Abstract

We present a technique to estimate the pose of a three-dimensional object from a two-dimensional view. We first compute the correlation between the unknown image and several synthetic-discriminant-function filters constructed with known views of the object. We consider both linear and nonlinear correlations. The filters are constructed in such a way that the obtained correlation values depend on the pose parameters. We show that this dependence is not perfectly linear, in particular for nonlinear correlation. Therefore we use a two-layer neural network to retrieve the pose parameters from the correlation values. We demonstrate the technique by simultaneously estimating the in-plane and out-of-plane orientations of an airplane within an 8-deg portion. We show that a nonlinear correlation is necessary to identify the object and also to estimate its pose. On the other hand, linear correlation is more accurate and more robust. A combination of linear and nonlinear correlations gives the best results.

© 2003 Optical Society of America

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References

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  1. T. Horprasert, Y. Yacoob, L. S. Davis, “Computing 3D head orientation from a monocular image sequence,” in 25th AIPR Workshop: Emerging Application of Computer Vision, D. H. Schaefer, E. F. Williams, eds., Proc. SPIE2962, 244–252 (1997).
    [CrossRef]
  2. H. Wu, T. Fukumoto, Q. Chen, M. Yachida, “Face detection and rotations estimation using color information,” in Proceedings of the Fifth IEEE International Workshop on Robot and Human Communication (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 341–346.
  3. I. Shimizu, Z. Zhang, S. Akamatsu, K. Deguchi, “Head pose determination from one image using a generic model,” Proceedings of the Third IEEE International Conference on Automatic Face and Gesture Recognition (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 100–105.
    [CrossRef]
  4. W. Wilson, “Visual servo control of robots using Kalman filter estimates of robot pose relative to work-pieces,” in Visual Serving, K. Hashimoto, ed. (Word Scientific, Singapore, 1994), pp. 71–104.
  5. M. Bajura, H. Fuchs, R. Ohbuchi, “Merging virtual objects with the real world: seeing ultrasound imagery within the patient,” Comput. Graph. 26, 203–210 (1992).
    [CrossRef]
  6. N. Ezquerra, R. Mullick, “An approach to 3D pose determination,” ACM Trans. Graphics 15, 99–120 (1996).
    [CrossRef]
  7. G. H. Rosenfield, “The problem of exterior orientation in photogrammetry,” Photogramm. Eng. 25, 536–553 (1959).
  8. R. M. Haralick, C.-N. Lee, K. Ottenberg, M. Nolle, “Review and analysis of solutions of the three point perspective pose estimation problem,” Int. J. Comput. Vision 13, 331–56 (1994).
    [CrossRef]
  9. C.-P. Lu, G. D. Hager, E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 610–622 (2000).
    [CrossRef]
  10. D. P. Huttenlocher, S. Ullman, “Recognizing solid objects by alignment with an image,” Int. J. Comput. Vision 5, 195–212 (1990).
    [CrossRef]
  11. S. E. Monroe, R. D. Juday, “Multidimensional synthetic estimation filter,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 179–185 (1990).
    [CrossRef]
  12. L. G. Hassebrook, M. E. Lhamon, M. Wang, J. P. Chatterjee, “Postprocessing of correlation for orientation estimation,” Opt. Eng. 36, 2710–2718 (1997).
    [CrossRef]
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  21. A. Mahalanobis, “Correlation filters for object tracking, target reacquisition, and smart aim-point selection,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 25–32 (1997).
    [CrossRef]
  22. R. Beale, T. Jackson, Neural Computing: An Introduction (Institute of Physics, Bristol, UK, 1992).
  23. D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT, Cambridge, Mass., 1986).
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    [CrossRef]
  31. C. Chesnaud, P. Réfrégier, V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise model,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
    [CrossRef]

2002

2000

C.-P. Lu, G. D. Hager, E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 610–622 (2000).
[CrossRef]

1999

C. Chesnaud, P. Réfrégier, V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise model,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

1997

L. G. Hassebrook, M. E. Lhamon, M. Wang, J. P. Chatterjee, “Postprocessing of correlation for orientation estimation,” Opt. Eng. 36, 2710–2718 (1997).
[CrossRef]

1996

1995

1994

P. Réfrégier, V. Laude, B. Javidi, “Nonlinear joint-transform correlation: an optimal solution for adaptive image discrimination and input noise robustness,” Opt. Lett. 19, 405–407 (1994).
[PubMed]

R. M. Haralick, C.-N. Lee, K. Ottenberg, M. Nolle, “Review and analysis of solutions of the three point perspective pose estimation problem,” Int. J. Comput. Vision 13, 331–56 (1994).
[CrossRef]

