Abstract

In recent years, studies have shown that independent components of local windows of natural images resemble the receptive fields of cells in the early stages of the mammalian visual pathway. However, the role of the independence in visual recognition is not well understood. We argue that the independence resolves the curse of dimensionality by reducing the complexity of probability models to the linear order of the dimension. In addition, we show empirically that the complexity reduction does not degrade the recognition performance on all the data sets that we have used with an independent spectral representation. In this representation, an input image is first decomposed into independent channels given by the estimated independent components from training images, and each channel’s response is then summarized by using its histogram as an estimate of the underlying probability model along that dimension. We demonstrate the sufficiency of the proposed representation for image characterization by synthesizing textures and objects through sampling and for recognition by applying it to large data sets. Our comparisons show that the independent spectral representation often gives improved recognition performance.

© 2003 Optical Society of America

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  1. D. H. Ballard, An Introduction to Natural Computation (MIT Press, Cambridge, Mass., 1997).
  2. D. Marr, Vision (Freeman, New York, 1982).
  3. D. C. Knill, W. Richards, eds., Perception As Bayesian Inference (Cambridge U. Press, Cambridge, UK, 1996).
  4. H. von Helmholtz, Treatise on Physiological Optics (Dover, New York, 1867).
  5. R. Bellman, Adaptive Control Processes: A Guided Tour (Princeton U. Press, Princeton, N.J., 1961).
  6. H. Hotelling, “Analysis of a complex of statistical variables in principal components,” J. Educ. Psychol. 24, 417–441, 498–520 (1933).
    [CrossRef]
  7. M. M. Loève, Probability Theory (Van Nostrand, Princeton, N. J., 1955).
  8. L. Sirovich, M. Kirby, “Low-dimensional procedure for the characterization of human faces,” J. Opt. Soc. Am. A 4, 519–524 (1987).
    [CrossRef] [PubMed]
  9. P. Comon, “Independent component analysis: a new concept?” Signal Process. 36, 287–314 (1994).
    [CrossRef]
  10. P. J. Huber, “Projection pursuit,” Ann. Statistics 13, 435–475 (1985).
    [CrossRef]
  11. H. B. Barlow, “Unsupervised learning,” Neural Comput. 1, 295–311 (1989).
    [CrossRef]
  12. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
    [CrossRef] [PubMed]
  13. D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559–601 (1994).
    [CrossRef]
  14. B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
    [CrossRef] [PubMed]
  15. A. J. Bell, T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
    [CrossRef]
  16. E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
    [CrossRef] [PubMed]
  17. A. Srivastava, A. Lee, E. P. Simoncelli, S. C. Zhu, “On advances in statistical modeling of natural images,” J. Math. Imaging Vision 18, 17–33 (2003).
    [CrossRef]
  18. N. Vasconcelos, G. Carneiro, “What is the role of independence for visual recognition?” in Proceedings of the 7th European Conference on Computer Vision (Springer, Berlin, 2002), Vol. 1, pp. 297–311.
  19. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).
  20. R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1988).
  21. A. Hyvärinen, “Survey on independent component analysis,” Neural Comput. Surv. 2, 194–128 (1999).
  22. A. Hyvärinen, “Fast and robust fixed-point algorithm for independent component analysis,” IEEE Trans. Neural Netw. 10, 626–634 (1999).
    [CrossRef]
  23. R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification, 2nd ed. (Wiley, New York, 2000).
  24. X. Liu, D. L. Wang, “A spectral histogram model for texton modeling and texture discrimination,” Vision Res. 42, 2617–2634 (2002).
    [CrossRef] [PubMed]
  25. D. A. Socolinsky, A. Selinger, “A comparative analysis of face recognition performance with visible and thermal infrared imagery,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 4, pp. 217–222.
  26. J. R. Bergen, E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–367 (1988).
    [CrossRef] [PubMed]
  27. C. Chubb, J. Econopouly, M. S. Landy, “Histogram contrast analysis and the visual segregation of IID textures,” J. Opt. Soc. Am. A 11, 2350–2374 (1994).
    [CrossRef]
  28. D. J. Heeger, J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPHS (Addison-Wesley, Boston, Mass., 1995), pp. 229–238.
  29. S. C. Zhu, Y. N. Wu, D. Mumford, “Minimax entropy principle and its application to texture modeling,” Neural Comput. 9, 1627–1660 (1997).
    [CrossRef]
  30. S. C. Zhu, X. Liu, Y. N. Wu, “Exploring texture ensembles by efficient Markov chain Monte Carlo,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 554–569 (2000).
    [CrossRef]
  31. X. Liu, A. Srivastava, “3D object recognition using perceptual components,” in Proceedings of the International Joint Conference on Neural Networks (IEEE Computer Society Press, Los Alamitos, Calif., 2001), Vol. 1, pp. 553–558.
  32. X. Liu, D. L. Wang, “Appearance-based recognition using perceptual components,” in Proceedings of the International Joint Conference on Neural Networks (IEEE Computer Society Press, Los Alamitos, Calif., 2001), Vol. 3, pp. 1943–1948.
  33. X. Liu, D. L. Wang, A. Srivastava, “Image segmentation using local spectral histograms,” in Proceedings of the International Conference on Image Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 1, pp. 70–73.
  34. J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).
  35. T. Randen, J. H. Husoy, “Filtering for texture classification: a comparative study,” IEEE Trans. Pattern Recog. Mach. Intell. 21, 291–310 (1999).
    [CrossRef]
  36. Images in the ORL data set are available at http://www.uk.research.att.com/facedatabase.html .
  37. J. Zhang, Y. Yan, M. Lades, “Face recognition: eigenface, elastic matching, and neural nets,” Proc. IEEE 85, 1423–1435 (1997).
    [CrossRef]
  38. A. Srivastava, X. Liu, “Statistical hypothesis pruning for identifying faces from infrared images,” Image Vision Comput. (to be published).
  39. S. T. Roweis, L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
    [CrossRef] [PubMed]
  40. A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
    [CrossRef]
  41. A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topology from natural images,” Vision Res. 41, 2413–2423 (2001).
    [CrossRef]
  42. M. J. Wainwright, E. Simoncelli, A. S. Willsky, “Random cascades on wavelet trees and their use in analyzing and modeling natural images,” Appl. Comput. Harmonic Anal. 11, 89–123 (2001).
    [CrossRef]
  43. P. Domingos, M. Pazzani, “On the optimality of the simple Bayesian classifier under zero-one loss,” Machine Learning 29, 103–130 (1997).
    [CrossRef]

