## Statistics of Natural Images and Models (0)

Citations: | 209 - 5 self |

### BibTeX

@INPROCEEDINGS{Huang_statisticsof,

author = {Jinggang Huang and David Mumford},

title = {Statistics of Natural Images and Models},

booktitle = {},

year = {},

pages = {541--547}

}

### Years of Citing Articles

### OpenURL

### Abstract

Large calibrated datasets of `random' natural images have recently become available. These make possible precise and intensive statistical studies of the local nature of images. We report results ranging from the simplest single pixel intensity to joint distribution of 3 Haar wavelet responses. Some of these statistics shed light on old issues such as the near scale-invariance of image statistics and some are entirely new. We fit mathematical models to some of the statistics and explain others in terms of local image features. 1

### Citations

8867 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ... by H(X), and denote the mutual information between X and Y by I(X; Y ), both in bits. We use differential entropy instead of discrete entropy, because the variables are real valued. For details, see =-=[2]-=-. All our pictures of probability distributions (or of normalized histograms) will be shown with the vertical scale not probability but log of probability: this is very important as it shows the non-G... |

633 | Relations between the statistics of natural images and the response properties of cortical cells - Field - 1987 |

239 | The Steerable Pyramid: A flexible architecture for multi-scale derivative computation
- Simoncelli, Freeman
- 1995
(Show Context)
Citation Context ...the Haar Wavelet and QMF Wavelet. The following paragraph is a simple introduction(Copied from the manual of EPWIC package, which is available at http://www.cns.nyu.edu/ eero/). For more details, see =-=[20]-=-. The steerable pyramid is a multi-scale representation that is translation-invariant, but that also includes representation of orientation. Furthermore, the representation of orientation is designed ... |

202 | Image compression via joint statistical characterization in the wavelet domain
- Buccigrossi, Simoncelli
- 1999
(Show Context)
Citation Context ...linked the design of the biological vision system to the statistics of natural images. Zhu, Wu and Mumford [9] set up a general frame work for natural image modeling via exponential models. Simoncelli=-=[1]-=- uncovered significant dependencies of wavelet coefficients in natural image statistics. In most of these papers, simple statistics are calculated from which some properties are derived to prove some ... |

200 | random fields and maximum entropy: Towards a unified theory for texture modeling
- Zhu, Wu, et al.
- 1998
(Show Context)
Citation Context ...rman [7] discusses the approximate scale invariance property of natural images and Field [4] linked the design of the biological vision system to the statistics of natural images. Zhu, Wu and Mumford =-=[9]-=- set up a general frame work for natural image modeling via exponential models. Simoncelli[1] uncovered significant dependencies of wavelet coefficients in natural image statistics. In most of these p... |

164 | Statistics of natural images: Scaling in the woods - Ruderman, Bialek - 1994 |

85 | Natural image statistics and efficient coding
- Olshausen, Field
- 1996
(Show Context)
Citation Context ...s. 1 Introduction There has been much attention recently to the statistics of natural images. For example, Ruderman [7] discusses the approximate scale invariance property of natural images and Field =-=[4]-=- linked the design of the biological vision system to the statistics of natural images. Zhu, Wu and Mumford [9] set up a general frame work for natural image modeling via exponential models. Simoncell... |

84 | Origins of scaling in natural images
- Ruderman
- 1997
(Show Context)
Citation Context ... models to some of the statistics and explain others in terms of local image features. 1 Introduction There has been much attention recently to the statistics of natural images. For example, Ruderman =-=[7]-=- discusses the approximate scale invariance property of natural images and Field [4] linked the design of the biological vision system to the statistics of natural images. Zhu, Wu and Mumford [9] set ... |

78 | Stochastic models for generic images
- Mumford, Gidas
(Show Context)
Citation Context ...f histograms for each category can be modeled with three parameters: a) their standard deviation, b) the anomalous dimension and c) a `shape' parameter for the histogram which has been identied in =-=[16]-=- as the parameter in an innitely divisible family of probability distributions. 23 Category Scale H 1 D(p 0 k p 1 ) 2 D(p 0 k p 2 ) Sky 1 0.069 59 -3 0.165 0.0158 0.386 0.12 2 0.037 57.3 -3.5... |

77 | A Bayesian treatment of the stereo correspondence problem using half-occluded regions
- Belhumeur, Mumford
- 1992
(Show Context)
Citation Context ...estigating the statistics underlying all images. We also studied the statistics of range images, which by themselves are important in applications, for example they give priors for stereo algorithms (=-=[1]-=-,[2]). We are interested in them because they lead to a direct understanding of the stochastic nature of the geometry of the world and make it possible to construct more realistic models of intensity ... |

