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

[CrossRef]
[PubMed]

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]

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]

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]

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]

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]

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

[CrossRef]

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

[CrossRef]
[PubMed]

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

[CrossRef]

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

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

[CrossRef]

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

[CrossRef]
[PubMed]

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

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

[CrossRef]

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

[CrossRef]

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

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.

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

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.

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

[CrossRef]

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

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

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

[CrossRef]

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

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

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

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

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

[CrossRef]

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]

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

[CrossRef]

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, 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]

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

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

[CrossRef]

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, 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.

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

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

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

[CrossRef]

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]

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

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

[CrossRef]

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

[CrossRef]

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

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

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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

[CrossRef]

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.

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]

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]

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.

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.

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

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.

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

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]

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.

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]

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]

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

[CrossRef]

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

[CrossRef]

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]

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

[CrossRef]

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

[CrossRef]
[PubMed]

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]

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

[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]

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

[CrossRef]

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

[CrossRef]

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]

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]

L. Sirovich, M. Kirby, “Low-dimensional procedure for the characterization of human faces,” J. Opt. Soc. Am. A 4, 519–524 (1987).

[CrossRef]
[PubMed]

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]

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

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

[CrossRef]

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]

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]

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

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

[CrossRef]

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

[CrossRef]
[PubMed]

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

[CrossRef]

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]

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 .