2003

A. Srivastava, A. Lee, E. P. Simoncelli, S. C. Zhu, “On advances in statistical modeling of natural images,” J. Math. Imaging Vision 18, 17–33 (2003).
[CrossRef]

2002

X. Liu, D. L. Wang, “A spectral histogram model for texton modeling and texture discrimination,” Vision Res. 42, 2617–2634 (2002).
[CrossRef] [PubMed]

2001

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topology from natural images,” Vision Res. 41, 2413–2423 (2001).
[CrossRef]

M. J. Wainwright, E. Simoncelli, A. S. Willsky, “Random cascades on wavelet trees and their use in analyzing and modeling natural images,” Appl. Comput. Harmonic Anal. 11, 89–123 (2001).
[CrossRef]

2000

S. T. Roweis, L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
[CrossRef] [PubMed]

A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef]

S. C. Zhu, X. Liu, Y. N. Wu, “Exploring texture ensembles by efficient Markov chain Monte Carlo,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 554–569 (2000).
[CrossRef]

1999

T. Randen, J. H. Husoy, “Filtering for texture classification: a comparative study,” IEEE Trans. Pattern Recog. Mach. Intell. 21, 291–310 (1999).
[CrossRef]

A. Hyvärinen, “Survey on independent component analysis,” Neural Comput. Surv. 2, 194–128 (1999).

A. Hyvärinen, “Fast and robust fixed-point algorithm for independent component analysis,” IEEE Trans. Neural Netw. 10, 626–634 (1999).
[CrossRef]

1997

A. J. Bell, T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

J. Zhang, Y. Yan, M. Lades, “Face recognition: eigenface, elastic matching, and neural nets,” Proc. IEEE 85, 1423–1435 (1997).
[CrossRef]

S. C. Zhu, Y. N. Wu, D. Mumford, “Minimax entropy principle and its application to texture modeling,” Neural Comput. 9, 1627–1660 (1997).
[CrossRef]