M. T. Hagan, M. Menhaj, “Training feedforward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
[CrossRef] [PubMed]

1992

M. Bajura, H. Fuchs, R. Ohbuchi, “Merging virtual objects with the real world: seeing ultrasound imagery within the patient,” Comput. Graph. 26, 203–210 (1992).
[CrossRef]

1991

1990

D. P. Huttenlocher, S. Ullman, “Recognizing solid objects by alignment with an image,” Int. J. Comput. Vision 5, 195–212 (1990).
[CrossRef]

1989

1985

R. M. Haralick, L. M. Shapiro, “Survey: image segmentation,” Comput. Vision Graph. Image Process. 29, 100–132 (1985).
[CrossRef]

1984

1980

1969

1959

G. H. Rosenfield, “The problem of exterior orientation in photogrammetry,” Photogramm. Eng. 25, 536–553 (1959).

Akamatsu, S.

I. Shimizu, Z. Zhang, S. Akamatsu, K. Deguchi, “Head pose determination from one image using a generic model,” Proceedings of the Third IEEE International Conference on Automatic Face and Gesture Recognition (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 100–105.
[CrossRef]

Bajura, M.

M. Bajura, H. Fuchs, R. Ohbuchi, “Merging virtual objects with the real world: seeing ultrasound imagery within the patient,” Comput. Graph. 26, 203–210 (1992).
[CrossRef]

Beale, R.

R. Beale, T. Jackson, Neural Computing: An Introduction (Institute of Physics, Bristol, UK, 1992).

Boulet, V.

C. Chesnaud, P. Réfrégier, V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise model,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

Casasent, D.

Castleman, K. R.

K. R. Castleman, “Pattern recognition: image segmentation,” in Digital Image Processing (Prentice-Hall, Upper Saddle River, N.J., 1996), pp. 447–485.

Caulfield, H. J.

Chatterjee, J. P.

L. G. Hassebrook, M. E. Lhamon, M. Wang, J. P. Chatterjee, “Postprocessing of correlation for orientation estimation,” Opt. Eng. 36, 2710–2718 (1997).
[CrossRef]

Chen, Q.

H. Wu, T. Fukumoto, Q. Chen, M. Yachida, “Face detection and rotations estimation using color information,” in Proceedings of the Fifth IEEE International Workshop on Robot and Human Communication (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 341–346.

Chesnaud, C.

C. Chesnaud, P. Réfrégier, V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise model,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

Connelly, J. M.

B. V. K. Vijaya Kumar, A. J. Lee, J. M. Connelly, “Correlation filters for orientation estimation,” in Digital and Optical Shape Representation and Pattern Recognition, Proc. SPIE938, 190–197 (1988).
[CrossRef]

Davis, L. S.

T. Horprasert, Y. Yacoob, L. S. Davis, “Computing 3D head orientation from a monocular image sequence,” in 25th AIPR Workshop: Emerging Application of Computer Vision, D. H. Schaefer, E. F. Williams, eds., Proc. SPIE2962, 244–252 (1997).
[CrossRef]

Deguchi, K.

I. Shimizu, Z. Zhang, S. Akamatsu, K. Deguchi, “Head pose determination from one image using a generic model,” Proceedings of the Third IEEE International Conference on Automatic Face and Gesture Recognition (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 100–105.
[CrossRef]

Dubois, F.

Ezquerra, N.

N. Ezquerra, R. Mullick, “An approach to 3D pose determination,” ACM Trans. Graphics 15, 99–120 (1996).
[CrossRef]

Fuchs, H.

M. Bajura, H. Fuchs, R. Ohbuchi, “Merging virtual objects with the real world: seeing ultrasound imagery within the patient,” Comput. Graph. 26, 203–210 (1992).
[CrossRef]

Fukumoto, T.

H. Wu, T. Fukumoto, Q. Chen, M. Yachida, “Face detection and rotations estimation using color information,” in Proceedings of the Fifth IEEE International Workshop on Robot and Human Communication (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 341–346.

Hagan, M. T.

M. T. Hagan, M. Menhaj, “Training feedforward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
[CrossRef] [PubMed]

Hager, G. D.

C.-P. Lu, G. D. Hager, E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 610–622 (2000).
[CrossRef]

Haralick, R. M.

R. M. Haralick, C.-N. Lee, K. Ottenberg, M. Nolle, “Review and analysis of solutions of the three point perspective pose estimation problem,” Int. J. Comput. Vision 13, 331–56 (1994).
[CrossRef]

R. M. Haralick, L. M. Shapiro, “Survey: image segmentation,” Comput. Vision Graph. Image Process. 29, 100–132 (1985).
[CrossRef]

Hassebrook, L. G.