39 | A binocular stereo algorithm for reconstructing sloping, creased, and broken surfaces in the presence of half-occlusion
- Belhumeur
- 1993
(Show Context)
Citation Context ...gating the statistics underlying all images. We also studied the statistics of range images, which by themselves are important in applications, for example they give priors for stereo algorithms ([1],=-=[2]-=-). We are interested in them because they lead to a direct understanding of the stochastic nature of the geometry of the world and make it possible to construct more realistic models of intensity imag... |

21 |
The design and use of steerable
- Freeman, Adelson
(Show Context)
Citation Context ...her three pairs show dierent level curves, especially the horizontal-diagonal pair. 2.5.2 Joint Statistics for Steerable Pyramids Steerable pyramid decomposition was developed by Freeman and Adelson =-=[8]-=-, which is quite dierent from the Haar Wavelet and QMF Wavelet. The following paragraph is a simple introduction(Copied from the manual of EPWIC package, which is available at http://www.cns.nyu.edu/... |

16 | Probability Models for Complex Systems
- Chi
- 1998
(Show Context)
Citation Context ...ggested a model using the product of Gaussian random variables, and from this model he derived a family of distributions for derivative statistics. Here we introduce a dierent approach. First, as in =-=[4]-=-, we assume a real scene (x; y) is a function(or more properly a generalized function ,see [16]) dened on R 2 . A (digitized) image I of is a function dened on integer grid Z 2 , such that the va... |

13 | Random-Collage Model for Natural Images
- Lee, Huang, et al.
(Show Context)
Citation Context ...lead to a direct understanding of the stochastic nature of the geometry of the world and make it possible to construct more realistic models of intensity images. For example, authors in [17], [4] and =-=[14]-=- have modeled intensity images as a perspective view of the 3D world, with objects of random geometry (size, shape, position) and intensity. The object geometries in these models are usually based on ... |

6 |
Self Similar Probability Distributions
- Sinai
- 1976
(Show Context)
Citation Context ...e \Gammaj log rsj log r giving us the model D 1 (x) = C 1 + C 2 log(jxj) (6.2) which is the model implied by the assumption that 2 \Theta 2 block averages of the image I have the same distribion as I =-=[8]-=-. The best fitting constants Ruderman found from his image dataset are: C 1 = 0:79, C 2 = \Gamma0:64 and j = 0:19. We calculated the two dimensional D(x; y) from our data set. Using a Fourier transfor... |

1 | Chun Zhu and Basilis Gidas. "Stochastic Models for Generic Images", in preparation - Mumford |

1 |
Natural image statistics and eÆcient coding
- Olshausen, Field
(Show Context)
Citation Context ...s, the \noise" in images is more often \clutter", and the statistics of clutter are not Gaussian at all. There has been much attention recently to the statistics of natural images. For example, Field =-=[7]-=- discussed the scale invariance property of natural images and linked the design of the biological vision system to the statistics of natural images, Ruderman [17] proposed a model to explain why imag... |

1 |
Research 5
- \Clutter
(Show Context)
Citation Context ...imulated under some quite seemingly irrelevant assumptions. This lead us to believe that the statistical features we observed in natural images are caused by some simple stochastic process. Grenander =-=[9]-=- suggested a model using the product of Gaussian random variables, and from this model he derived a family of distributions for derivative statistics. Here we introduce a dierent approach. First, as ... |

1 | Statistics of range images". Accepted by - Huang, Mumford - 2000 |

1 |
J.Shi and T.Leung. \Textons, Contours and Regions
- Malik
- 1999
(Show Context)
Citation Context ...irect histogram methods used in previous sections do not work here, instead we apply some non-parametric statistics technique, e.g. k-means centers method. Similar methods was used by Malik et al. in =-=[15]-=- in analyzing `textons'. Butsrst, we follow the ideas in [15] and preprocess our data. For each 8 8 patch, we calculate the 3-level Haar Wavelet transformation to get 63 AC coeÆcients, and we renorm... |

1 |
Transforms". Subband Coding,P379-383, edited by
- \Subband
- 1990
(Show Context)
Citation Context ...cursive pyramid decomposition based on separable Quadrature Mirror Filters(QMFs) in image compression. Figure 2.39 shows the horizontal, vertical, diagonal and low passslters. Details can be found in =-=[19]-=-. Figure 2.40 shows empirical joint distribution of dierent QMFslter pairs. The horizontal-vertical coeÆcient pair of QMF and that of Haarslters(see 2.25) have very similar distributions. But the con... |

1 |
random and maximum entropy(FRAME) -towards the uni theory for texture modeling
- \Filters
- 1996
(Show Context)
Citation Context ...perty of natural images and linked the design of the biological vision system to the statistics of natural images, Ruderman [17] proposed a model to explain why images are scale invariant. Zhu et al. =-=[23]-=- set up a general frame work for natural image modeling via exponential models. Buccigrossi et al. [3] and Wainwright et al. [22] uncovered signicant dependencies of wavelet coeÆcients in natural ima... |