Statistics of natural images and models

By Jinggang Huang, David Mumford. 1999

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.

Subfields: Statistics and Probability

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Citations in the corpus

Multiview Transformers for Video Recognition (2022, background): “In the image domain, multiscale processing is typically performed with pyramids as the statistics of natural images are isotropic (all orientations are equally likely) and shift invariant [30, 67].”
SlowFast Networks for Video Recognition (2018, background): “This is justified by the statistics of natural images, which are to a first approximation isotropic—all orientations are equally likely—and shift-invariant [41, 26].”
Deep Image Prior (2017, background): “Later, [26] noted that image response distribution w.”
Visualizing Deep Convolutional Neural Networks Using Natural Pre-images (2015, background): “Natural image statistics Natural images are well known to have certain statistical regularities; for example, the magnitude of image gradients have an exponential distribution (Huang and Mumford 1999).”
Pixel Recursive Super Resolution (2017, background): “Enhancing linear methods with rich image priors such as sparsity [2] or Gaussian mixtures [51] have substantially improved the quality of the methods; likewise, leveraging low-level image statistics such as edge gradients improves predictions [47, 41, 8, 16, 39, 22].”
A Deep Journey into Super-resolution (2019, methodology): “mage prior ( ). According to Yang et al. [21], based on the image prior, super-resolution methods can be roughly categorized into: prediction methods [22], edgebased methods [23], statistical methods [24], patch-based methods [25], [26], [27], and deep learning methods [28]. In this article, our foc”
Occlusion Models for Natural Images: A Statistical Study of a Scale-Invariant Dead Leaves Model (2004, background): “The two functions are otherwise equivalent as In Huang and Mumford (1999), Huang shows that the “difference function” for natural images (in a ﬁxed direction) is best modeled by where x is the separation distance between two pixels, and a 1 , a 2 , a 3 are constants.”
Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization (2009, methodology): “We will achieve this starting from a random sensing matrix (and its corresponding ), and progressively improving it in order to reduce this error.7 This is detailed next.”
A Bilevel Optimization Approach for Parameter Learning in Variational Models (2013, background): “, DCT filters) on natural images has heavily tailed distributions [15].”
Image super-resolution using gradient profile prior (2008, methodology): “The learning based methods [10, 9, 26, 5, 28, 2, 7, 20, 31] “hallucinate” high frequency details from a training set of HR/LR image pairs.”
Fields of Experts (2009, background): “It has been often observed that, for a wide variety of linear filters, the marginal filter responses are non-Gaussian, and that the responses of different filters are usually not independent (Huang and Mumford 1999; Srivastava et al. 2002; Portilla et al. 2003).”
Geometric blur for template matching (2001, unknown): “However much work indicates that oriented edge fi lter responses from images are sparse [4] [5].”
On Advances in Statistical Modeling of Natural Images (2004, background): “Scaling of different types of scenes was studied by Huang [43].”
Learning a Variational Network for Reconstruction of Accelerated MRI Data (2017, methodology): “We can identify functions with student-t characteristics also used in (28), which are reported to ﬁt the statistics of natural images better than, e.g., the l 1 -norm (50).”
Adapting to unknown sparsity by controlling the false discovery rate (2005, background): “…and image processing, the wavelet coefficients of a typical object can be modeled as a sparse vector; the interested reader might consult literature going back to Field (1987), extending through DeVore, Jawerth, and Lucier (1992), Ruderman (1994), Simoncelli (1999) and Huang and Mumford (1999).”
A nonparametric statistical method for image segmentation using information theory and curve evolution (2005, unknown): “In particular, the technique proposed by Heiler et al. [19] is motivated by recent work on natural image statistics [33], [20], and is based on parametric modeling of filter responses by generalized Laplacian distributions.”