ABSTRACT
The class of all natural images is an extremely small fraction of all possible images. Some of the structure of natural images can be modeled statistically, revealing striking regularities. Moreover, the human visual system appears to be optimized to view natural images. Images that do not behave statistically as natural images are harder for the human visual system to interpret. This paper reviews second order image statistics as well as their implications for computer graphics. We show that these statistics are predominantly due to geometric modeling, while being largely unaffected by the choice of rendering parameters. As a result, second order image statistics are useful for modeling applications, which we show in direct examples (recursive random displacement terrain modeling and solid texture synthesis). Finally, we present an image reconstruction filter based on second order image statistics.
- BALBOA, R. M., TYLER, C. W., AND GRZYWACZ, N. M. 2001. Occlusions contribute to scaling in natural images. Vision Research 41, 7, 955--964.Google ScholarCross Ref
- BOX, G. E. P., AND MULLER, M. E. 1958. A note on the generation of random normal deviates. Annals Math. Stat 29, 610--611.Google ScholarCross Ref
- BURTON, G. J., AND MOORHEAD, I. R. 1987. Color and spatial structure in natural scenes. Applied Optics 26, 1 (January), 157--170.Google ScholarCross Ref
- CROVELLA, M. E., AND TAQQU, M. S. 1999. Estimating the heavy tail index from scaling properties. Methodology and Computing in Applied Probability 1, 1, 55--79. Google ScholarDigital Library
- DE BONET, J., AND VIOLA, P. 1998. A non-parametric multi-scale statistical model for natural images. In Proceedings of the 1997 conference on Advances in Neural Information Processing Systems 10, 773--779. Google ScholarDigital Library
- DONG, D. W., AND ATICK, J. J. 1995. Statistics of natural time-varying images. Network: Computation in Neural Systems 6, 3, 345--358.Google ScholarCross Ref
- FIELD, D. J., AND BRADY, N. 1997. Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes. Vision Research 37, 23, 3367--3383.Google ScholarCross Ref
- FIELD, D. J. 1987. Relations between the statistics of natural images and the response properties of cortical cells. J. Opt. Soc. Am. A 4, 12 (December), 2379--2394.Google ScholarCross Ref
- FIELD, D. J. 1993. Scale-invariance and self-similar 'wavelet' transforms: An analysis of natural scenes and mammalian visual systems. In Wavelets, fractals and Fourier transforms, M. Farge, J. C. R. Hunt, and J. C. Vassilicos, Eds. Clarendon Press, Oxford, 151--193.Google Scholar
- FOURNIER, A., FUSSELL, D., AND CARPENTER, L. 1982. Computer rendering of stochastic models. Communications of the ACM 25, 6 (June), 371--384. Google ScholarDigital Library
- GLASSNER, A. S. 1995. Principles of digital image synthesis. Morgan Kaufmann, San Fransisco, CA. Google ScholarDigital Library
- HARRIS, F. J. 1978. On the use of windows for harmonic analysis with the discrete fourier transform. Proc. IEEE 66, 1, 51--84.Google ScholarCross Ref
- HEEGER, D. J., AND BERGEN, J. R. 1995. Pyramid-based texture analysis/synthesis. In Proceeding of the 22nd annual conference on Computer Graphics and Interactive Techniques, 229--238. Google ScholarDigital Library
- HILL, B. M. 1975. A simple general approach to inference about the tail of a distribution. The Annals of Statistics 3, 5, 1163--1174.Google ScholarCross Ref
- LANGER, M. S. 2000. Large-scale failures of f-α scaling in natural image spectra. J. Opt. Soc. Am. A 17, 1 (January), 28--33.Google ScholarCross Ref
- LEWIS, J. P. 1989. Algorithms for solid noise synthesis. Computer Graphics 23, 3 (July), 263--270. Google ScholarDigital Library
- LI, X., AND ORCHAR, M. T. 2001. New edge-directed interpolation. IEEE Transactions on Image Processing 10, 10, 1521--1527. Google ScholarDigital Library
- MANDELBROT, B. B. 1983. The Fractal Geometry of Nature. W. H. Freeman and Co.Google Scholar
- MITCHELL, D. P., AND NETRAVALI, A. N. 1988. Reconstruction filters in computer graphics. Computer Graphics 22, 4 (August), 221--228. Google ScholarDigital Library
- NIKIAS, C. L., AND PETROPULU, A. P. 1993. Higher-order spectra analysis. Signal Processing Series. Prentice Hall.Google Scholar
- PÁRRAGA, C. A., BRELSTAFF, G., AND TROSCIANKO, T. 1998. Color and luminance information in natural scenes. J. Opt. Soc. Am. A 15, 3, 563--569.Google ScholarCross Ref
- PEITGEN, H.-O., AND SAUPE, D., Eds. 1988. The Science of Fractal Images. Springer Verlag. Google ScholarDigital Library
- PERLIN, K. 1985. An image synthesizer. Computer Graphics 19, 3 (July), 287--296. Google ScholarDigital Library
- RUDERMAN, D. L., AND BIALEK, W. 1992. Seeing beyond the Nyquist limit. Neural Computation 4, 5, 682--690.Google ScholarDigital Library
- RUDERMAN, D. L., AND BIALEK, W. 1994. Statistics of natural images: Scaling in the woods. Physical Review Letters 73, 6, 814--817.Google ScholarCross Ref
- RUDERMAN, D. L. 1997. The statistics of natural images. Network: Computation in Neural Systems 5, 4, 517--548.Google ScholarCross Ref
- VAN DER SCHAAF, A. 1998. Natural image statistics and visual processing. PhD thesis, Rijksuniversiteit Groningen, The Netherlands.Google Scholar
- TOLHURST, D. J., TADMOR, Y., AND CHIAO, T. 1992. Amplitude spectra of natural images. Ophthalmic and Physiological Optics 12, 229--232.Google ScholarCross Ref
- TORRALBA, A., AND OLIVA, A. 2003. Statistics of natural image categories. Network: Comput. Neural Syst. 14, 391--412.Google ScholarCross Ref
- UPSTILL, S. 1990. The Renderman Companion. Addison-Wesley, Reading, MA.Google Scholar
- WARD LARSON, G., AND SHAKESPEARE, R. A. 1998. Rendering with Radiance. Morgan Kaufmann Publishers.Google Scholar
- Second order image statistics in computer graphics
Recommendations
Second Order Natural Scene Statistics Model of Blind Image Quality Assessment
2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)The univariate statistics of bandpass-filtered images provide powerful features that drive many successful image quality assessment (IQA) algorithms. Bivariate Natural Scene Statistics (NSS), which model the joint statistics of multiple bandpass image ...
Image statistics: from data collection to applications in graphics
SIGGRAPH '10: ACM SIGGRAPH 2010 CoursesNatural images exhibit statistical regularities that differentiate them from random collections of pixels. Moreover, the human visual system appears to have evolved to exploit such statistical regularities. As computer graphics is concerned with ...
Comments