Practical reliable bayesian recognition of 2d and 3d objects using implicit polynomials and algebraic invariants

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 18, Issue 5, 1996, Pages 505-519

  Subrahmonia, Jayashree ^a   Cooper, David B ^a   Keren, Daniel ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Algebraic invariants; Bayesian recognition; Implicit polynomials; Mahalanobis distance

Indexed keywords

ALGEBRAIC INVARIANTS; BAYESIAN RECOGNITION; DIMENSIONALITY; IMPLICIT POLYNOMIALS; LINEAR TRANSFORMATION; MAHALANOBIS DISTANCE; POSITION ESTIMATION;

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; COMPUTER VISION; DATA STRUCTURES; DATABASE SYSTEMS; INVARIANCE; MATHEMATICAL TRANSFORMATIONS; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM SOLVING; SYSTEM STABILITY;

OBJECT RECOGNITION;

EID: 0030143069     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.494640     Document Type: Article

References (29)

1. R. Bolle and D. Cooper, "Bayesian Recognition of Local 3D Shape by Approximating Image'Intensity Functions with Quadric Polynomials/7 IEEE Trans, or. Pattern-Arialysis ana Machine-Intelligence, vol. 6, no. 4, pp. 418-429, July 1-984.
2. R. Bolle and D. Cooper, "On,Optimally.Combining Pieces of. Information , with Applications to Estimatng 3D Complex-Object Position from Range Data," IEEE Trans. On Pattern Analysis 'and Machine Intelligence, vol. 8, no.;5, pp. 619-638, Sept. 1986.
3. R. Bolles and P. Horaud, "3DPO: A Three-Dimensional Part Orientation System," The Int'l ]. of Robotics Research, vol. 5, no. 3, pp. 3-26, 1986.
4. B. Cernuschi-Frias, "Orientation and Location' Parameter Estimatin of Quadric Surfaces irr 3D from' a- Sequence- of Images," PhD thesis, Brown Univ., Providence, R.I., May 1984.
5. C. Chen and A. Kak, "A Robot Vision System for Recognizing 3D Objects in Low-Order Polynomial Time," IEEE Trais. Or. Systems, Man, and Cybernetics," vol. 19, no. 6; pp. 1,535-1,563, Nov./Dec. 1989.
6. D. Cooper, "When Should a '-Learning Machine A'sk for Help," IEEE Trans. On Pattern Analysis and Machine Intelligence, vol. 20, no. 4, July 1974.
7. D. Cooper and N. Yalabik, "On the Computational Cost of Approximating and Recognising Noise-Perturbed Straight Lines and Quadratic Arcs in the Plane," IEEE Trans. On Computers, vol. 25; no. 10, pp. 1,020-1032, Oct. 1976.
8. D.B. Cooper and F. Sung, "Multiple-Window Parallel Adaptive Boundary Finding in Computer Vision," IEEE T-ans. On Pattern Analysis arid Machine Intelligence, vol. 5, pp. 299-316, May 1983.'
9. D. Forsyth, J.L. Mundy, A. Zisserman, C. Coelho, A. Heller, and C. Rothwell, "Invariant Descriptors for 3-D Object Recognition and Pose," IEEE Trans. On Pattern Analysis and Machine Intelligence, vol. 13, pp. 971-991, Oct. 1991.
10. J. Grace and A. Young, The Algebra of Invariants. Cambridge Univ. Press, 1903.
11. D. Keren, "Some New Invariants in Computer Vision." IEEE Trans. On Pattern Analysis and Machine Intelligence, pp. 1,143-1,149, Nov. 1994.
12. D. Keren, D.B. Cooper, and J. Subrahmonia, "Describing Complicated Objects by Implicit Polynomials," IEEE Trans. On PatternAnalysis and Machine Intelligence, vol. 16, pp. 38-54/Jani 1994.
13. D. Keren, Subrahmonia, and D.B. Cooper, "Robust Object Recognition based on Implicit Algebraic Curves and Surfaces," IEEE Con/.' On Computer Vision and Pattern Recognition, pp. 791-794', Champaign, 111., Time 1992.
