This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Algorithms for Matching 3D Line Sets
May 2004 (vol. 26 no. 5)
pp. 582-593

Abstract—Matching two sets of lines is a basic tool that has applications in many computer vision problems such as scene registration, object recognition, motion estimation, and others. Line sets may be composed of infinitely long lines or finite length line segments. Depending on line lengths, three basic cases arise in matching sets of lines: 1) finite-finite, 2) finite-infinite, and 3) infinite-infinite. Case 2 has not been treated in the literature. For Cases 1 and 3, existing algorithms for matching 3D line sets are not completely satisfactory in that they either solve special situations, or give approximate solutions, or may not converge, or are not invariant with respect to coordinate system transforms. In this paper, we present new algorithms that solve exactly all three cases for the general situation. The algorithms are provably convergent and invariant to coordinate transforms. Experiments with synthetic and real 3D image data are reported.

[1] A. Bartoli and P. Sturm, The 3D Line Motion Matrix and Alignment of Line Reconstructions Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 287-292, Dec. 2001.
[2] H.H. Chen and T.S. Huang, Matching 3-D Line Segments with Applications to Multiple-Object Motion Estimation IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, pp. 1002-1008, 1990.
[3] K. Daniilidis, Hand-Eye Calibration Using Dual Quaternions Int'l J. Robotics Research, vol. 18, no. 3, pp. 286-298, 1999.
[4] O.D. Faugeras and M. Hebert, The Representation, Recognition, and Locating of 3-D Objects Int'l J. Robotics Research, vol. 5, no. 3, pp. 27-52, 1986.
[5] W.E.L. Grimson, Object Recognition by Computer: The Role of Geometric Constraints. Cambridge, Mass.: MIT Press, 1990.
[6] C. Guerra and V. Pascucci, On Matching Sets of 3D Segments Proc. Conf. Vision Geometry, vol. 3811, pp. 157-167, July 1999.
[7] D.R. Heisterkamp and P. Bhattacharya, Matching of 3D Polygonal Arcs IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, pp. 68-73, 1997.
[8] B.K.P. Horn, Closed-Form Solution of Absolute Orientation Using Quaternions J. Optical Soc. Am. A, vol. 4, pp. 629-642, 1987.
[9] A. Jonas and N. Kiryati, Length Estimation in 3-D Using Cube Quantization J. Math. Imaging and Vision, vol. 8, pp. 215-238, 1998.
[10] B. Kamgar-Parsi, B. Johnson, D.L. Folds, and E.O. Belcher, High-Resolution Underwater Acoustic Imaging with Lens-Based Systems Int'l J. Imaging Systems Technology, vol. 8, pp. 377-385, 1997.
[11] B. Kamgar-Parsi and B. Kamgar-Parsi, Matching Sets of 3D Line Segments with Application to Polygonal Arc Matching IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, pp. 1090-1099, 1997.
[12] B. Kamgar-Parsi and B. Kamgar-Parsi, An Open Problem in Matching Sets of 3D Lines Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 651-656, Dec. 2001.
[13] B. Kamgar-Parsi, B. Kamgar-Parsi, and N. Netanyahu, A Nonparametric Method for Fitting a Straight Line to a Noisy Image IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, pp. 998-1001, 1989.
[14] B. Kamgar-Parsi, B. Kamgar-Parsi, and H. Wechsler, Simultaneous Fitting of Several Planes to Point Sets Using Neural Networks Computer Vision, Graphics, and Image Processing, vol. 52, pp. 341-359, 1990.
[15] P. Meer, D. Mintz, D. Kim, and A. Rosenfeld, Robust Regression Methods in Computer Vision: A Review Int'l J. Computer Vision, vol. 6, pp. 59-70, 1991.
[16] P. Rousseeuw and A. Leroy, Robust Regression and Outlier Detection. New York: John Wiley&Sons, 1987.
[17] C.J. Taylor and D.J. Kriegman, Structure and Motion from Line Segments in Multiple Images IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 11, pp. 1021-1032, Nov. 1995.
[18] M.W. Walker, L. Shao, and R.A. Volz, Estimating 3-D Location Parameters Using Dual Number Quaternions CVGIP: Image Understanding, vol. 54, pp. 358-367, 1991.
[19] M. Werman and D. Keren, A Bayesian Method for Fitting Parametric and Non-Parametric Models to Noisy Data IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 5, pp. 528-534, May 2001.
[20] Z. Zhang, Estimating Motion and Structure from Correspondences of Line Segments between Two Perspective Images Proc. Int'l Conf. Computer Vision, pp. 257-262, June 1995.
[21] Z. Zhang and O. Faugeras, 3D Dynamic Scene Analysis. Springer-Verlag, 1992.
[22] Z. Zhang and O.D. Faugeras, Determining Motion from 3D Line Segment Matches: A Comparative Study Image and Vision Computing, vol. 9, no. 1, pp. 10-19, 1991.

Index Terms:
Line matching, motion estimation, object recognition, pose estimation, 3D registration.
Citation:
Behzad Kamgar-Parsi, Behrooz Kamgar-Parsi, "Algorithms for Matching 3D Line Sets," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 5, pp. 582-593, May 2004, doi:10.1109/TPAMI.2004.1273930
Usage of this product signifies your acceptance of the Terms of Use.