www.cs.toronto.edu/ ~roweis/lle/
37. Duchon J,. Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces. Rairo Analyse Numérique 1976; 10: 5-12.
38. Bookstein FL,. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence 1989; 11: 567-585.
39. Lu F, Milios E,. Optimal spline fitting to planar shape. Signal Process 1994; 37: 129-140.
40. Mamic G, Bennamoun M,. Automatic bayesian knot placement for spline fitting, In Proceedings of the IEEE International Conference on Image Processing, Thessaloniki, Greece, 2001.
41. Pottmann H, Leopoldseder S, Hofer M,. Approximation with active b-spline curves and surfaces, In Proceedings of the 10th Pacific Conference on Computer Graphics and Applications, Beijing, China, 2002.
42. Yang H, Wang W, Sun J,. Control point adjustment for b-spline curve aproximation. Computer-Aided Design 2004; 36: 639-652.
43. Triggs B, McLauchlan P, Hartley R, Fitzgibbon A,. Bundle adjustment-A modern synthesis. In Vision algorithms: Theory and Practice, Triggs W, Zisserman A, Szeliski R, (eds), LNCS. Springer Verlag, Amsterdam, 2000; 298-375. citeseer.ist.psu.edu/triggs00bundle.html
44. Salvi J, Pagès J, Battle J,. Pattern codification strategies in structure light systems. Pattern Recognition 2004; 37: 827-849.
45. Park J, Kak AC,. Specularity elimination in range sensing for accurate 3D modeling of specular objects, In International Symposium on 3D Data Processing, Visualization and Transmission, Thessaloniki, Greece, 2004.