| | This Article | |
| |
| |
| | Share | |
| |
| |
| | Bibliographic References | |
| |
| |
| | Add to: | |
| |
 Digg
 Furl
 Spurl
 Blink
 Simpy
 Google
 Del.icio.us
 Y!MyWeb
| |
| | Search | |
| |
| |
| | |
Characterizing Three-Dimensional Surface Structures from Visual Images
January 1991 (vol. 13 no. 1)
pp. 52-60
A new technique for computing intrinsic surface properties is presented. Intrinsic surface properties are those properties of a surface that are not affected by the choice of the coordinate system, the position of the viewer relative to the surface, and the particular parametric representation used to describe the imaged surface. Since intrinsic properties are characteristics of a surface, they are ideal for the purposes of representation and recognition. The intrinsic properties of interest are the principal curvatures, the Gaussian curvatures, and the lines of curvature. It is proposed that a structured-light sensing configuration where a grid pattern is projected to encode the imaged surfaces for analysis be adopted. At each stripe junction, the curvatures of the projected stripes on the imaged surface are computed and related to those of the normal sections that share the same tangential directional as the projected curves. The principal curvatures and their directions at the stripe junction under consideration are then recovered using Euler's theorem. Results obtained using both synthetic and real images are presented.
[1] J. K. Aggarwal and Y. F. Wang, "Inference of object surface structure from structured lighting-An overview," inMachine Vision Algorithms, Architectures, and Systems, H. Freeman, Ed. San Diego, CA: Academic, 1988, pp. 193-220.
[2] G. J. Agin and T. O. Binford, "Computer description of curved objects," inProc. Int. Joint Conf. Artificial Intelligence, Stanford, CA, Aug. 1973, pp. 624-640.
[3] P. J. Besl and R. C. Jain, "Three-dimensional object recognition,"ACM Comput. Surveys, vol. 17, no. 1, pp. 75-145, Mar. 1985.
[4] P. J. Besl and R. C. Jain, "Range image understanding," inProc. Comput. Vision and Pattern Recognition, San Francisco, CA, June 1985, pp. 430-449.
[5] K.L. Boyer and A.C. Kak, "Color-encoded structure light for rapid range sensing,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 1, pp. 14-28, Jan. 1987.
[6] 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.
[7] A. K. Cline, "Smoothing by splines under tension," Tech. Rep. Center for Numerical Analysis CNA-170, Univ. Texas, Austin, TX, 1981.
[8] M. P. Do Carmo,Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall, 1976.
[9] J.D. Foley and A. Van Dam,Fundamentals of Interactive Computer Graphics(The System Programming Series). Reading, MA: Addison-Wesley, 1982.
[10] W. Frobin and E. Hierholzer, "Rasterstereography: A photogrammetric method for measurement of body surfaces,"Photogrammetr. Eng. Remote Sensing, vol. 47, no. 12, pp. 1717-1724, Dec. 1981.
[11] W. Frobin and E. Hierholzer, "Calibration and model reconstruction in analytical close-range stereophotogrammetry part I: Mathematical fundamentals,"Photogrammetr. Eng. Remote Sensing, vol. 48, no. 1, pp. 67-72, Jan. 1982.
[12] W. Frobin and E. Hierholzer, "Calibration and model reconstruction in analytical close-range stereophotogrammetry part II: Special evaluation procedures for rasterstereography and moire topography,"Photogrammetr. Eng. Remote Sensing, vol. 48, no. 2, pp. 215-220, Feb. 1982.
[13] A. Goetz,Introduction to Differential Geometry. Reading, MA: Addison-Wesley, 1970.
[14] D. G. Hakala, R. C. Hillyard, P. F. Malraison, and F. F. Nource, "Natural quadrics in mechanical design," presented at the Siggraph Seminar: Solid Modeling, Dallas, TX, Aug. 1981.
[15] E.L. Hallet al., "Measuring curved surfaces for robot vision,"Computer, pp. 42-54, Dec. 1982.
[16] R.A. Jarvis, "A perspective on range finding techniques for computer vision,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-5, no. 2, pp. 122-139, Mar. 1983.
[17] E. Kreyszig,Differential Geometry. Toronto: University of Toronto Press, 1959.
[18] J. Le Moigne and A.M. Waxman, "Projected light grids for short range navigation of autonomous robots," inProc. 7th Int. Conf. Pattern Recognition, July 30-Aug. 2, 1984, pp. 203-206.
[19] P. Liang, "Measurement, orientation determination and recognition of surface shapes in range images," Ph.D. dissertation, Univ. of Pittsburgh, 1987.
[20] B. O'Neill,Elementary Differential Geometry. New York: Academic, 1966.
[21] K. S. Pennington and P. M. Will, "A grid-coded technique for recording 3-dimensional scenes illuminated with ambient light,"Opt. Commun., vol. 2, no. 4, pp. 167-169, Sept. 1970.