P. Domingos, M. Pazzani, “On the optimality of the simple Bayesian classifier under zero-one loss,” Machine Learning 29, 103–130 (1997).
[CrossRef]

1996

B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
[CrossRef] [PubMed]

1994

D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559–601 (1994).
[CrossRef]

P. Comon, “Independent component analysis: a new concept?” Signal Process. 36, 287–314 (1994).
[CrossRef]

C. Chubb, J. Econopouly, M. S. Landy, “Histogram contrast analysis and the visual segregation of IID textures,” J. Opt. Soc. Am. A 11, 2350–2374 (1994).
[CrossRef]

1989

H. B. Barlow, “Unsupervised learning,” Neural Comput. 1, 295–311 (1989).
[CrossRef]

1988

J. R. Bergen, E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–367 (1988).
[CrossRef] [PubMed]

1987

1985

P. J. Huber, “Projection pursuit,” Ann. Statistics 13, 435–475 (1985).
[CrossRef]

1968

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).

1933

H. Hotelling, “Analysis of a complex of statistical variables in principal components,” J. Educ. Psychol. 24, 417–441, 498–520 (1933).
[CrossRef]

Adelson, E. H.

J. R. Bergen, E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–367 (1988).
[CrossRef] [PubMed]

Ballard, D. H.

D. H. Ballard, An Introduction to Natural Computation (MIT Press, Cambridge, Mass., 1997).

Barlow, H. B.

H. B. Barlow, “Unsupervised learning,” Neural Comput. 1, 295–311 (1989).
[CrossRef]

Bell, A. J.

A. J. Bell, T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

Bellman, R.

R. Bellman, Adaptive Control Processes: A Guided Tour (Princeton U. Press, Princeton, N.J., 1961).

Bergen, J. R.

J. R. Bergen, E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–367 (1988).
[CrossRef] [PubMed]

D. J. Heeger, J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPHS (Addison-Wesley, Boston, Mass., 1995), pp. 229–238.

Campbell, F. W.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).

Carneiro, G.

N. Vasconcelos, G. Carneiro, “What is the role of independence for visual recognition?” in Proceedings of the 7th European Conference on Computer Vision (Springer, Berlin, 2002), Vol. 1, pp. 297–311.

Chubb, C.

Comon, P.

P. Comon, “Independent component analysis: a new concept?” Signal Process. 36, 287–314 (1994).
[CrossRef]

De Valois, K. K.

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1988).

De Valois, R. L.

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1988).

Domingos, P.

P. Domingos, M. Pazzani, “On the optimality of the simple Bayesian classifier under zero-one loss,” Machine Learning 29, 103–130 (1997).
[CrossRef]

Duda, R. O.

R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification, 2nd ed. (Wiley, New York, 2000).

Econopouly, J.

Field, D. J.

B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
[CrossRef] [PubMed]

D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559–601 (1994).
[CrossRef]

D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
[CrossRef] [PubMed]

Hart, P. E.

R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification, 2nd ed. (Wiley, New York, 2000).

Heeger, D. J.

D. J. Heeger, J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPHS (Addison-Wesley, Boston, Mass., 1995), pp. 229–238.

Hertz, J.

J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).

Hotelling, H.

H. Hotelling, “Analysis of a complex of statistical variables in principal components,” J. Educ. Psychol. 24, 417–441, 498–520 (1933).
[CrossRef]

Hoyer, P. O.

A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topology from natural images,” Vision Res. 41, 2413–2423 (2001).
[CrossRef]

A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef]

Huber, P. J.

P. J. Huber, “Projection pursuit,” Ann. Statistics 13, 435–475 (1985).
[CrossRef]

Husoy, J. H.

T. Randen, J. H. Husoy, “Filtering for texture classification: a comparative study,” IEEE Trans. Pattern Recog. Mach. Intell. 21, 291–310 (1999).
[CrossRef]

Hyvärinen, A.

A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topology from natural images,” Vision Res. 41, 2413–2423 (2001).
[CrossRef]

A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef]

A. Hyvärinen, “Survey on independent component analysis,” Neural Comput. Surv. 2, 194–128 (1999).

A. Hyvärinen, “Fast and robust fixed-point algorithm for independent component analysis,” IEEE Trans. Neural Netw. 10, 626–634 (1999).
[CrossRef]

Kirby, M.

