This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Matching of 3D Polygonal Arcs
January 1997 (vol. 19 no. 1)
pp. 68-73

Abstract—We define a distance measure between 3D polygonal arcs of equal length, and show that the minimum value of this distance measure is the smallest eigenvalue of a certain matrix. Using this, we develop a mismatch measure and a matching algorithm for 3D polygonal arcs of unequal lengths.

[1] N. Ayache, Artificial Vision for Mobile Robots.Cambridge, Mass.: MIT Press, 1991.
[2] B. Bascle and R. Deriche, "Stereo Matching, Reconstruction and Refinement of 3D Curves Using Deformable Contours," Proc. IEEE Int'l Conf. Computer Vision, pp. 421-428,Berlin, 1993.
[3] B. Bhanu and O.D. Faugeras, "Shape Matching of Two Dimensional Objects, IEEE Trans Pattern Analysis and Machine Intelligence, vol. 6, pp. 60-72, 1984.
[4] P. Bhattacharya and A. Rosenfeld, "Polygons in Three Dimensions," J. Visual Comm. and Image Rep., vol. 50, pp. 353-363, 1994.
[5] R.O. Eason and R.C. Gonzalez, "Least-Squares Fusion of Multisensory Data, Data Fusion in Robotics and Machine Intelligence, M.A. Abidi and R.C. Gonzalez, eds. San Diego, Calif.: Academic Press, 1992.
[6] H. Freeman, "On the Encoding of Arbitrary Geometric Configurations," IRE Trans. Electron. Comput., vol. 10, pp. 260-268, 1961.
[7] A. Gueziec and N. Ayache, "Smoothing and Matching of 3D Spatial Curves, Int'l J. Computer Vision, vol. 12, no. 1, pp. 79-104, 1994.
[8] B.K.P. Horn, Robot Vision,Cambridge, Mass.: MIT Press, 1986.
[9] E. Kishon, T. Hastie, and H. Wolfson, "3D Curve Matching Using Splines, J. Robotic Systems, vol. 8, no. 6, pp. 723-743, 1991.
[10] P. Maillot, "Using Quaternions For Coding 3D Transformations," Graphic Gems, A.S. Glassner, ed. New York: Academic Press, pp. 498-515, 1990.
[11] F. Mokhtarian and A. Mackworth, "Scale-Based Description and Recognition of Planar Curves and Two Dimensional Shapes," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 1, pp. 34-43, 1986.
[12] T. Pajdla and L. van Gool, "Matching of 3-D Curves Using Semi-Differential Invariants," Proc. Int'l Conf. Computer Vision, IEEE, Press, 1995, pp. 390-395.
[13] B. Parsi, A. Margalit, and A. Rosenfeld, "Matching General Polygonal Arcs," Computer Vision, Graphics and Image Processing: Image Understanding, vol. 53, pp. 227-234, 1991.
[14] J.T. Schwartz and M. Sharir, "Identification of Partially Obscured Objects in Two and Three Dimensions by Matching Noisy Characteristic Curves," Int'l J. Robotics Res., vol. 6, no. 2, pp. 29-44, 1987.
[15] K. Shoemake, "Quaternions and 4×4 Matrices," Graphic Gems II, J. Arvo, ed. New York: Academic Press, pp 351-354, 1991.

Index Terms:
Polygonal arcs, matching, distance measure, mismatch measure, quaternions, rotation matrix, eigenvalues.
Citation:
Douglas R. Heisterkamp, Prabir Bhattacharya, "Matching of 3D Polygonal Arcs," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 1, pp. 68-73, Jan. 1997, doi:10.1109/34.566813
Usage of this product signifies your acceptance of the Terms of Use.