L. G. Hassebrook, M. E. Lhamon, M. Wang, J. P. Chatterjee, “Postprocessing of correlation for orientation estimation,” Opt. Eng. 36, 2710–2718 (1997).
[CrossRef]

Hester, C. F.

Hinton, G. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT, Cambridge, Mass., 1986).

Hong, S.

Horprasert, T.

T. Horprasert, Y. Yacoob, L. S. Davis, “Computing 3D head orientation from a monocular image sequence,” in 25th AIPR Workshop: Emerging Application of Computer Vision, D. H. Schaefer, E. F. Williams, eds., Proc. SPIE2962, 244–252 (1997).
[CrossRef]

Huttenlocher, D. P.

D. P. Huttenlocher, S. Ullman, “Recognizing solid objects by alignment with an image,” Int. J. Comput. Vision 5, 195–212 (1990).
[CrossRef]

Jackson, T.

R. Beale, T. Jackson, Neural Computing: An Introduction (Institute of Physics, Bristol, UK, 1992).

Javidi, B.

Juday, R. D.

S. E. Monroe, R. D. Juday, “Multidimensional synthetic estimation filter,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 179–185 (1990).
[CrossRef]

Laude, V.

Lee, A. J.

B. V. K. Vijaya Kumar, A. J. Lee, J. M. Connelly, “Correlation filters for orientation estimation,” in Digital and Optical Shape Representation and Pattern Recognition, Proc. SPIE938, 190–197 (1988).
[CrossRef]

Lee, C.-N.

R. M. Haralick, C.-N. Lee, K. Ottenberg, M. Nolle, “Review and analysis of solutions of the three point perspective pose estimation problem,” Int. J. Comput. Vision 13, 331–56 (1994).
[CrossRef]

Lhamon, M. E.

L. G. Hassebrook, M. E. Lhamon, M. Wang, J. P. Chatterjee, “Postprocessing of correlation for orientation estimation,” Opt. Eng. 36, 2710–2718 (1997).
[CrossRef]

Lu, C.-P.

C.-P. Lu, G. D. Hager, E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 610–622 (2000).
[CrossRef]

Mahalanobis, A.

A. Mahalanobis, “Review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing, B. Javidi, Kristina M. Johnson, eds., in Vol. CR65 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1996), pp. 240–260.

A. Mahalanobis, “Correlation filters for object tracking, target reacquisition, and smart aim-point selection,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 25–32 (1997).
[CrossRef]

Maloney, W. T.

Menhaj, M.

M. T. Hagan, M. Menhaj, “Training feedforward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
[CrossRef] [PubMed]

Mjolsness, E.

C.-P. Lu, G. D. Hager, E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 610–622 (2000).
[CrossRef]

Monroe, S. E.

S. E. Monroe, R. D. Juday, “Multidimensional synthetic estimation filter,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 179–185 (1990).
[CrossRef]

Mullick, R.

N. Ezquerra, R. Mullick, “An approach to 3D pose determination,” ACM Trans. Graphics 15, 99–120 (1996).
[CrossRef]

Nolle, M.

R. M. Haralick, C.-N. Lee, K. Ottenberg, M. Nolle, “Review and analysis of solutions of the three point perspective pose estimation problem,” Int. J. Comput. Vision 13, 331–56 (1994).
[CrossRef]

Ohbuchi, R.

M. Bajura, H. Fuchs, R. Ohbuchi, “Merging virtual objects with the real world: seeing ultrasound imagery within the patient,” Comput. Graph. 26, 203–210 (1992).
[CrossRef]

Ottenberg, K.

R. M. Haralick, C.-N. Lee, K. Ottenberg, M. Nolle, “Review and analysis of solutions of the three point perspective pose estimation problem,” Int. J. Comput. Vision 13, 331–56 (1994).
[CrossRef]

Painchaud, D.

Réfrégier, P.

C. Chesnaud, P. Réfrégier, V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise model,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

P. Réfrégier, V. Laude, B. Javidi, “Nonlinear joint-transform correlation: an optimal solution for adaptive image discrimination and input noise robustness,” Opt. Lett. 19, 405–407 (1994).
[PubMed]

Rosenfield, G. H.

G. H. Rosenfield, “The problem of exterior orientation in photogrammetry,” Photogramm. Eng. 25, 536–553 (1959).

Rumelhart, D. E.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT, Cambridge, Mass., 1986).