Krogh, A.

J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).

Lades, M.

J. Zhang, Y. Yan, M. Lades, “Face recognition: eigenface, elastic matching, and neural nets,” Proc. IEEE 85, 1423–1435 (1997).
[CrossRef]

Landy, M. S.

Lee, A.

A. Srivastava, A. Lee, E. P. Simoncelli, S. C. Zhu, “On advances in statistical modeling of natural images,” J. Math. Imaging Vision 18, 17–33 (2003).
[CrossRef]

Liu, X.

X. Liu, D. L. Wang, “A spectral histogram model for texton modeling and texture discrimination,” Vision Res. 42, 2617–2634 (2002).
[CrossRef] [PubMed]

S. C. Zhu, X. Liu, Y. N. Wu, “Exploring texture ensembles by efficient Markov chain Monte Carlo,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 554–569 (2000).
[CrossRef]

X. Liu, D. L. Wang, A. Srivastava, “Image segmentation using local spectral histograms,” in Proceedings of the International Conference on Image Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 1, pp. 70–73.

X. Liu, D. L. Wang, “Appearance-based recognition using perceptual components,” in Proceedings of the International Joint Conference on Neural Networks (IEEE Computer Society Press, Los Alamitos, Calif., 2001), Vol. 3, pp. 1943–1948.

A. Srivastava, X. Liu, “Statistical hypothesis pruning for identifying faces from infrared images,” Image Vision Comput. (to be published).

X. Liu, A. Srivastava, “3D object recognition using perceptual components,” in Proceedings of the International Joint Conference on Neural Networks (IEEE Computer Society Press, Los Alamitos, Calif., 2001), Vol. 1, pp. 553–558.

Loève, M. M.

M. M. Loève, Probability Theory (Van Nostrand, Princeton, N. J., 1955).

Marr, D.

D. Marr, Vision (Freeman, New York, 1982).

Mumford, D.

S. C. Zhu, Y. N. Wu, D. Mumford, “Minimax entropy principle and its application to texture modeling,” Neural Comput. 9, 1627–1660 (1997).
[CrossRef]

Olshausen, B. A.

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
[CrossRef] [PubMed]

Palmer, R. G.

J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).

Pazzani, M.

P. Domingos, M. Pazzani, “On the optimality of the simple Bayesian classifier under zero-one loss,” Machine Learning 29, 103–130 (1997).
[CrossRef]

Randen, T.

T. Randen, J. H. Husoy, “Filtering for texture classification: a comparative study,” IEEE Trans. Pattern Recog. Mach. Intell. 21, 291–310 (1999).
[CrossRef]

Robson, J. G.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).

Roweis, S. T.

S. T. Roweis, L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
[CrossRef] [PubMed]

Saul, L. K.

S. T. Roweis, L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
[CrossRef] [PubMed]

Sejnowski, T. J.

A. J. Bell, T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

Selinger, A.

D. A. Socolinsky, A. Selinger, “A comparative analysis of face recognition performance with visible and thermal infrared imagery,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 4, pp. 217–222.

Simoncelli, E.

M. J. Wainwright, E. Simoncelli, A. S. Willsky, “Random cascades on wavelet trees and their use in analyzing and modeling natural images,” Appl. Comput. Harmonic Anal. 11, 89–123 (2001).
[CrossRef]

Simoncelli, E. P.

A. Srivastava, A. Lee, E. P. Simoncelli, S. C. Zhu, “On advances in statistical modeling of natural images,” J. Math. Imaging Vision 18, 17–33 (2003).
[CrossRef]

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

Sirovich, L.

Socolinsky, D. A.

D. A. Socolinsky, A. Selinger, “A comparative analysis of face recognition performance with visible and thermal infrared imagery,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 4, pp. 217–222.

Srivastava, A.

A. Srivastava, A. Lee, E. P. Simoncelli, S. C. Zhu, “On advances in statistical modeling of natural images,” J. Math. Imaging Vision 18, 17–33 (2003).
[CrossRef]

X. Liu, A. Srivastava, “3D object recognition using perceptual components,” in Proceedings of the International Joint Conference on Neural Networks (IEEE Computer Society Press, Los Alamitos, Calif., 2001), Vol. 1, pp. 553–558.

