Capturing Visual Image Properties with Probabilistic Models

The Essential Guide to Image Processing

Volumn , Issue , 2009, Pages 205-223

  Simoncelli, Eero P ^a  

^a NEW YORK UNIVERSITY   (United States)

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EID: 84882549314     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-0-12-374457-9.00009-3     Document Type: Chapter

References (58)

1. G. Buchsbaum and A. Gottschalk (1983) Trichromacy, opponent color coding, and optimum colour information transmission in the retina. Proc. R. Soc. Lond., B, Biol. Sci 220 89-113.
2. D.L. Ruderman, T.W. Cronin and C.-C. Chiao. (1998) Statistics of cone responses to natural images: implications for visual coding. J. Opt. Soc. Am. A 15(8), 2036-2045.
3. D.W. Dong and J.J. Atick (1995) Statistics of natural time-varying images. Network Comp. Neural 6 345-358.
4. D.L. Ruderman (1996) The statistics of natural images. Network Comp. Neural 5 517-548.
5. E.T. Jaynes (1978) Where do we stand on maximum entropy? R.D. Levine, M. Tribus (Eds) The Maximal Entropy Formalism Cambridge, MA: MIT Press
6. G. Strang (1980) Linear Algebra and its Applications Orlando, FL: Academic Press
7. N.G. Deriugin (1956) The power spectrum and the correlation function of the television signal. Telecomm 1(7), 1-12.
8. D.J. Field (1987) Relations between the statistics of natural images and the response properties of cortical cells. J. Opt. Soc. Am. A 4(12), 2379-2394.
9. D.J. Tolhurst, Y. Tadmor and T. Chao (1992) Amplitude spectra of natural images. Ophthalmic Physiol. Opt 12 229-232.
10. D.L. Ruderman and W. Bialek (1994) Statistics of natural images: scaling in the woods. Phys. Rev. Lett 73(6), 814-817.
11. A. van der Schaaf and J.H. van Hateren (1996) Modelling the power spectra of natural images: statistics and information. Vision Res 28(17), 2759-2770.
12. A. Turiel and N. Parga (2000) The multi-fractal structure of contrast changes in natural images: from sharp edges to textures. Neural. Comput 12 763-793.
13. A.V. Oppenheim and J.S. Lim (1981) The importance of phase in signals. Proc. IEEE 69 529-541.
14. P.J. Burt and E.H. Adelson (1983) The Laplacian pyramid as a compact image code. IEEE Trans. Comm COM-31(4), 532-540.
15. J.G. Daugman (1988) Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression. IEEE Trans. Acoust 36(7), 1169-1179.
16. S.G. Mallat (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell 11 674-693.
17. C. Zetzsche and E. Barth (1990) Fundamental limits of linear filters in the visual processing of two-dimensional signals. Vision Res 30 1111-1117.
18. B.A. Olshausen and D.J. Field (1997) Sparse coding with an overcomplete basis set: a strategy employed by V1? Vision Res 37 3311-3325.
19. A.J. Bell and T.J. Sejnowski (1997) The independent components of natural scenes are edge filters. Vision Res 37(23), 3327-3338.
20. E.P. Simoncelli (1999) Bayesian denoising of visual images in the wavelet domain. P. Müller, B. Vidakovic (Eds) Bayesian Inference in Wavelet Based Models Lecture Notes in Statistics 141 New York: Springer-Verlag 291-308.
21. P. Moulin and J. Liu (1999) Analysis of multiresolution image denoising schemes using a generalized Gaussian and complexity priors. IEEE Trans. Inf. Theory 45 909-919.
22. B.A. Olshausen and D.J. Field (1996) Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381 607-609.
23. E.P. Simoncelli and E.H. Adelson (1996) Noise removal via Bayesian wavelet coring. Proc. 3rd IEEE Int. Conf. on Image Process IEEE Signal Processing Society, Lausanne, September 16–19 I 379-382.
24. H.A. Chipman, E.D. Kolaczyk and R.M. McCulloch (1997) Adaptive Bayesian wavelet shrinkage. J Am. Stat. Assoc 92(440), 1413-1421.
25. F. Abramovich, T. Sapatinas and B.W. Silverman (1998) Wavelet thresholding via a Bayesian approach. J. Roy. Stat. Soc. B 60 725-749.
26. S.C. Zhu, Y.N. Wu and D. Mumford (1998) FRAME: filters, random fields and maximum entropy – towards a unified theory for texture modeling. Int. J. Comput. Vis 27(2), 1-20.
27. R.R. Coifman and D.L. Donoho (1995) Translationinvariant de-noising. A. Antoniadis, G. Oppenheim (Eds) Wavelets and Statistics Lecture notes San Diego, CA: Springer-Verlag
28. F. Abramovich, T. Sapatinas and B.W. Silverman (2000) Stochastic expansions in an overcomplete wavelet dictionary. Probab. Theory Rel 117 133-144.
29. X. Li and M.T. Orchard (2000) Spatially adaptive image denoising under overcomplete expansion. IEEE Int. Conf. on Image Process Vancouver, September
30. M. Raphan and E.P. Simoncelli (2008) Optimal denoising in redundant representations. IEEE Trans. Image Process 17(8), 1342-1352.
