3D Regularized B-Spline Surface Reconstruction from Occluding Contours of a Sequence of Images. Reconstruction de Surfaces B-Splines Tridimensionnelles Etrégularisées Àpartirde Contours d'Occultation d'une Séquence d'Images

3D Regularized B-Spline Surface Reconstruction from Occluding Contours of a Sequence of Images

Reconstruction de Surfaces B-Splines Tridimensionnelles Etrégularisées Àpartirde Contours d'Occultation d'une Séquence d'Images

ChangSheng Zhao Roger Mohr  Boubakeur Boufama 

LIFTA-INRIA,46, avenue Félix Viallet 38031 Grenoble

Page: 
129-143
|
Received: 
9 February 1994
|
Accepted: 
N/A
|
Published: 
30 April 1995
| Citation

OPEN ACCESS

Abstract: 

The three dimensional surface reconstruction of a non polyhedral object is a difficult problem in computer vision. In this paper, a new methodfor reconstructing three dimensional surface from the recovered motion of occluding contours is presented through calibrated image sequences. We use the uniform bicubic Bspline surface patches to give a parametric representation of an object surface . Finally, the problem of three dimensional B-spline surface patches reconstruction is equivalent to find their control points by solving a nonlinear system. Two numerical methods are outlined :Levenberg-Marquardt, Quasi-Newton. To avoid the classic camera calibration that needs a calibration pattern, we propose a direct nonlinear method of the autocalibration of a camera using the stable points in the scene. Our approach can be applied in the case where the camera is calibrated, the object is smooth, specifically, that its surface is at least C2. Results for reconstruction based on synthetic and real data are presented. 

Résumé

La reconstruction de surfaces tridimensionnelles d'un objet non polyédrique est un problème difficile de la vision par ordinateur. Dans cet article, une nouvelle approche est presentée pour la reconstruction des surfaces tridimensionnelles à partir de l'observation du mouvement des contours occultants dans une séquence d'images calibrées. La surface de cet objet est modélisée par des surfaces 13splines uniformes et bicubiques. Nous ramenons le problème de la reconstruction des surfaces au problème de résolution d'un système d'équations non linéaires déterminant leurs points de contrôle . Deux méthodes numériques de résolution du problème sont utilisées : Levenberg-Marquardt et Quasi-Newton. Pour éviter le calibrage classique nécessitant une mire, nous avons utilisé des points stables de la scène pour autocalibrer la caméra. L'approche proposée s'applique dans le cas d'un mouvement d'une caméra calibrée avec des surfaces C2. Des résultats expérimentaux sur des données simulées et réelles sont présentés.

Keywords: 

representation of three dimensional surface, reconstruction of three dimensional surface, spatiotemporal surface, occluding contours, B-spline curves and surface patches.

Mots clés 

représentation de surfaces tridimensionnelles, reconstruction de surfaces tridimensionnelles, surface spatio-temporelle, contours d'occultation, courbes et surfaces B-splines.

1. Introduction
2. Définitions et Notations
3. Calibrage d'une Caméra en Mouvement
4. Modélisation Mathématique
5. Résolution du Système
6. Résultats Expérimentaux
7. Conclusion
Remerciements
  References

[1] E. Arbogast,Modélisation automatique d'objets non polyèdriques par observationmononucléaire. Thèsededoctorat, InstitutNationalPolytechniquede Grenoble, France, 1991. 

[2] E. Arbogast and R. Mohr. 3D structures inference from images sequences. International journal of Pattern Recognition and Artificial intelligence, 5(5) 749, 1991. 

[3] R.H. Bartels, J.C. Beatty and B.A. Barsky.An introdudction to splines for use in computer graphics and geometric modeling. Morgan Kaufman Pu. Inc., 1987.

[4] A. Blake and A. Zisserman.Visual Reconstruction.The MIT Press, Cambridge, Massachusetts, 1987. 

[5] R.M. Belle and B.C. Venturi.On Three-Dimensional Surface Reconstruction Methodes. IEEE Transactions on PAMI, 13(1): 1-13, January 1991.

[6] R.C. Bolles, H.H. Baker and D.H. Marimont. Epipolar plane image analysis an approach to determining structure from motion .International Journal ofComputer Vision, 1 :7-55, 1987. 

[7] B. Boufama, R. Mohr and F. Veillon. Euclidian constaints for uncalibrated reconstruction. In Proceedings of the 4th International Conference on Computer Vision, Berlin, Germany, pages 466-470, May 1993.

[8] M. Brady, J. Ponce, A. Yuille and H. Asada. Describing Surfaces. In Hideo Hansufa and Hirochika Inoue, editors, The second International Symposium of Robotic Research, pages 5-16. The MIT Press, 1985. 

[9] M.P. Do Carmo. Diffential geometry of curves and surfaces. Prentice Hall, 1976. 

[10] R. Cipolla. Active Visual Inference of Qualitative Geometry . Technical Report OUEL 1795/89, University of Oxford, Departement of engineering science, Park Road, Oxford OX 3PJ, U.K., July 1989.

[11] R. Deriche. Using Canny's criteria to derive a recursively implemented optimal edge detector. International Journal of Computer Vision, 1(2) : 167187,1987. 

[12] O.D. Faugeras, Q.T. Luong and S.J. Maybank. Camera Self-Calibration Theory and Experiments. In G. Sandini, editor, Proceedings of the 2nd European Conference on Computer Vision, Santa Margherita Ligure, Italy, pages 321-334. Springer-Verlag, May 1992. 

[13] O.D. Faugeras and S. Maybank. Motion from point matches : multiplicity of solutions. InIEEE workshop on Computer Vision, 1989. 