A. Srivastava, X. Liu, “Statistical hypothesis pruning for identifying faces from infrared images,” Image Vision Comput. (to be published).

X. Liu, D. L. Wang, A. Srivastava, “Image segmentation using local spectral histograms,” in Proceedings of the International Conference on Image Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 1, pp. 70–73.

Stork, D. G.

R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification, 2nd ed. (Wiley, New York, 2000).

Vasconcelos, N.

N. Vasconcelos, G. Carneiro, “What is the role of independence for visual recognition?” in Proceedings of the 7th European Conference on Computer Vision (Springer, Berlin, 2002), Vol. 1, pp. 297–311.

von Helmholtz, H.

H. von Helmholtz, Treatise on Physiological Optics (Dover, New York, 1867).

Wainwright, M. J.

M. J. Wainwright, E. Simoncelli, A. S. Willsky, “Random cascades on wavelet trees and their use in analyzing and modeling natural images,” Appl. Comput. Harmonic Anal. 11, 89–123 (2001).
[CrossRef]

Wang, D. L.

X. Liu, D. L. Wang, “A spectral histogram model for texton modeling and texture discrimination,” Vision Res. 42, 2617–2634 (2002).
[CrossRef] [PubMed]

X. Liu, D. L. Wang, “Appearance-based recognition using perceptual components,” in Proceedings of the International Joint Conference on Neural Networks (IEEE Computer Society Press, Los Alamitos, Calif., 2001), Vol. 3, pp. 1943–1948.

X. Liu, D. L. Wang, A. Srivastava, “Image segmentation using local spectral histograms,” in Proceedings of the International Conference on Image Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 1, pp. 70–73.

Willsky, A. S.

M. J. Wainwright, E. Simoncelli, A. S. Willsky, “Random cascades on wavelet trees and their use in analyzing and modeling natural images,” Appl. Comput. Harmonic Anal. 11, 89–123 (2001).
[CrossRef]

Wu, Y. N.

S. C. Zhu, X. Liu, Y. N. Wu, “Exploring texture ensembles by efficient Markov chain Monte Carlo,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 554–569 (2000).
[CrossRef]

S. C. Zhu, Y. N. Wu, D. Mumford, “Minimax entropy principle and its application to texture modeling,” Neural Comput. 9, 1627–1660 (1997).
[CrossRef]

Yan, Y.

J. Zhang, Y. Yan, M. Lades, “Face recognition: eigenface, elastic matching, and neural nets,” Proc. IEEE 85, 1423–1435 (1997).
[CrossRef]

Zhang, J.

J. Zhang, Y. Yan, M. Lades, “Face recognition: eigenface, elastic matching, and neural nets,” Proc. IEEE 85, 1423–1435 (1997).
[CrossRef]

Zhu, S. C.

A. Srivastava, A. Lee, E. P. Simoncelli, S. C. Zhu, “On advances in statistical modeling of natural images,” J. Math. Imaging Vision 18, 17–33 (2003).
[CrossRef]

S. C. Zhu, X. Liu, Y. N. Wu, “Exploring texture ensembles by efficient Markov chain Monte Carlo,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 554–569 (2000).
[CrossRef]

S. C. Zhu, Y. N. Wu, D. Mumford, “Minimax entropy principle and its application to texture modeling,” Neural Comput. 9, 1627–1660 (1997).
[CrossRef]

Ann. Statistics

P. J. Huber, “Projection pursuit,” Ann. Statistics 13, 435–475 (1985).
[CrossRef]

Annu. Rev. Neurosci.

E. P. Simoncelli, B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
[CrossRef] [PubMed]

Appl. Comput. Harmonic Anal.

M. J. Wainwright, E. Simoncelli, A. S. Willsky, “Random cascades on wavelet trees and their use in analyzing and modeling natural images,” Appl. Comput. Harmonic Anal. 11, 89–123 (2001).
[CrossRef]

IEEE Trans. Neural Netw.

A. Hyvärinen, “Fast and robust fixed-point algorithm for independent component analysis,” IEEE Trans. Neural Netw. 10, 626–634 (1999).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

S. C. Zhu, X. Liu, Y. N. Wu, “Exploring texture ensembles by efficient Markov chain Monte Carlo,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 554–569 (2000).
[CrossRef]

IEEE Trans. Pattern Recog. Mach. Intell.