Shapiro, L. M.

R. M. Haralick, L. M. Shapiro, “Survey: image segmentation,” Comput. Vision Graph. Image Process. 29, 100–132 (1985).
[CrossRef]

Shimizu, I.

I. Shimizu, Z. Zhang, S. Akamatsu, K. Deguchi, “Head pose determination from one image using a generic model,” Proceedings of the Third IEEE International Conference on Automatic Face and Gesture Recognition (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 100–105.
[CrossRef]

Ullman, S.

D. P. Huttenlocher, S. Ullman, “Recognizing solid objects by alignment with an image,” Int. J. Comput. Vision 5, 195–212 (1990).
[CrossRef]

Vijaya Kumar, B. V. K.

B. V. K. Vijaya Kumar, A. J. Lee, J. M. Connelly, “Correlation filters for orientation estimation,” in Digital and Optical Shape Representation and Pattern Recognition, Proc. SPIE938, 190–197 (1988).
[CrossRef]

Wang, J.

Wang, M.

L. G. Hassebrook, M. E. Lhamon, M. Wang, J. P. Chatterjee, “Postprocessing of correlation for orientation estimation,” Opt. Eng. 36, 2710–2718 (1997).
[CrossRef]

Williams, R. J.

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT, Cambridge, Mass., 1986).

Wilson, W.

W. Wilson, “Visual servo control of robots using Kalman filter estimates of robot pose relative to work-pieces,” in Visual Serving, K. Hashimoto, ed. (Word Scientific, Singapore, 1994), pp. 71–104.

Wu, H.

H. Wu, T. Fukumoto, Q. Chen, M. Yachida, “Face detection and rotations estimation using color information,” in Proceedings of the Fifth IEEE International Workshop on Robot and Human Communication (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 341–346.

Yachida, M.

H. Wu, T. Fukumoto, Q. Chen, M. Yachida, “Face detection and rotations estimation using color information,” in Proceedings of the Fifth IEEE International Workshop on Robot and Human Communication (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 341–346.

Yacoob, Y.

T. Horprasert, Y. Yacoob, L. S. Davis, “Computing 3D head orientation from a monocular image sequence,” in 25th AIPR Workshop: Emerging Application of Computer Vision, D. H. Schaefer, E. F. Williams, eds., Proc. SPIE2962, 244–252 (1997).
[CrossRef]

Zhang, Z.

I. Shimizu, Z. Zhang, S. Akamatsu, K. Deguchi, “Head pose determination from one image using a generic model,” Proceedings of the Third IEEE International Conference on Automatic Face and Gesture Recognition (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 100–105.
[CrossRef]

ACM Trans. Graphics

N. Ezquerra, R. Mullick, “An approach to 3D pose determination,” ACM Trans. Graphics 15, 99–120 (1996).
[CrossRef]

Appl. Opt.

Comput. Graph.

M. Bajura, H. Fuchs, R. Ohbuchi, “Merging virtual objects with the real world: seeing ultrasound imagery within the patient,” Comput. Graph. 26, 203–210 (1992).
[CrossRef]

Comput. Vision Graph. Image Process.

R. M. Haralick, L. M. Shapiro, “Survey: image segmentation,” Comput. Vision Graph. Image Process. 29, 100–132 (1985).
[CrossRef]

IEEE Trans. Neural Netw.

M. T. Hagan, M. Menhaj, “Training feedforward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell.

C.-P. Lu, G. D. Hager, E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 610–622 (2000).
[CrossRef]

C. Chesnaud, P. Réfrégier, V. Boulet, “Statistical region snake-based segmentation adapted to different physical noise model,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1145–1157 (1999).
[CrossRef]

Int. J. Comput. Vision

D. P. Huttenlocher, S. Ullman, “Recognizing solid objects by alignment with an image,” Int. J. Comput. Vision 5, 195–212 (1990).
[CrossRef]

R. M. Haralick, C.-N. Lee, K. Ottenberg, M. Nolle, “Review and analysis of solutions of the three point perspective pose estimation problem,” Int. J. Comput. Vision 13, 331–56 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

L. G. Hassebrook, M. E. Lhamon, M. Wang, J. P. Chatterjee, “Postprocessing of correlation for orientation estimation,” Opt. Eng. 36, 2710–2718 (1997).
[CrossRef]

Opt. Lett.

Photogramm. Eng.

