This Article 
 Bibliographic References 
 Add to: 
The Complex EGI: A New Representation for 3-D Pose Determination
July 1993 (vol. 15 no. 7)
pp. 707-721

The complex extended Gaussian image (CEGI), a 3D object representation that can be used to determine the pose of an object, is described. In this representation, the weight associated with each outward surface normal is a complex weight. The normal distance of the surface from the predefined origin is encoded as the phase of the weight, whereas the magnitude of the weight is the visible area of the surface. This approach decouples the orientation and translation determination into two distinct least-squares problems. The justification for using such a scheme is twofold: it not only allows the pose of the object to be extracted, but it also distinguishes a convex object from a nonconvex object having the same EGI representation. The CEGI scheme has the advantage of not requiring explicit spatial object-model surface correspondence in determining object orientation and translation. Experiments involving synthetic data of two polyhedral and two smooth objects are presented to illustrate the feasibility of this method.

[1] P. Balakumar, J. C. Robert, R. Hoffman, K. Ikeuchi, and T. Kanade, VANTAGE: AFrame-Based Geometric Modeling System-Programmer/User's Manual. Pittsburgh, PA: CMU, Dec. 1988.
[2] P. J. Besl and R. C. Jain, "Three-dimensional object recognition,"ACM Comput. Surveys, vol. 17, no. 1, pp. 75-145, Mar. 1985.
[3] B. Bhanu, "Representation and shape matching of 3-D objects,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, no. 3, pp. 340-350, 1984.
[4] R. M. Bolle and D.B. Cooper, "On optimally combining pieces of information, with application to estimating 3-D complex-object position from range data,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 619-638, Sept. 1986.
[5] R. C. Bolles, P. Horaud, and M. J. Hannah, "3DPO: A three-dimensional part orientation system," inProc. First Int. Symp. Robotic Res., 1984, pp. 413-424.
[6] P. Brou, "Using the Gaussian image to find the orientation of objects,"Int. J. Robotics Res., vol. 3, no. 4, pp. 89-125, Winter 1984.
[7] T. J. Fan, G. Medioni, and R. Nevatia, "Matching 3-D objects using surface descriptions," inProc. Int. Conf. Robotics Automat., Apr. 1988, pp. 1400-1406.
[8] O. D. Faugeras, "New steps toward a flexible 3-D vision system for robotics," inProc. Int. Conf. Patt. Recogn., July 1984, pp. 796-805.
[9] O. D. Faugeras and M. Hebert, "A 3-D recognition and positioning algorithm using geometrical matching between primitive surfaces," inProc. Int. Joint Conf. Artificial Intell., Aug. 1983, pp. 996-1002.
[10] W. E. L. Grimson and T. Lozano-Perez, "Recognition and localization of overlapping parts from sparse data," inThree-Dimensional Machine Vision(T. Kanade, Ed.). Boston: Kluwer, 1987, pp. 451-510.
[11] B. K. P. Horn, "Extended Gaussian images,"Proc. IEEE, vol. 72, no. 12, pp. 1671-1686, Dec. 1984.
[12] B. K. P. Horn and K. Ikeuchi, "The mechanical manipulation of randomly oriented parts,"Sci. Amer., vol. 251, no. 2, pp. 100-113, Aug. 1984.
[13] K. Ikeuchi, "Recognition of 3-D objects using the extended Gaussian image," inProc. Seventh IJCAI, 1981, pp. 595-600.
[14] K. Ikeuchi, "Determining attitude of object from needle map using extended Gaussian image," Tech. Rep. AI Memo 714, MIT, 1983.
[15] S. B. Kang and K. Ikeuchi, "3-D object pose determination using complex EGI," Tech. Rep. CMU-RI-TR-90-18, Carnegie Mellon Univ., Oct. 1990.
[16] J. J. Little, "Recovering shape and determining attitude from extended Gaussian image," Tech. Rep. TR 85-2, Univ. of British Columbia, Apr. 1985.
[17] D. Lowe, Perceptual Organization And Visual Recognition. Boston: Kluwer, 1985.
[18] H. Minkowski, "Allgemeine Lehrsatze uber die konvexe Polyeder,"Nachr. GHes. Wiss. Gottingen, 1897.
[19] V. S. Nalwa, "Representing oriented piecewise C2surfaces," inProc. 2nd Int. Conf. Comput. Vision, Dec. 1988, pp. 40-51.
[20] R. Nevatia and T. O. Binford, "Description and recognition of curved objects,"Artificial Intell., no. 8, pp. 77-98, 1977.
[21] J. Ponce and D. J. Kriegman, "On recognizing and positioning curved 3D objects from image contours," inProc. DARPA Image Understanding Workshop, Palo Alto, CA, 1989, pp. 461-470.
[22] J. W. Roach, J. S. Wright, and V. Ramesh, "Spherical dual images: A 3-D representation method for solid objects that combines dual space and Gaussian spheres," inProc. CVPR, June 1986, pp. 236-241.
[23] K. Sato, H. Yamamoto, and S. Inokuchi, "Range imaging system utilizing nematic liquid crystal mask," inProc. Int. Conf. Comput. Vision, 1987, pp. 657-661.
[24] T. M. Silberberg, D. Harwood, and L. S. Davis, "Three dimensional object recognition using oriented model points," inTechniques for 3-D Machine Perception(A. Rosenfeld, Ed.). New York: Elsevier, 1986, pp. 271-320.
[25] F. Stein and G. Medioni, "Structural indexing: Efficient 3-D recognition,"IEEE Trans. Patt. Anal. Machine Intell., vol. 4, no. 2, pp. 125-145, 1992.

Index Terms:
image recognition; image processing; complex extended Gaussian image; 3D object representation; outward surface normal; orientation; translation; least-squares problems; encoding; image processing; image recognition; least squares approximations
S.B. Kang, K. Ikeuchi, "The Complex EGI: A New Representation for 3-D Pose Determination," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 7, pp. 707-721, July 1993, doi:10.1109/34.221171
Usage of this product signifies your acceptance of the Terms of Use.