T. Randen, J. H. Husoy, “Filtering for texture classification: a comparative study,” IEEE Trans. Pattern Recog. Mach. Intell. 21, 291–310 (1999).
[CrossRef]

J. Educ. Psychol.

H. Hotelling, “Analysis of a complex of statistical variables in principal components,” J. Educ. Psychol. 24, 417–441, 498–520 (1933).
[CrossRef]

J. Math. Imaging Vision

A. Srivastava, A. Lee, E. P. Simoncelli, S. C. Zhu, “On advances in statistical modeling of natural images,” J. Math. Imaging Vision 18, 17–33 (2003).
[CrossRef]

J. Opt. Soc. Am. A

J. Physiol. (London)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).

Machine Learning

P. Domingos, M. Pazzani, “On the optimality of the simple Bayesian classifier under zero-one loss,” Machine Learning 29, 103–130 (1997).
[CrossRef]

Nature

B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
[CrossRef] [PubMed]

J. R. Bergen, E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–367 (1988).
[CrossRef] [PubMed]

Neural Comput.

S. C. Zhu, Y. N. Wu, D. Mumford, “Minimax entropy principle and its application to texture modeling,” Neural Comput. 9, 1627–1660 (1997).
[CrossRef]

A. Hyvärinen, P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
[CrossRef]

D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559–601 (1994).
[CrossRef]

H. B. Barlow, “Unsupervised learning,” Neural Comput. 1, 295–311 (1989).
[CrossRef]

Neural Comput. Surv.

A. Hyvärinen, “Survey on independent component analysis,” Neural Comput. Surv. 2, 194–128 (1999).

Proc. IEEE

J. Zhang, Y. Yan, M. Lades, “Face recognition: eigenface, elastic matching, and neural nets,” Proc. IEEE 85, 1423–1435 (1997).
[CrossRef]

Science

S. T. Roweis, L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
[CrossRef] [PubMed]

Signal Process.

P. Comon, “Independent component analysis: a new concept?” Signal Process. 36, 287–314 (1994).
[CrossRef]

Vision Res.

A. Hyvärinen, P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topology from natural images,” Vision Res. 41, 2413–2423 (2001).
[CrossRef]

X. Liu, D. L. Wang, “A spectral histogram model for texton modeling and texture discrimination,” Vision Res. 42, 2617–2634 (2002).
[CrossRef] [PubMed]

A. J. Bell, T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
[CrossRef]

Other

M. M. Loève, Probability Theory (Van Nostrand, Princeton, N. J., 1955).

D. H. Ballard, An Introduction to Natural Computation (MIT Press, Cambridge, Mass., 1997).

D. Marr, Vision (Freeman, New York, 1982).

D. C. Knill, W. Richards, eds., Perception As Bayesian Inference (Cambridge U. Press, Cambridge, UK, 1996).

H. von Helmholtz, Treatise on Physiological Optics (Dover, New York, 1867).

R. Bellman, Adaptive Control Processes: A Guided Tour (Princeton U. Press, Princeton, N.J., 1961).

R. O. Duda, P. E. Hart, D. G. Stork, Pattern Classification, 2nd ed. (Wiley, New York, 2000).

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1988).

N. Vasconcelos, G. Carneiro, “What is the role of independence for visual recognition?” in Proceedings of the 7th European Conference on Computer Vision (Springer, Berlin, 2002), Vol. 1, pp. 297–311.

D. A. Socolinsky, A. Selinger, “A comparative analysis of face recognition performance with visible and thermal infrared imagery,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), Vol. 4, pp. 217–222.

D. J. Heeger, J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPHS (Addison-Wesley, Boston, Mass., 1995), pp. 229–238.

X. Liu, A. Srivastava, “3D object recognition using perceptual components,” in Proceedings of the International Joint Conference on Neural Networks (IEEE Computer Society Press, Los Alamitos, Calif., 2001), Vol. 1, pp. 553–558.

X. Liu, D. L. Wang, “Appearance-based recognition using perceptual components,” in Proceedings of the International Joint Conference on Neural Networks (IEEE Computer Society Press, Los Alamitos, Calif., 2001), Vol. 3, pp. 1943–1948.