31. D. Heeger and J. Bergen (1995) Pyramid-based texture analysis/synthesis. Proc. ACM SIGGRAPH Association for Computing Machinery, August 229-238.
32. J. Shapiro (1993) Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Process 41(12), 3445-3462.
33. J.S. Lee (1980) Digital image enhancement and noise filtering by use of local statistics. IEEE T. Pattern Anal PAMI-2 165-168.
34. M. Malfait and D. Roose (1997) Wavelet-based image denoising using a Markov random field a priori model. IEEE Trans. Image Process 6 549-565.
35. E.P. Simoncelli (1997) Statistical models for images: compression, restoration and synthesis. Proc. 31st Asilomar Conf. on Signals, Systems and Computers IEEE Computer Society, Pacific Grove, CA, November 2–5 1 673-678.
36. S.G. Chang, B. Yu and M. Vetterli (1998) Spatially adaptive wavelet thresholding with context modeling for image denoising. Fifth IEEE Int. Conf. on Image Process IEEE Computer Society, Chicago, October
37. M.K. Mihçak, I. Kozintsev, K. Ramchandran and P. Moulin (1999) Low-complexity image denoising based on statistical modeling of wavelet coefficients. Signal Process. Lett 6(12), 300-303.
38. M.J. Wainwright, E.P. Simoncelli and A.S. Willsky (2001) Random cascades on wavelet trees and their use in modeling and analyzing natural imagery. Appl. Comput. Harmonic Anal 11(1), 89-123.
39. F. Abramovich, T. Besbeas and T. Sapatinas (2002) Empirical Bayes approach to block wavelet function estimation. Comput. Stat. Data. Anal 39 435-451.
40. H. Brehm and W. Stammler (1987) Description and generation of spherically invariant speech-model signals. Signal Processing 12 119-141.
41. T. Bollersley, K. Engle and D. Nelson (1994) ARCH models. B. Engle, D. McFadden (Eds) North Holland, Amsterdam Handbook of Econometrics IV
42. A. Turiel, G. Mato, N. Parga and J.P. Nadal (1998) The self-similarity properties of natural images resemble those of turbulent flows. Phys. Rev. Lett 80 1098-1101.
43. D. Andrews and C. Mallows (1974) Scale mixtures of normal distributions. J. Roy. Stat. Soc 36 99-102.
44. M.S. Crouse, R.D. Nowak and R.G. Baraniuk (1998) Wavelet-based statistical signal processing using hidden Markov models. IEEE Trans. Signal Process 46 886-902.
45. J. Romberg, H. Choi and R. Baraniuk (1999) Bayesian wavelet domain image modeling using hidden Markov trees. Proc. IEEE Int. Conf. on Image Process Kobe, Japan, October
46. S.M. LoPresto, K. Ramchandran and M.T. Orchard (1997) Wavelet image coding based on a new generalized Gaussian mixture model. Data Compression Conf Snowbird, Utah, March
47. J. Portilla, V. Strela, M.J. Wainwright and E.P. Simoncelli (2003) Image denoising using a scale mixture of Gaussians in the wavelet domain. IEEE Trans. Image Process 12(11), 1338-1351.
48. S. Lyu and E.P. Simoncelli (2008) Modeling multiscale subbands of photographic images with fields of Gaussian scale mixtures. IEEE Trans. Pattern Anal. Mach. Intell Accepted for publication, 4/08
49. M.J. Wainwright and E.P. Simoncelli (2000) Scale mixtures of Gaussians and the statistics of natural images. S.A. Solla, T.K. Leen, K.-R. Müller (Eds) Advances in Neural Information Processing Systems (NIPS*99) 12 Cambridge, MA: MIT Press 855-861.
50. J. Portilla and E.P. Simoncelli (2000) A parametric texture model based on joint statistics of complex wavelet coefficients. Int. J. Comput. Vis 40(1), 49-71.
51. A. Hyvärinen and P. Hoyer (2000) Emergence of topography and complex cell properties from natural images using extensions of ICA. S.A. Solla, T.K. Leen, K.-R. Müller (Eds) Advances in Neural Information Processing Systems 12 Cambridge, MA: MIT Press 827-833.
52. Y. Karklin and M.S. Lewicki (2003) Learning higher-order structures in natural images. Network 14 483-499.
53. A. Hyvärinen, J. Hurri and J. Väyrynen (2003) Bubbles: a unifying framework for low-level statistical properties of natural image sequences. J. Opt. Soc. Am. A 20(7),
54. M. Sigman, G.A. Cecchi, C.D. Gilbert and M.O. Magnasco (2001) On a common circle: natural scenes and Gestalt rules. Proc. Natl. Acad. Sci 98(4), 1935-1940.
55. J.H. Elder and R.M. Goldberg (2002) Ecological statistics of gestalt laws for the perceptual organization of contours. J. Vis 2(4), 324-353. DOI 10:1167/2.4.5
56. W.S. Geisler, J.S. Perry, B.J. Super and D.P. Gallogly (2001) Edge co-occurance in natural images predicts contour grouping performance. Vision Res 41(6), 711-724.
57. P. Hoyer and A. Hyvärinen (2002) A multi-layer sparse coding network learns contour coding from natural images. Vision Res 42(12), 1593-1605.
58. S.-C. Zhu (2003) Statistical modeling and conceptualization of visual patterns. IEEE Trans. Pattern Anal. Mach. Intell 25(6), 691-712.