This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Error Guided Design of a 3D Vision System
April 1998 (vol. 20 no. 4)
pp. 366-379

Abstract—We argue that for a method to be useful in practice, it is necessary to perform its sensitivity analysis and to investigate its robustness to measurement errors. We present here a complete sensitivity analysis of the 3D reconstruction method based on projective geometry. We use this sensitivity analysis to best design a system for the inference of the shape of a block of granite from cameras placed at 90 degrees angular separation. The system has been tested on both real and synthetic data.

[1] S.J. Maybank, "Ambiguity in Reconstruction From Image Correspondences," Image and Vision Computing, vol. 9, pp. 93-99, 1991.
[2] S.J. Maybank, Theory of Reconstruction From Image Motion. Springer-Verlag, 1992.
[3] "Performance Versus Methodology in Computer Vision," NSF/APRA Workshop,Seattle, Wash., June24-25, 1994. Los Alamitos, Calif.: IEEE CS Press.
[4] R.M. Haralick, "Propagating Covariance in Computer Vision," Proc. 12th IAPR, pp. 493-498,Jerusalem, Israel, Oct.9-13, 1994. Los Alamitos, Calif.: IEEE CS Press.
[5] R. Mohr and L. Morin, "Relative Positioning From Geometric invariants," Proc. Conf. Computer Vision and Pattern Recognition, pp. 134-144, 1991.
[6] R. Mohr and E. Arbogast, "It Can Be Done Without Camera Calibration," Pattern Recognition Letters, vol. 12, pp. 39-43, 1991.
[7] A. Shashua, "Projective Structure From Uncalibrated Images: Structure-From-Motion and Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 8, pp. 778-790, Aug. 1994.
[8] A. Shashua and N. Navab, "Relative Affine Structure: Theory and Application to 3D Reconstruction From Perspective Views," Proc. CVPR '94, pp. 483-489, 1994.
[9] P. Anandan, K. Hanna, and R. Kumar, "Shape Recovery From Multiple Views: A Parallax Based Approach," Proc. ICPR '94, vol. A, pp. 685-688, 1994.
[10] H.S. Sawhney, "3D Geometry From Planar Parallax," Proc. CVPR '94, pp. 929-934, 1994.
[11] R. Tsai, "A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses," IEEE J. Robotics and Automation, vol. 3, no. 4, pp. 323-344, Aug. 1987.
[12] A. Cumani and A. Guiducci, "A New Camera Calibration Method for High Accuracy Non-Contact Metrology," Pattern Recognition Letters, vol. 14, pp. 415-419, 1993.
[13] Z.Q. Hong and J.Y. Yang, "An Algorithm for Camera Calibration Using a Three-Dimensional Reference Point," Pattern Recognition, vol. 26, pp. 1,655-1,660, 1993.
[14] S Carlsson, "Projectively Invariant Decomposition and Recognition of Planar Shapes," Proc. Int'l Conf. Computer Vision, pp. 471-475, 1993.
[15] H. Chabbi and M. Berger, "Recovering Planar Surfaces by Stereo-Vision Based on Projective Geometry," Tech. Rep. 93-R-054, CRIN/CNRS-INRIA, Lorraine, 1993.
[16] R.T. Collins and R.J. Beveridge, "Matching Perspective Views of Coplanar Structures Using Projective Unwarping and Similarity Matching," Proc. Conf. Computer Vision and Pattern Recognition, pp. 240-245, New York, June 1993.Los Alamitos, Calif.: IEEE CS Press.
[17] O.D. Faugeras, "What Can Be Seen in Three Dimension With an Uncalibrated Stereo Rig?" Proc. Second European Conf. Computer Vision, pp. 563-578,Santa Margherita Ligure, Italy, May 1992.
[18] H.S.M. Coxeter, Projective Geometry. University of Toronto Press, 1974.
[19] I. Herman, "The Use of Projective Geometry in Computer Graphics," no. 564, Lecture Notes in Computer Science. Springer-Verlag, 1992.
[20] J.L. Mundy and A. Zisserman, "Geometric Invariance in Computer Vision," Artificial Intelligence. MIT Press, 1992.
[21] P. Meer, S. Ramakrishna, and R. Lenz, "Correspondence of Coplanar Features Through P2-Invariant Representations," Proc. 12th Int'l Conf. IAPR Pattern Recognition, vol. 1, pp. 196-200,Jerusalem, Israel, Oct.9-13 1994.
[22] D. Chetverikov and A. Lerch, "A Multi-Resolution Algorithm for Rotation-Invariant Matching of Planar Shapes," Pattern Recognition Letters, vol. 13, pp. 669-676, 1992.
[23] N.S.V. Rao, W. Wu, and C.W. Glover, "Algorithms for Recognizing Planar Polygonal Configurations Using Perspective Images," IEEE Trans. Robotics and Automation, vol. 8, pp. 480-486, 1992.
[24] Z. Pizlo and A. Rosenfeld, "Recognition of Planar Shapes from Perspective Images Using Contour-Based Invariants," Proc. DARPA Image Understanding Workshop, vol. 56, pp. 330-350, 1992.
[25] S. Sull and N. Ahuja, "Estimation of Motion and Structure of Planar Surfaces From a Sequence of Monocular Images," Proc. Conf. Computer Vision and Pattern Recognition, pp. 732-733, 1991.
[26] D.W. Jacobs, "Optimal Matching of Planar Models in 3D Scenes," Proc. Conf. Computer Vision and Pattern Recognition, pp. 269-274, 1991.
[27] J. Aloimonos and J.Y. Herv, "Correspondence-Less Stereo and Motion: Planar Surfaces," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, pp. 504-510, 1990.
[28] J. Weng, N. Ahuja, and T.S. Huang, "Motion and Structure From Point Correspondences: A Robust Algorithm for Planar Case With Error Estimation," Proc. Int'l Conf. Pattern Recognition, pp. 247-251, 1988.
[29] N. Georgis, Three Dimensional Reconstruction and Lay Planning for Industrial Automation, PhD thesis, Univ. of Surrey, Dec. 1994.
[30] N. Georgis, M. Petrou, and J. Kittler, "Obtaining Correspondences From Two Perspective Views With Wide Angular Separation of Non-Coplanar Points," Proc. Europe-China Workshop on Geometrical Modeling and Invariants for Computer Vision, pp. 376-379,Xian, China, Apr. 1995.

Index Terms:
Performance evaluation, projective geometry, 3D reconstruction.
Citation:
Nikos Georgis, Maria Petrou, Joseph Kittler, "Error Guided Design of a 3D Vision System," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 4, pp. 366-379, April 1998, doi:10.1109/34.677262
Usage of this product signifies your acceptance of the Terms of Use.