14. Z. Lei, D. Keren, and D.B. Cooper, "Recognition of Complex FreeForm Objects Based on Mutual Algebraic Invariants for Paris of Patches of Data," Tech. Report MO, LEMS, Division of Engineering, Brown Univ., Providence, R..L, Jan. 1995.'
15. V. Markandey and R.J.P. deFigueiredo,' "Robot Sensing T.ech-' niques Based on High-Dimensional Movement Invariants and Tensors," IEEE Trans. On-Patte.rn .Analysis ana Machine Intelligence, vol 8, pp. 186-195, Apr. 1992.
16. O.D. Faugeras, M. Hebert, and E. Pauchon, "Segmentation of Range Data into Planar and quadratic Patches," Proc. IEEE Cora/, On Computer Vision and Pattern Recognition, pp. 8-13, Washington,D.C., June 1983. ' '
17. V. Prall, "Direct Least Squares Fitting of Algebraic Surfaces," Computer Graphics, vol. 21, pp. 145-152, July 1987.
18. P. Sampson, "Fitting Coriic Sections to Very Scattered Data:. An Iterative Improvement of the Bookstein Algorithm," Computer Vision, Graphics, and Image Processing, vol. 18, pp. 97-108,1982.
19. K. Siddiqi and B.B. Kimia, "Parts of Visual Form: Computational Aspects," IEEE Trans. On Pattern Analysis and Machine Intelligence, vol. 17, no. 3, pp. 239-251, Mar. 1995.
20. J. Silverman and D. Cooper, "Bayesian Clustering for Unsupervised Estimation of Surface and Texture Models.," IEEE Trans. On Pattern Analysis and Machine Intelligence, vol. 10, pp. 482-495, July 1988.
21. J. Subrahmonia, D.B. Cooper, and D. Keren, "Practical Reliable Bayesian Recognition of 2D and. 3D Objects Usng Implicit Polynomials and Algebraic Invariants," Tech. Report LEMS-107, Brown Univ., Providence, R.I., May 1992.
22. J. Subrahmonia, D. Keren, and D.B. Cooper, "Bayesian Methods for the Use of Implicit Polynomials andAlgebraic Invariants in Practical Computer Vision," Proc. SP1E Conf., Boston, Mass., June 1992.
23. G. Taubin, "Estimation of Planar Curves, Surfaces and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation," 7EEE Trans. On Pattern Analysis and Machine Intelligence, vol. 13, pp. 1,115-1,138, Nov. 1991'.
24. G. Taubin and D.B. Cooper, "3D Object Recognition and Positioning with Algebraic Invariants and Covariants," pp. 147-182, July 1990. A chapter in Symbolic and Numerical Computations Towards Integration, pp. 147-182. B.R. Donald, D. Kapur, and J. Mundy, cds., Academic Press, 1992.
25. G. Taubin and D.B. Cooper, "2D and 3D Object Recognition and Positioning System Based on Moment Invariants," Geometric Invariance in Machine Vision, J. Mundy and A. Zisserman, eds., pp. 375-397,1992.
26. [261 G. Taubin, F. Cukierman, S. Sullivan, J. Ponce, and D.J. Kriegman, "Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting," IEEE Trans. On Pattern Analysis and Machine Intelligence, vol. 16, pp. 287-304, Mar. 1994.
27. A. Wald, "Tests of Statistical Hypotheses Concerning Several Parameters when the Number of Observations is Large," Trans. Of American Math. Society, vol. 54, pp. 426-482,1948.
28. I. Weiss, P. Meer, and S.M. Dunn, "Robustness of Algebraic Invariants," First DARPA-ESPIRIT Workshop on Invariants, pp. 345359, Rikjavik, Iceland, Mar. 1991.
29. P. Whaite and F.P. Ferrie, "From Uncertainty to Visual Exploration," IEEE Trans. On Pattern Analysis and Machine. Intelligence, vol. 13, pp. 1,038-1,049, Oct. 1991.