Occlusion Models for Natural Images: A Statistical Study of a Scale-Invariant Dead Leaves Model
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
We develop a scale-invariant version of Matheron's “dead leaves model” for the statistics of natural images. The model takes occlusions into account and resembles the image formation process by randomly adding independent elementary shapes, such as disks, in layers. We compare the empirical statistics of two large databases of natural images with the statistics of the occlusion model, and find an excellent qualitative, and good quantitative agreement. At this point, this is the only image model which comes close to duplicating the simplest, elementary statistics of natural images—such as, the scale invariance property of marginal distributions of filter responses, the full co-occurrence statistics of two pixels, and the joint statistics of pairs of Haar wavelet responses.
- Alvarez, L., Gousseau Y., and Morel J.-M. 1999. The size of objects in natural and artificial images. Advances in Imaging and Electron Physics, vol. 111. Academic Press: San Diego, CA, pp. 167-242.
- Buccigrossi, R.W. and Simoncelli, E.P. 1999. Image compression via joint statistical characterization in the wavelet domain. Proc. IEEE Trans. on Image Processing, 8(12):1688-1701.
- Field, D.J. 1987. Relations between the statistics of natural images and the response properties of cortical cells.J. Optical Society of America, A4:2379-2394.
- Freeman, W.T. and Pasztor, E.C. 1999. Learning low-level vision. In Proc. IEEE Int. Conf. on Computer Vision, Corfu, Greece.
- Grenander, U. and Srivastava, A. 2000. Probability models for clutter in natural images, IEEE Trans. PAMI, in press.
- Hallinan P.W., Gordon G.G., Yuille, A.L., Giblin, P., and Mumford, D. 1999. Two-and three-dimensional patterns of the face. A.K. Peters Ltd, Natick, MA.
- Heeger, D.J. and Bergen, J.R. 1995. Pyramid based texture analysis/ synthesis. In Computer Graphics Proc., pp. 229-238.
- Huang, J., Lee, A., and Mumford, D. 2000. Statistics of range images. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Vol. 1, Hilton Head Island, SC, pp. 324-331.
- Huang, J. and Mumford, D. 1999. Statistics of natural images and models. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Vol. 1, Fort Collins, CO, pp. 541-547.
- Isard, M. and Blake, A. 1998. CONDENSATION-conditional density propagation for visual tracking. Int. J. Computer Vision, 291:5-28.
- Kendall, W.S. and ThÔnnes, E. 1998. Perfect Simulation in Stochastic Geometry. Preprint 323, Department of Statistics, University of Warwick, UK.
- Kingman, J.F.C. 1993. Poisson Processes. Oxford Studies in Probability. Clarendon Press, Oxford.
- Lee, A.B. and Mumford, D. 1999. An occlusion model generating scale-invariant images. In Proc. IEEEWorkshop on Statistical and Computational Theories of Vision, Fort Collins, CO.
- Malik, J., Belongie, S., Shi, J., and Leung, T. 1999. Textons, contours and regions: Cue integration in image segmentation. In Proc. IEEE Int. Conf. Computer Vision, Corfu, Greece.
- Mallat, S.G. 1989. A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. PAMI, 11:674-693.
- Matheron, G. 1968. Modèle séquentiel de partition aléatoire. Technical report, CMM, 1968.
- Matheron, G. 1975. Random Sets and Integral Geometry. JohnWiley and Sons: New York. Occlusion Models for Natural Images 59
- Moulin, P. and Liu, J. 1999. Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors. IEEE Trans. on Information Theory, 453:909-919.
- Mumford, D. and Gidas, B. 2000. Stochastic models for generic images. Quarterly Journal of Applied Mathematics Volume LIX, Number 1, March 2001, pp. 85-111.
- Olshausen, B.A. and Field, D.J. 1996. Natural image statistics and efficient coding. Network, 7:333-339.
- Ruderman, D.L. 1994. The statistics of natural images. Network, 5(4):517-548.
- Ruderman, D.L. 1997. Origins of scaling in natural images. Vision Research, 37(23):3385-3395.
- Ruderman, D.L. and Bialek, W. 1994. Statistics of natural images: scaling in the woods. Physical Review Letters, 73(6):814-817.
- Serra, J.P. 1982. Image Analysis and Mathematical Morphology. Academic Press: London.
- Simoncelli, E.P. 1999. Modeling the joint statistics of images in the wavelet domain. In Proc. SPIE 44th Annual Meeting, Vol. 3813, Denver, Colorado.
- Simoncelli, E.P. and Adelson, E.H. 1996. Noise removal via bayesianwavelet coring. In Third Int'l Conf. on Image Processing, Lausanne, Switzerland, pp. 379-383.
- Sullivan, J., Blake, A., Isard, M., and MacCormick, J. 1999. Object localization by Bayesian correlation. In Proc. Int. Conf. Computer Vision, pp. 1068-1075.
- van Hateren, J.H. and van der Schaaf, A. 1998. Independent component filters of natural images compared with simple cells in primary visual cortex. Proc. R. Soc. Lond., B265:359-366.
- Wainwright, M.J. and Simoncelli, E.P. 2000. Scale mixtures of gaussians and the statistics of natural images. In Advances in Neural Information Processing Systems 12, Solla, Leen, and Müller(Eds.), MIT Press: Cambridge, MA, pp. 885-861.
- Zetzsche, B., Wegmann, B., and Barth, E. 1993. Nonlinear aspects of primary vision: Entropy reduction beyond decorrelation. In Int'l Symp. Soc. for Info. Display, Vol. 24, pp. 933-936.
- Zhu, S.C. and Guo, C. 2000. Mathematical modeling of clutter: Descriptive vs. generative models. In Proc. of the SPIE AeroSense Conf. on Automatic Target Recognition, Orlando, FL.
- Zhu, S.C., Luo, Q., and Zhang, R. 1999. Effective statistical inference by data-driven markov chain Monte-Carlo. Technical Report, Dept. of Computer and Information Sciences, Ohio State University, Columbus, OH.
- Zhu, S. and Mumford, D. 1997. Prior learning and Gibbs reactiondiffusion. IEEE Trans PAMI, 19(11):1236-1250.
- Zhu, S.C., Wu, Y.N., and Mumford, D. 1998. FRAME: Filters, random field and maximum entropy-towards a unified theory for texture modeling.Int'l J. Computer Vision, 27(2):1-20.
- Occlusion Models for Natural Images: A Statistical Study of a Scale-Invariant Dead Leaves Model
International Journal of Computer Vision
Volume 41, Issue 1-2 , pp 35-59
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- natural images
- stochastic image model
- non-Gaussian statistics
- dead leaves model
- Industry Sectors