## Independent spectral representations of images for recognition

JOSA A, Vol. 20, Issue 7, pp. 1271-1282 (2003)

http://dx.doi.org/10.1364/JOSAA.20.001271

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### 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

**OCIS Codes**

(100.2960) Image processing : Image analysis

(100.5010) Image processing : Pattern recognition

(330.4060) Vision, color, and visual optics : Vision modeling

(330.6110) Vision, color, and visual optics : Spatial filtering

**Citation**

Xiuwen Liu and Lei Cheng, "Independent spectral representations of images for recognition," J. Opt. Soc. Am. A **20**, 1271-1282 (2003)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-7-1271

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### References

- D. H. Ballard, An Introduction to Natural Computation (MIT Press, Cambridge, Mass., 1997).
- D. Marr, Vision (Freeman, New York, 1982).
- D. C. Knill and 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).
- H. Hotelling, “Analysis of a complex of statistical variables in principal components,” J. Educ. Psychol. 24, 417–441, 498–520 (1933).
- M. M. Loève, Probability Theory (Van Nostrand, Princeton, N. J., 1955).
- L. Sirovich and M. Kirby, “Low-dimensional procedure for the characterization of human faces,” J. Opt. Soc. Am. A 4, 519–524 (1987).
- P. Comon, “Independent component analysis: a new concept?” Signal Process. 36, 287–314 (1994).
- P. J. Huber, “Projection pursuit,” Ann. Statistics 13, 435–475 (1985).
- H. B. Barlow, “Unsupervised learning,” Neural Comput. 1, 295–311 (1989).
- 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).
- D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559–601 (1994).
- B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
- A. J. Bell and T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
- E. P. Simoncelli and B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
- A. Srivastava, A. Lee, E. P. Simoncelli, and S. C. Zhu, “On advances in statistical modeling of natural images,” J. Math. Imaging Vision 18, 17–33 (2003).
- N. Vasconcelos and 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.
- F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).
- R. L. De Valois and K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1988).
- 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).
- R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (Wiley, New York, 2000).
- X. Liu and D. L. Wang, “A spectral histogram model for texton modeling and texture discrimination,” Vision Res. 42, 2617–2634 (2002).
- D. A. Socolinsky and 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.
- J. R. Bergen and E. H. Adelson, “Early vision and texture perception,” Nature 333, 363–367 (1988).
- C. Chubb, J. Econopouly, and M. S. Landy, “Histogram contrast analysis and the visual segregation of IID textures,” J. Opt. Soc. Am. A 11, 2350–2374 (1994).
- D. J. Heeger and J. R. Bergen, “Pyramid-based texture analysis/synthesis,” in Proceedings of SIGGRAPHS (Addison-Wesley, Boston, Mass., 1995), pp. 229–238.
- S. C. Zhu, Y. N. Wu, and D. Mumford, “Minimax entropy principle and its application to texture modeling,” Neural Comput. 9, 1627–1660 (1997).
- S. C. Zhu, X. Liu, and Y. N. Wu, “Exploring texture ensembles by efficient Markov chain Monte Carlo,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 554–569 (2000).
- X. Liu and 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 and 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, and 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, and R. G. Palmer, Introduction to the Theory of Neural Computation (Addison-Wesley, Reading, Mass., 1991).
- T. Randen and J. H. Husoy, “Filtering for texture classification: a comparative study,” IEEE Trans. Pattern Recog. Mach. Intell. 21, 291–310 (1999).
- Images in the ORL data set are available at http://www.uk.research.att.com/facedatabase.html.
- J. Zhang, Y. Yan, and M. Lades, “Face recognition: eigenface, elastic matching, and neural nets,” Proc. IEEE 85, 1423–1435 (1997).
- A. Srivastava and X. Liu, “Statistical hypothesis pruning for identifying faces from infrared images,” Image Vision Comput. (to be published).
- S. T. Roweis and L. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science 290, 2323–2326 (2000).
- A. Hyvärinen and 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).
- A. Hyvärinen and 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).
- M. J. Wainwright, E. Simoncelli, and 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).
- P. Domingos and M. Pazzani, “On the optimality of the simple Bayesian classifier under zero-one loss,” Machine Learning 29, 103–130 (1997).

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