G. H. Rosenfield, “The problem of exterior orientation in photogrammetry,” Photogramm. Eng. 25, 536–553 (1959).

Other

T. Horprasert, Y. Yacoob, L. S. Davis, “Computing 3D head orientation from a monocular image sequence,” in 25th AIPR Workshop: Emerging Application of Computer Vision, D. H. Schaefer, E. F. Williams, eds., Proc. SPIE2962, 244–252 (1997).
[CrossRef]

H. Wu, T. Fukumoto, Q. Chen, M. Yachida, “Face detection and rotations estimation using color information,” in Proceedings of the Fifth IEEE International Workshop on Robot and Human Communication (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 341–346.

I. Shimizu, Z. Zhang, S. Akamatsu, K. Deguchi, “Head pose determination from one image using a generic model,” Proceedings of the Third IEEE International Conference on Automatic Face and Gesture Recognition (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 100–105.
[CrossRef]

W. Wilson, “Visual servo control of robots using Kalman filter estimates of robot pose relative to work-pieces,” in Visual Serving, K. Hashimoto, ed. (Word Scientific, Singapore, 1994), pp. 71–104.

B. V. K. Vijaya Kumar, A. J. Lee, J. M. Connelly, “Correlation filters for orientation estimation,” in Digital and Optical Shape Representation and Pattern Recognition, Proc. SPIE938, 190–197 (1988).
[CrossRef]

A. Mahalanobis, “Review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing, B. Javidi, Kristina M. Johnson, eds., in Vol. CR65 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1996), pp. 240–260.

A. Mahalanobis, “Correlation filters for object tracking, target reacquisition, and smart aim-point selection,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 25–32 (1997).
[CrossRef]

R. Beale, T. Jackson, Neural Computing: An Introduction (Institute of Physics, Bristol, UK, 1992).

D. E. Rumelhart, G. E. Hinton, R. J. Williams, “Learning internal representations by error propagation,” in Parallel Distributed Processing, D. E. Rumelhart, J. L. McClelland, eds. (MIT, Cambridge, Mass., 1986).

S. E. Monroe, R. D. Juday, “Multidimensional synthetic estimation filter,” in Optical Information Processing Systems and Architectures II, B. Javidi, ed., Proc. SPIE1347, 179–185 (1990).
[CrossRef]

K. R. Castleman, “Pattern recognition: image segmentation,” in Digital Image Processing (Prentice-Hall, Upper Saddle River, N.J., 1996), pp. 447–485.

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Figures (11)

Fig. 1
Fig. 1

Composition of the three sets of images. The construction set is used to design the composite filter. The training set is used for the linear least-squares fit and for training the neural network. The evaluation set is used to test the pose estimation.

Fig. 2
Fig. 2

Some of the images used for the pose estimation and object recognition. (a) Reference object, an F-15 airplane. (b) Out-of-plane-rotated and (c) in-plane-rotated versions of the plane. (a), (b), and (c) are included in the construction set. (d) and (e) are false targets.

Fig. 3
Fig. 3

Relationship between the correlation values and one pose parameter in between two construction images—linear correlation.

Fig. 4
Fig. 4

Pose estimation with a linear least-squares fit of the correlation values—linear correlation.

Fig. 5
Fig. 5

Proposed neural network to estimate the pose. A two-layer feedforward backpropagation neural network. The inputs are the correlation values provided by the composite filters. The outputs are the pose parameters.

Fig. 6
Fig. 6

Pose estimation results with a two-layer neural network—linear correlation.

Fig. 7
Fig. 7

Relationship between the correlation values and one pose parameter in between two construction images—nonlinear correlation.

Fig. 8
Fig. 8

Pose estimation with a linear least-squares fit of the correlation values—nonlinear correlation.

Fig. 9
Fig. 9

Pose estimation results with a two-layer neural network—nonlinear correlation.

Fig. 10
Fig. 10

Pose estimation results with a two-layer neural network taking as a correlation value the mean around the center—nonlinear correlation.

Fig. 11
Fig. 11

Examples of noisy images. (a) Noiseless, (b) additive noise 20%, (c) multiplicative noise 20%, and (d) illumination noise 10%.

Tables (1)

Tables Icon

Table 1 Error (in deg) for Shift-Invariant Pose Estimation with Linear Correlation and a Two-Layer ANN

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

h=VconstVconstTVconst-1c,
Cconst3×9=T3×3Pconst3×9,
Ceval=TPeval,
Peval=T-1Ceval.
F=PtrainCtrainTCtrainCtrainT-1,
Pˆeval=FCeval.
Ĩk=|Ĩ|k expiφĨ,
h˜k=V˜constk+V˜constk-1 c.
c=Tp.
T=10.80.80.810.80.80.81008088111-1.

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