## Bubbles: a unifying framework for low-level statistical properties of natural image sequences

JOSA A, Vol. 20, Issue 7, pp. 1237-1252 (2003)

http://dx.doi.org/10.1364/JOSAA.20.001237

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### Abstract

Recently, different models of the statistical structure of natural images have been proposed. These models predict properties of biological visual systems and can be used as priors in Bayesian inference. The fundamental model is independent component analysis, which can be estimated by maximization of the sparsenesses of linear filter outputs. This leads to the emergence of principal simple cell properties. Alternatively, simple cell properties are obtained by maximizing the temporal coherence in natural image sequences. Taking account of the basic dependencies of linear filter outputs permit modeling of complex cells and topographic organization as well. We propose a unifying framework for these statistical properties, based on the concept of spatiotemporal activity “bubbles.” A bubble means here an activation of simple cells (linear filters) that is contiguous both in space (the cortical surface) and in time.

© 2003 Optical Society of America

**OCIS Codes**

(330.3790) Vision, color, and visual optics : Low vision

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

(330.4270) Vision, color, and visual optics : Vision system neurophysiology

**Citation**

Aapo Hyvärinen, Jarmo Hurri, and Jaakko Väyrynen, "Bubbles: a unifying framework for low-level statistical properties of natural image sequences," J. Opt. Soc. Am. A **20**, 1237-1252 (2003)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-7-1237