X. Liu, D. L. Wang, A. Srivastava, “Image segmentation using local spectral histograms,” in Proceedings of the International Conference on Image Processing (IEEE Press, Piscataway, N.J., 2001), Vol. 1, pp. 70–73.

J. Hertz, A. Krogh, R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).

A. Srivastava, X. Liu, “Statistical hypothesis pruning for identifying faces from infrared images,” Image Vision Comput. (to be published).

Images in the ORL data set are available at http://www.uk.research.att.com/facedatabase.html .

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Figures (10)

Fig. 1
Fig. 1

Independent filters computed from the 40-texture data set shown in Fig. 6 below. In each panel, the left image corresponds to one column of S, the middle image corresponds to one row of W, and the right image corresponds to one row of Wo. (a)–(c) Independent filters of scales 5 × 5, 7 × 7, and 11 × 11 respectively.

Fig. 2
Fig. 2

Number of cells required to represent a joint distribution (solid line) and the corresponding distributions discretely with respect to the dimensionality, assuming each dimension is quantized into 10 bins. The vertical axis is shown on a logarithmic scale.

Fig. 3
Fig. 3

Textures synthesized through matching independent spectral representations. In each row of three, the left texture shows the original image and the remaining two show two typical examples of synthesized images. (a) Texture with rough periodic elements, (b) texture with stochastic horizontal elements, (c) texture with no obvious repeated patterns, (d) texture with detailed elements.

Fig. 4
Fig. 4

Synthesized images of an object. (a) Telephone object given as an image; (b) input with the boundary condition used for synthesis; (c) initial condition for synthesis, which is a white-noise image; (d)–(f) three images of the object synthesized through matching independent spectral representation; (g) image synthesized by using principal filters.

Fig. 5
Fig. 5

Synthesized images of objects and faces. In each row, the leftmost image is the input image, and the rest are typical examples synthesized by matching independent spectral representations. Similar objects are used as boundary conditions, as in Fig. 4, but are not shown here. (a) A stapler, (b) and (c) two faces.

Fig. 6
Fig. 6

Forty natural textures used in the classification experiments (available at http://www-dbv.cs.uni-bonn.de/image/texture.tar.gz). The input image size is 256×256.

Fig. 7
Fig. 7

Forty filters selected for the texture data set shown in Fig. 6.

Fig. 8
Fig. 8

Ten-texture image groups used in Ref. 35. Each image is 128×128. (a) Texture images in Fig. 11(h) of Ref. 35, (b) texture images in Figure 11(i) of Ref. 35.

Fig. 9
Fig. 9

Correct classification rate for all the methods in Ref. 35 for Fig. 8(a) and 8(b), respectively, and the proposed method. In each plot, each data point represents one result (corresponding to one texture-classification method) in Tables 3, 6, 8, and 9 of Ref. 35, and the dashed line is the result of the proposed method.

Fig. 10
Fig. 10

(a) Example images from the Florida State University infrared face database (available at http://fsvision.fsu.edu). (b) Long-wavelength infrared image examples from a data set of 3893 images generated by Equinox company (available at http://www.equinoxsensors.com/products/HID.html.

Tables (3)

Tables Icon

Table 1 Average Recognition Results for the Texture Data Set Shown in Fig. 6

Tables Icon

Table 2 Recognition Results for ORL Face Data Set of 100 Trials

Tables Icon

Table 3 Average Recognition Results with Principal and Independent Filters for the Texture Data Set Shown in Fig. 6

Equations (11)

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P(S|I)=P(I|S)P(S)P(I)P(I|S)P(S),
y=i=1KxiSi=Sx,
x=Wy.
W*=argminW KL[p(x), p(x1)p(xK)],
KL[p1(x1,,xK), p2(x1,,xK)]
=x1xKp1(x1,,xK)logp1(x1,,xK)p2(x1,,xK)dx1dxK
=x1xKp1(x1)p1(xK)i=1Klogp1(xi)p2(xi)dx1dxK
=i=1Kxip1(xi)logp1(xi)p2(xi)dxi=i=1KKL[p1(xi), p2(xi)],
Ω(Iobs)={I|pI(xi)=pIobs(xi), i=1,, K}.
q(I|T, pIobs(x1), pIobs(xK))
exp-i=1KD[pI(xi), pIobs(xi)]/T,

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