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  • Abstract - Part I: Modeling Image Curves Using Invariant 3-D Object Curve Models/spl minus/a Path to 3-D Recognition and Shape Estimation from Image Contours
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Part I: Modeling Image Curves Using Invariant 3-D Object Curve Models/spl minus/a Path to 3-D Recognition and Shape Estimation from Image Contours
January 1994 (vol. 16 no. 1)
pp. 1-12

This paper and its companion are concerned with the problems of 3-D object recognition and shape estimation from image curves using a 3-D object curve model that is invariant to affine transformation onto the image space, and a binocular stereo imaging system. The objects of interest here are the ones that have markings (e.g., characters, letters, special drawings and symbols, etc.) on their surfaces. The 3-D curves on the object are modeled as B-splines, which are characterized by a set of parameters (the control points) from which the 3-D curve can be totally generated. The B-splines are invariant under affine transformations. That means that the affine projected object curve onto the image space is a B-spline whose control points are related to the object control points through the affine transformation. Part I deals with issues relating to the curve modeling process. In particular, the authors address the problems of estimating the control points from the data curve, and of deciding on the "best" order B-spline and the "best" number of control points to be used to model the image or object curve(s). A minimum mean-square error (mmse) estimation technique which is invariant to affine transformations is presented as a noniterative, simple, and fast approach for control point estimation. The "best" B-spline is decided upon using a Bayesian selection rule. Finally, we present a matching algorithm that allocates a sample curve to one of p prototype curves when the sample curve is an a priori unknown affine transformation of one of the prototype curves stored in the data base. The approach is tried on a variety of images of real objects.

[1] C. de Boor, "On calculation withB-splines,"J. Approx. Theory, vol. 6, pp. 50-62, 1972.
[2] C. de Boor,A Practical Guide to Splines. New York: Springer, 1978.
[3] D. F. Rogers and J. A. Adams,Mathemational Elements for Computer Graphics, 2nd ed. New York: McGraw-Hill, 1990.
[4] D. W. Paglieroni and A. K. Jain, "Control point transforms for shape representation and measurement,"Computer Vision, Graphics, Image Proc., vol. 42, pp. 87-111, 1988.
[5] E. Persoon and K. Fu, "Shape discrimination using Fourier descriptors,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, no. 3, pp. 388-397, May 1986.
[6] C. T. Zahn and R. Z. Roskies, "Fourier descriptors for plane closed curves,"IEEE Trans. Comput., vol. C-21, pp. 269-281, Mar. 1972.
[7] J. A. Saghri and H. Freeman, "Analysis of the precision of generalized chain codes for the representation of planar curves,"IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-3, pp. 533-539, Sept. 1981.
[8] T. Pavlidis and F. Ali, "Computer recognition of handwriten numerals by polygonal approximations,"IEEE Trans. Syst., Man, Cybern., vol. SMC-6, pp. 610-614, Nov. 1975.
[9] H. Asada and M. Brady, "The curvature primal sketch,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 1, pp. 2-14, 1986.
[10] O. Philbrick, "Shape description with the medial axis transformation," inPictorial Pattern Recognition, G. C. Cheng, Ed. Washington, DC: Thompson, 1968, pp. 395-407.
[11] R. L. Kashyap and R. Chellappa, "Stochastic models for closed boundary analysis: Representation and reconstruction,"IEEE Trans. Inform. Theory, vol. IT-27, no. 5, pp. 627-637, Sept. 1981.
[12] N. Otsu, "A threshold selection method from gray-level histograms,"IEEE Trans. Syst., Man, Cybern., vol. SMC-9, no. 1, pp. 62-66, Jan. 1979.
[13] A. Rosenfeld and A. Kak,Digital Picture Processing, New York: Academic, 1976.
[14] W. J. Gordon and R. F. Riesenfeld, "B-spline curves and surfaces," inComputer Aided Geometric Design, R. E. Barnhill and R. F. Riesenfeld, Eds. New York: Academic, 1974, pp. 95-126.
[15] I. Faux and M. Pratt,Computational Geometry for Design and Manufacture. Ellis Horwood, 1979.
[16] I. J. Schoenberg, "Contributions to the problem of approximation of equidistant data by analytic functions,"Q. Appl. Math., vol. 4, pp. 45-99 and pp. 112-141, 1946.
[17] R. O. Duda and P. E. Hart,Pattern Classification and Scene Analysis. New York: Wiley, 1973.
[18] S. Zacks,Parametric Statistical Inference. New York: Pergamon, 1981.
[19] D. B. Cooper, "When should a machine ask for help?"IEEE Trans. Inform. Theory, vol. 12, no. 4, July 1974.
[20] R. Kayshap, "Optimal choice of AR and MA parts in autoregressive moving average processes,"IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-4, 1982.
[21] R. M. Bolle and D. B. Cooper, "Bayesian recognition of local 3-D shape by approximating image intensity functions with quadric polynomials,"IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-6, no. 4, July 1984.
[22] J. Y. Wang, "3-D shape estimation and object recognition from image contours using B-splines, unwarping techniques, and neural networks," Ph.D. dissertation, Dept. Elec. Comput. Eng., Drexel Univ., Philadelphia, PA, 1991.
[23] F. S. Cohen, Z. Huang, and Z. Yang, "Invariant matching and identification of curves usingB-spline representation," inProc. IEEE Workshop Applications of Computer Vision, Palm Springs, CA, Nov. 30-Dec. 2, 1992, pp. 213-221.
[24] P. Besl,Analysis and Interpretation of Range Images, A. Jain and R. Jain, Eds. New York: Springer, 1989.
[25] Z. Huang and F. S. Cohen, "Affine-invariant moments and B-splines for object recognition from image curves," inProc. 93 SPIE Conf. Applications of Artificial Intelligence XI: Machine Vision and Robotics, Orlando, FL, Apr. 12-16, 1993.
[26] D. Keren, J. Subrahmonia, G. Taubin, and D. B. Cooper, "Bounded and unbounded implicit polynomials curves and surfaces, Mahalanobis distances, and geometric invariants, for robust object recognition," inProc. DARPA Image Understanding Workshop, Jan. 1992.
[27] F. S. Cohen and M. Patel, "Modeling and synthesis of images of 3D textured surfaces,"Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, vol. 53, no. 6, pp. 501-510, Nov. 1991.
[28] W. Press, B. Flannery, S. Teukolsky, and W. Vetterling,Numeric Recipes in C-The Art of Scientific Computing.Cambridge, UR: Cambridge University Press, 1988.

Index Terms:
splines (mathematics); stereo image processing; Bayes methods; image recognition; image curves; invariant 3-D object curve models; 3-D recognition; shape estimation; image contours; affine transformation; binocular stereo imaging system; B-splines; control points; minimum mean-square error estimation technique; Bayesian selection rule; matching algorithm; prototype curves; sample curve
Citation:
F.S. Cohen, Jin-Yinn Wang, "Part I: Modeling Image Curves Using Invariant 3-D Object Curve Models/spl minus/a Path to 3-D Recognition and Shape Estimation from Image Contours," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 1, pp. 1-12, Jan. 1994, doi:10.1109/34.273721
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