This Article 
 Bibliographic References 
 Add to: 
An Abstraction-Based Approach to 3-D Pose Determination from Range Images
July 1993 (vol. 15 no. 7)
pp. 722-736

An abstraction-based paradigm that makes explicit the process of imposing assumptions on data is discussed. The units of abstraction are models in which levels of abstraction are determined by the degree of assumption necessary for their application. A general-to-specific refinement process provides a mechanism to proceed gracefully through the abstraction hierarchy. This strategy was applied to the recognition and pose determination of objects comprising simple and compound cylindrical and planar surfaces in dense range data. A method of computing reliable Gaussian and mean curvature sign-map descriptors from the polynomial approximations of surfaces is demonstrated. A means for determining the pose of constructed geometric forms whose algebraic surface descriptions are nonlinear in terms of their orienting parameters is developed. It is shown that biquadratic surfaces are suitable companion-linear forms for cylinder approximation and parameter estimation. The estimates provide the initial parametric approximations necessary for a nonlinear regression stage to fine tune the estimates by fitting the actual nonlinear form to the data.

[1] H. Asada and M. Brady, "A curvature primal sketch," inProc. IEEE Workshop Comput. Vision: Representation Cont.(Annapolis, MD), May 1984 pp. 8-17.
[2] M. F. Augusteijn and C. R. Dyer, "Recognition and recovery of three-dimensional orientation of planar point patterns,"Computer Vision Graphics Image Processing, vol. 36, pp. 76-99, 1986.
[3] D. H. Ballard and D. Sabbah, "Viewer independent shape recognition,"IEEE Trans. Patt. Analysis Machine Intell., vol. PAMI-5, no. 6, pp. 653-659, Nov. 1983.
[4] H. G. Barrow and J. M. Tenenbaum, "Interpreting line drawings as three dimensional surfaces,"Artificial Intell., vol. 17, pp. 75-117, 1981.
[5] P. R. Beaudet, "Rotationally invariant image operators," inProc. 4th Int. Joint Conf. Patt. Recogn., (Kyoto, Japan) Nov. 7-10, 1978.
[6] P. J. Besl and R. C. Jain, "Three-dimensional object recognition,"ACM Comput. Surveys, vol. 17, no. 1, pp. 75-145, Mar. 1985.
[7] P. J. Besl,Surfaces in Range Image Understanding. Berlin: Springer-Verlag, 1988.
[8] P. J. Besl and R. Jain, "Segmentation through variable-order surface fitting,"IEEE Trans. Patt. Anal. Machine Intell., vol. 10, no. 2, pp. 167-192, Mar. 1988.
[9] T. O. Binford, "Survey of model-based image analysis systems,"Int. J. Robotics Res., vol. 1, no. 1, pp. 18-64, Spring 1982.
[10] R. C. Bolles, P. Horaud, and M. J. Hannah, "3DPO: A three-dimensional part orientation system," inProc. First Int. Symp. Robotics Res., 1984 pp. 413-424.
[11] B. A. Boyter and J. K. Aggarwal, "Recognition of polyhedra from range data,"IEEE Expert, pp. 47-59, Spring 1986.
[12] M. Brady and A. Yuille, "An extremum principle for shape from contour,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, no. 3, pp. 288-301, 1984.
[13] M. Brady, "Representing shape," inProc. IEEE Int. Conf. Robots, 1984, pp. 256-265.
[14] R. A. Brooks, R. Greiner, and T. O. Binford, "The ACRONYM model-based vision system," inProc. of the 76h IJCAI, 1979 pp. 105-113.
[15] R. A. Brooks, "Symbolic reasoning among 3-D models and 2-D images,"Artificial Intell., vol. 17, pp. 285-348, Aug. 1981.
[16] R. A. Brooks, "Model-based three-dimensional interpretations of two-dimensional images,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-5, no. 2, pp. 140-149, Mar. 1983.
[17] 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.
[18] J. K. Cheng and T. S. Huang, "Recognition of curvilinear objects by matching relational structures," inProc. PRIP, 1982 pp. 343-348.
[19] R.T. Chin and C. R. Dyer, "Model-based recognition in robot vision,"ACM Comput. Surveys, vol. 18, no. 1, pp. 67-108, Mar. 1986.