[14] O.D. Faugeras and G. Toscani. Camera calibration for 3D computer vision. In Proceedings of International Workshop on Machine Vision and Machine intelligence, Tokyo, Japan, 1987. 

[15] P. Gliblin and R. Weiss. Reconstruction of surfaces from profiles. In Proceedings of the 1st International Conference on Computer Vision, London, England,pages 136-144, London, England, 1987.

[16] P. Gill, W. Murray and M.H. Wright.Practical Optimization.Harcourt Brace Jovanovich, Publishers, 1989. 

[17] W.E.L. Grimson. A computational Theory of visual Surface Interpolation . Technical report, Artificial Intelligence Laboratory, MIT, Cambridge, Massachusetts, USA, 1982. 

[18] L. Gruiser, R. Payrissat and S. Castan. Perception 3D de surfacesd'objetspar projectiond'unegrille. InActesduSèmeCongrés AFCET de Reconnaissance des Formes et IntelligenceArtificielle, Lyon- Villeurbanne, France, volume 2, pages 771-789, November 1991. 

[19] J.J. Koenderink. What does the ocluding contour tell us about solid shape? Perception, 13 :321-330, 1984. 

[20] J.J. Koenderink. Solid Shape. The MIP Press, Cambridge Massachusetts, 1990. 

[21] D.J. Kriegman and J. Ponce. On Recognizing and Positioning Curved 3-D Objets from Images Contours. IEEE Transactions on PAMI, 12(12) :11271137, December 1990. 

[22] K.N. Kutulakos and C.R. Dyer. Recovering shape by purposive viewpoint adjustment. Technical Report 1935, University of Wisconsin, Madison, USA, August 1991, 

[23] P.J. Laurent. Courbes ouvertes ou ferméspar B-splinesrégularisées. Technical Report RR 652-M-, IMAG, Grenoble,France, March 1987. 

[24] H.S. Lim and T.O. Binford. Curved surface recontruction using stereo correspondance. Image Understanding Workshop, pages 809-819, 1988. 

[25] S.J. Maybank and O.D. Faugeras. A theory of self calibration of a moving camera.International Journal of Computer Vision, 8(2) : 123-151, 1992. 

[26] R. Mohr, B. Boufama and P. Brand. Accurate projective reconstruction. In Proceeding of the DARPA-ESPRIT workshop on Applications of Invariants in Computer Vision, Azores, Portugal, pages 203-227, October 1993. 

[27] R. Mohr, L. Quan, F. Veillon and B. Boufama. Relative 3D reconstruction using multiples uncalibrated images. Technical Report RT84-I-IMAGLIFTA 12, LIFIA-IRIMAG, 1992. 

[28] A.P. Pentland. Surface interpolation using wavelets. In G. Sandini, editor,  Proceedings of the 2nd European Conference on Computer Vision, Santa Margherita ligure, Italy,pages 615-619. Springer-Verlag, May 1992. 

[29] T. Poggio, V. Torreand C. Koch. Computational vision and regularization theory. Nature,237 :314-319, September 1985.

[30] W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling W.T. Numerical Recipes in C. Cambridge University Press, 1988. 

[31] P.T. Sander and S.W.Zucker.Inferring surface trace and differential structure from 3D images. IEEE Transactions on PAMI, 12(9) : 833-854, September 1990. 

[32] W.B. Scales and C.R. Dyer. Viewpoint from occluding contour. Computer Vision, Graphics and Image Processing: Image Understanding, 55(2) :198211, March 1992.

[33] B.Q. Su and D.Y. Liu. Computational Geometry - Curve and surface Modeling. Harcourt Brace Jovanovich, Publishers, 1989.

[34] R. Szaliski and D. Tonnesen. Surface Modeling with Oriented Particle Systems. Technical Report CRL 91/14, Digital Equipment Corporation, Cambridge Research Lab, December 1991 . 

[35] G. Taubin, F. Cukierman, S. Sullivan, J. Ponce and D. Kriegman. Parameterized Families of Polynomialesfor Bounded Algebraic Curve and Surface Fitting. Technical Report RC- 18065, IBM, June 1992. 

[36] D. Terzopoulos. Regularization of Inverse Visual Problems Involving Discontinuities. IEEE Transcactions on PAMI, 8(4) :413-424, July 1986. 

[37] D. Terzopoulos. The computation of visible-surface representations. IEEE Transactions on PAMI, 10(4) : 417-438, July 1988. 

[38] R.Y. Tsai. A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses. IEEE Journal of Robotics and Automation, 3(4) :323-344, 1987. 

[39] R. Vaillant. Géométrie différentielle et vision parordinateur : détection et reconstructiondescontoursd'occultationde surfaces.PhD thesis,Université de Paris-Sud, Orsay, France, December 1990. 

[40] C.W. Wampler, A.P. Morgan and A.J. Sommese. Numerical continuation methods for solving polynomial systems arising in kinematics. Technical Report GMR-6372, General motors Research Labs, August 1988.

[41] C.S. Zhao and R. Mohr. B-spline patches for surface reconstruction in computer vision. In P.J. Laurent, A. Le Méhauté and L.L. Schumaker, editors, Wavelets, images and surface Fitting, pages 521-528, Academic Press, Boston, USA, 1994. 

[42] C.S. Zhao and R.Mohr.Relative 3D regularized B-spline surface reconstruction through image sequences. In J.O. Eklundh, editor, Proceedings of the 3rd European Conference on Computer Vision, Stockholm, Sweden, pages 417426. Springer-Verlag, May 1994.

[43] C.S. Zhao, R. Mohr and L. Quan. Global surface reconstruction through regularized B-Spline patches. In Geometric Methods in Computer Vision II, SPIE's 1993 International Symposium on Optical Instrumentation and Applied Science, pages 134-145, July 1993.