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### References

- H. B. Barlow, “Single units and sensation: a neuron doctrine for perceptual psychology?” Perception 1, 371–394 (1972).
- D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559–601 (1994).
- E. P. Simoncelli and B. A. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1216 (2001).
- B. A. Olshausen, “Principles of image representation in visual cortex,” in The Visual Neurosciences, L. M. Chalupa and J. S. Werner, eds. (MIT Press, Cambridge, Mass., 2003).
- A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley Interscience, New York, 2001).
- A. Hyvärinen, “Sparse code shrinkage: denoising of non-gaussian data by maximum likelihood estimation,” Neural Comput. 11, 1739–1768 (1999).
- E. P. Simoncelli and E. H. Adelson, “Noise removal via bayesian wavelet coring,” in Proceedings of the Third IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 379–382.
- G. E. Hinton and Z. Ghahramani, “Generative models for discovering sparse distributed representations,” Philos. Trans. R. Soc. London Ser. B 352, 1177–1190 (1997).
- D. C. Knill and W. Richards, eds., Perception as Bayesian Inference (Cambridge U. Press, Cambridge, UK, 1996).
- A. Hyvärinen, “Fast and robust fixed-point algorithms for independent component analysis,” IEEE Trans. Neural Netw. 10, 626–634 (1999).
- B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature (London) 381, 607–609 (1996).
- P. Földiák, “Learning invariance from transformation sequences,” Neural Comput. 3, 194–200 (1991).
- C. Kayser, W. Einhäuser, O. Dümmer, P. König, and K. Körding, “Extracting slow subspaces from natural videos leads to complex cells,” in Proceedings of the International Conference on Artificial Neural Networks (ICANN2001), (Springer-Verlag, Berlin, 2001), pp. 1075–1080.
- L. Wiskott and T. J. Sejnowski, “Slow feature analysis: unsupervised learning of invariances,” Neural Comput. 14, 715–770 (2002).
- P. Berkes and L. Wiskott, “Applying slow feature analysis to image sequences yields a rich repertoire of complex cell properties,” in Proceedings of the International Conference on Artificial Neural Networks (ICANN2002) (Springer-Verlag, Berlin, 2002), pp. 81–86.
- J. Hurri and A. Hyvärinen, “Simple-cell-like receptive fields maximize temporal coherence in natural video,” Neural Comput. 15, 663–691 (2003).
- A. Hyvärinen, “Blind source separation by nonstationarity of variance: cumulant-based approach,” IEEE Trans. Neural Netw. 12, 1471–1474 (2001).
- C. Zetzsche and G. Krieger, “Nonlinear neurons and high-order statistics: new approaches to human vision and electronic image processing,” in Human Vision and Electronic Imaging IV, B. Rogowitz and T. V. Pappas, eds., Proc. SPIE 3644, 2–33 (1999).
- E. P. Simoncelli and O. Schwartz, “Modeling surround suppression in V1 neurons with a statistically-derived normalization model,” in Advances in Neural Information Processing Systems 11, M. S. Kearns, S. A. Solla, and D. A. Cohn, eds. (MIT Press, Cambridge, Mass., 1999), pp. 153–159.
- A. Hyvärinen and P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspeces,” Neural Comput. 12, 1705–1720 (2000).
- A. Hyvärinen, P. O. Hoyer, and M. Inki, “Topographic independent component analysis,” Neural Comput. 13, 1527–1558 (2001).
- O. Schwartz and E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neurosci. 4, 819–825 (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. Harmon. Anal. 11, 89–123 (2001).
- D. H. Hubel and T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. (London) 195, 215–243 (1968).
- G. G. Blasdel, “Orientation selectivity, preference, and continuity in monkey striate cortex,” J. Neurosci. 12, 3139–3161 (1992).
- D. H. Hubel and T. N. Wiesel, “Functional architecture of macaque monkey visual cortex (Ferrier Lecture),” Proc. R. Soc. London Ser. B 198, 1–59 (1977).
- R. B. H. Tootell, M. S. Silverman, S. L. Hamilton, E. Switkes, and R. L. De Valois, “Functional anatomy of macaque striate cortex. V. Spatial frequency,” J. Neurosci. 8, 1610–1624 (1988).
- T. Kohonen, Self-Organizing Maps (Springer, Berlin, 1995).
- N. V. Swindale, “The development of topography in the visual cortex: a review of models,” Network 7, 161–247 (1996).
- C. von der Malsburg, “Self-organization of orientation-sensitive cells in the striate cortex,” Kybernetik 14, 85–100 (1973).
- A. Hyvärinen and P. O. Hoyer, “A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images,” Vision Res. 41, 2413–2423 (2001).
- A. J. Bell and T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
- J. H. van Hateren and A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London Ser. B 265, 359–366 (1998).
- P. Comon, “Independent component analysis—a new concept?” Signal Process. 36, 287–314 (1994).
- C. Jutten and J. Hérault, “Blind separation of sources. Part I: An adaptive algorithm based on neuromimetic architecture,” Signal Process. 24, 1–10 (1991).
- J. H. van Hateren and D. L. Ruderman, “Independent component analysis of natural image sequences yields spatiotemporal filters similar to simple cells in primary visual cortex,” Proc. R. Soc. London Ser. B 265, 2315–2320 (1998).
- J. Hurri and A. Hyvärinen, “A two-layer temporal generative model of natural video exhibits complex-cell-like pooling of simple cell outputs,” in Computational Neuroscience: Trends in Research 2003, E. De Schutter, ed. (Elsevier, Amsterdam, The Netherlands, 2003).
- B. A. Olshausen, “Sparse codes and spikes,” in Statistical Theories of the Brain, R. Rao and B. A. Olshausen, eds. (MIT Press, Cambridge, Mass. 2001).
- R. C. Emerson, J. R. Bergen, and E. H. Adelson, “Directionally selective complex cells and the computation of motion energy in cat visual cortex,” Vision Res. 32, 203–218 (1992).
- D. Pollen and S. Ronner, “Visual cortical neurons as localized spatial frequency filters,” IEEE Trans. Syst. Man Cybern. SMC-13, 907–916 (1983).
- M. Welicky, W. H. Bosking, and D. Fitzpatrick, “A systematic map of direction preference in primary visual cortex,” Nature (London) 379, 725–728 (1996).
- P. O. Hoyer and A. Hyvärinen, “A multi-layer sparse coding network learns contour coding from natural images,” Vision Res. 42, 1593–1605 (2002).
- J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Adaptive Wiener denoising using a Gaussian scale mixture model in the wavelet domain,” in Proceedings of the International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 2001).
- R. Durbin and G. Mitchison, “A dimension reduction framework for understanding cortical maps,” Nature (London) 343, 644–647 (1990).
- W. S. Geisler and D. G. Albrecht, “Cortical neurons: isolation of contrast gain control,” Vision Res. 32, 1409–1410 (1992).
- D. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–198 (1992).
- K. Matsuoka, M. Ohya, and M. Kawamoto, “A neural net for blind separation of nonstationary signals,” Neural Networks 8, 411–419 (1995).
- D.-T. Pham and J.-F. Cardoso, “Blind separation of instantaneous mixtures of non-stationary sources,” in Proceedings of the International Workshop on Independent Component Analysis and Blind Signal Separation (ICA2000) (Helsinki University of Technology, Espoo, Finland, 2000), pp. 187–193.
- R. F. Engle, ed., ARCH: Selected Readings (Oxford U. Press, Oxford, UK, 1995).
- B. A. Olshausen and D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
- A. Hyvärinen and M. Inki, “Estimating overcomplete independent component bases from image windows,” J. Math. Imaging Vision 17, 139–152 (2002).
- A. Pece, “The problem of sparse image coding,” J. Math. Imaging Vision 17, 87–106 (2002).
- B. A. Olshausen, P. Sallee, and M. S. Lewicki, “Learning sparse image codes using a wavelet pyramid architecture,” in Advances in Neural Information Processing Systems, (MIT Press, Cambridge, Mass., 2001), Vol. 13, pp. 887–893.
- P. Paatero and U. Tapper, “Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values,” Environmetrics 5, 111–126 (1994).
- D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature (London) 401, 788–791 (1999).
- P. O. Hoyer, “Modeling receptive fields with non-negative sparse coding,” in Computational Neuroscience: Trends in Research 2003, E. De Schutter, ed. (Elsevier, Amsterdam, The Netherlands, 2003).
- D. R. Tailor, L. H. Finkel, and G. Buchsbaum, “Color-opponent receptive fields derived from independent component analysis of natural images,” Vision Res. 40, 2671–2676 (2000).
- T. Wachtler, T-W. Lee, and T. J. Sejnowski, “Chromatic structure of natural scenes,” J. Opt. Soc. Am. A 18, 65–77 (2001).
- P. O. Hoyer and A. Hyvärinen, “Independent component analysis applied to feature extraction from colour and stereo images,” Network Comput. Neural Syst. 11, 191–210 (2000).

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