[20] M. Dhome and T. Kasvand, "Polyhedra recognition by hypothesis accumulation from range data,"Nat. Res. Council Canada, Div. Elect. Eng., ERB-985, NRCC No. 25655, May 1986.
[21] J. R. Engelbrecht and F. M. Wahl, "Polyhedral object recognition using Hough-space features,"Pattern Recog., vol. 21, no. 6, pp. 155-168, 1988.
[22] Environmental Res. Inst. Michigan, "Configuration description for ERIM/USPS range sensor--Dynamic and static modes," ERIM, Ann Arbor, MI, 1989.
[23] R. Horaud and R.C. Bolles, "3DPO's strategy for matching three-dimensional objects in range data," inProc. Int. Conf. Robotics, (Atlanta, GA), Mar. 1984, pp. 78-85.
[24] R. Horaud and M. Brady, "On the geometric interpretation of image contours," inProc. 1st Int. Conf. Comput. Vision(London UK), 1987, pp. 374-382.
[25] B. K. P. Horn, "Extended Gaussian images,"Proc. IEEE, vol. 72, no. 12, pp. 1671-1686, 1984.
[26] K. Ikeuchi, "Recognition of 3-D objects using the extended Gaussian image," inProc. 7th Int. Joint Conf. Artificial Intell.(Vancouver), Aug. 1981, pp. 595-600.
[27] K. Ikeuchi, B. K. P. Horn, and S. Nagata, "Picking up an object from a pile of objects," M.I.T. Artificial Intell. Lab., A.I. Memo No. 726, May 1983.
[28] T. Kanade, "Recovery of the three-dimensional shape of an object from a single view,"Artificial Intell., vol. 17, pp. 409-460, Aug. 1981.
[29] J. H. Kindle,Analytical Geometry, New York: McGraw-Hill, 1950.
[30] T. F. Knoll and R. C. Jain, "Learning to recognize objects using feature indexed hypotheses," inProc. 1st Int. Conf. Comput. vision(ICCV'87), 1987.
[31] J. J. Little, "An iterative method for reconstruction convex polyhedra from extended Gaussian images," inProc. Nat. Conf. Artificial Intell., (Washington, DC), Aug. 1983, pp. 247-250.
[32] D. L. Milgram and C. M. Bjorklund, "Range image processing: Planar surface extraction," inProc. IJCPR-5, 1980, pp. 912-919.
[33] R. S. Millman and G. D. Parker,Elements of Differential Geometry, Englewood Cliffs, NJ: Prentice-Hall, 1977.
[34] J. O'Rourke, "Polyhedra of minimal as 3D models," inProc. 7th Int. Joint Conf. Artificial Intell.(Vancouver, Canada), Aug. 1981, pp. 664-666.
[35] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling,Numerical Recipes. Cambridge, UK: Cambridge University Press, 1986.
[36] A. J. Riggs, L. M. Tomko, K. G. Wesolowicz, and C. J. Jacobus, "Design of a laser radar range imaging sensor for postal applications," Environmental Res. Inst. Michigan, Ann Arbor, Tech. Rep. 197301-1- S1, Oct. 1986.
[37] R. E. Sampson, "3D range sensor via phase shift detection,"IEEE Comput., vol. 20, no. 8, pp. 23-24, 1987.
[38] D. J. Svetkoff, "Towards a high resolution, video rate, 3D sensor for machine vision," inProc. SPIE Conf. Optics Illumination, Image Sensing Machine Vision(Cambridge, MA) Oct. 30-31, 1986, vol. 728.
[39] W. A. Wilson and J. I. Tracey,Analytic Geometry--Alternate Edition. Boston: D.C Heath, 1937.
[40] K. C. You and K-S Fu, "A syntactic approach to shape recognition using attributed grammars,"IEEE Trans. Syst. Man Cybern., vol. SMC-9, no. 6, pp. 334-345, June 1979.

Index Terms:
image recognition; cylindrical surfaces; Gaussian curvature sign-map descriptors; 3-D pose determination; range images; abstraction-based paradigm; planar surfaces; mean curvature sign-map descriptors; polynomial approximations; algebraic surface descriptions; biquadratic surfaces; cylinder approximation; parameter estimation; nonlinear regression; approximation theory; image recognition; parameter estimation
F. Quek, R. Jain, T.E. Weymouth, "An Abstraction-Based Approach to 3-D Pose Determination from Range Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 7, pp. 722-736, July 1993, doi:10.1109/34.221172
Usage of this product signifies your acceptance of the Terms of Use.