[22] A. V. Pogorelov, "Extrinsic geometry of convex surfaces," inTranslations of Mathematical Monographs, vol. 35. Providence, RI.: Amer. Math. Soc., 1973.
[23] R. J. Popplestone, C. M. Brown, A. P. Ambler, and G.F. Crawford, "Forming models of plane-and-cylinder faceted bodies from light stripes," inProc. 4th Int. Joint Conf. Artificial Intelligence, 1975, pp. 664-668.
[24] F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction. New York: Springer-Verlag, 1985.
[25] J. L. Posdamer and M. D. Altschuler, "Surface measurement by space-encoded projected beam systems,"Comput. Graphics Image Processing, vol. 18, pp. 1-17, 1982.
[26] M. Potmesil and H. Freeman, "Curved surface representation utilizing data extracted from multiple photographic images," inProc. Workshop Representation of Three-Dimensional Objects, Philadelphia, PA, May 1-2, 1979, pp. H1-H26.
[27] M. Potmesil, "Generating models of solid objects by matching 3D surface segments," inProc. 8th Int. Joint Conf. Artificial Intelligence, Karlsruhe, West Germany, Aug. 8-12, 1983.
[28] A. A. Requicha, "Representations for rigid solids: Theory, methods, and systems,"Comput. Surveys, vol. 12, no. 4, pp. 437-465, 1980.
[29] S. N. Srihara, "Representation of three-dimensional digital images,"Comput. Surveys, vol. 14, no. 4, pp. 399-424, Dec. 1981.
[30] Y. Shirai and M. Suwa, "Recognition of polyhedrons with a range finder," inProc. 2nd Int. Joint Conf. Artificial Intelligence, London, Sept. 1971, pp. 80-87.
[31] G. Stockman and G. Hu, "Sensing 3-D surface patches using a projected grid," inProc. IEEE Computer Soc. Conf. Comput. vision and Pattern Recognition, Miami Beach, FL, 1986, pp. 602-607.
[32] D. J. Struik,Differential Geometry, 2nd ed. Reading, MA: Addison-Wesley, 1961.
[33] K. Sugiharaet al., "Regular pattern projection for surface measurement," in2nd Int. Symp. Robotics Research, H. Hanafusa and H. Inoue, Eds. Cambridge, MA: MIT Press, 1985.
[34] Y. F. Wang, A. Mitiche, and J. K. Aggarwal, "Inferring local surface orientation with the aid of grid coding," inProc. Workshop Computer Vision: Representation and Control, Bellaire, MI, Oct. 13-16, 1985, pp. 96-104.
[35] Y. F. Wang, A. Mitiche, and J. K. Aggarwal, "Computation of surface orientation and structure of objects using grid coding,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 1, pp. 129-137, Jan. 1987.
[36] Y.F. Wang and J.K. Aggarwal, "On modeling 3-D objects using multiple sensory data," inProc. IEEE Int. Conf. Robotics Automat., Raleigh, NC, May 31-Apr. 3, 1987, pp. 1098-1103.
[37] Y. F. Wang and J. K. Aggarwal, "Geometric modeling using active sensing-An overview,"IEEE Control Systems Mag., vol. 3, no. 2, pp. 7-13, 1988.
[38] Y. F. Wang and J. K. Aggarwal, "Geometric modeling using both active and passive sensing," presented at the SPIE Sensor Fusion Workshop: Spatial Reasoning and Scene Interpretation, 1988.
[39] Y. F. Wang and J. K. Aggarwal, "Integration of active and passive sensing techniques for representing 3-D objects,"IEEE J. Robotics Automat., vol. 5, no. 4, pp. 460-471, Aug. 1989.
[40] D. Wei and M. Gini, "The use of taper light beam for object recognition," inRobot Vision, A. Pugh, Ed. London: IFS Ltd., U.K., 1983, pp. 143-153.
[41] P.M. Will and K.S. Pennington, "Grid coding: A preprocessing technique for robot and machine vision,"Artificial Intelligence, vol. 2, pp. 319-329, 1971.
[42] P.M. Will and K.S. Pennington, "Grid coding: A novel technique for image processing,"Proc. IEEE, vol. 60, no. 6, pp. 669-680, June 1972.
Index Terms:
synthetic images; surface representation; surface recognition; Euler theorem; three-dimensional surface structures; visual images; intrinsic surface properties; coordinate system; parametric representation; principal curvatures; Gaussian curvatures; lines of curvature; structured-light sensing configuration; grid pattern; stripe junction; projected stripes; normal sections; tangential directional; real images; computer vision; computerised pattern recognition; computerised picture processing
Citation:
Y.F. Wang, "Characterizing Three-Dimensional Surface Structures from Visual Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 1, pp. 52-60, Jan. 1991, doi:10.1109/34.67630
