Occlusion Models for Natural Images: A Statistical Study of a Scale-Invariant Dead Leaves Model

By Ann B. Lee, David Mumford, Jinggang Huang. 2004

262 citations recorded by the source corpus.

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.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

Deep Unsupervised Learning using Nonequilibrium Thermodynamics (2015, background): “Dead Leaf Images Dead leaf images [18, 27] consist of layered occluding circles, drawn from a power law distribution over scales.”
Generative Image Modeling Using Spatial LSTMs (2015, background): “Dead leaf images are generated by superimposing disks of random intensity and size on top of each other [22, 26].”
Mixtures of Conditional Gaussian Scale Mixtures Applied to Multiscale Image Representations (2011, neutral): “The statistics of a scale-invariant process are invariant under block-averaging and appropriate rescaling to compensate for the loss in variance [18].”
Pros and Cons of GAN Evaluation Measures (2018, background): “This means that marginal distribution of almost any zero mean linear filter response on virtually any dataset of images is sharply peaked at zero, with heavy tails and high kurtosis (greater than 3) [46].”
Visual Concepts and Compositional Voting (2017, methodology): “David’s work has long emphasized its significance [28, 18] and it is sufficiently important for computer vision researchers to have addressed it using deep networks [39].”
From Information Scaling of Natural Images to Regimes of Statistical Models (2007, methodology): “Section 2 describes an empirical study of a simple model treated by Lee, Mumford and Huang (2001) [32] to illustrate information scaling.”
On Advances in Statistical Modeling of Natural Images (2004, methodology): “Zhu and Mumford [98] used a Gibbs model on images and estimated model parameters using a minimax entropy criterion.”
Creating efficient codebooks for visual recognition (2005, unknown): “) occur far more frequently than others (faces, stop signs); and (ii) the amount of any given texture that appears is extremely variable owing to the multiscale region structure of natural scenes (the statistics of this is captured quite well by “dead leaves” [16] – sets of opaque, homogeneous patch”
"Natural Images, Gaussian Mixtures and Dead Leaves" (2012, background): “We now show that many of the properties of natural scenes that were captured by the GMM model can be derived from a variant of the dead leaves model [15].”
Learning a Generative Model of Images by Factoring Appearance and Shape (2011, methodology): “This generative process bears some resemblance to the dead-leaves model (Lee, Mumford, & Huang, 2001 ), although there are important differences (eg, in the current formulation of our model, the number of occluding objects covering an image is fixed and their maximum size is restricted while we all”
Image denoising with nonlocal spectral graph wavelets (2010, background): “A large part of the literature on statistical image modeling concerns describing the strongly related scale-invariance properties of natural images [2, 3, 4].”
Visual perception and the statistical properties of natural scenes. (2008, background): “For more discussion of scale invariance, see Ruderman (1997, 2002), Lee et al. (2001), and Balboa et al. (2001).”
The informed sampler: A discriminative approach to Bayesian inference in generative computer vision models (2014, methodology): “We chose this experiment such that it resembles the “dead leaves model” of Lee et al. (2001), because it has properties that are commonplace in computer vision.”
Iterative kernel principal component analysis for image modeling (2005, background): “profiles of objects [18] or geometrical primitives [29], [40], and”
Learning generative models of mid-level structure in natural images (2012, methodology): “This generative process bears some resemblance to the “dead-leaves model” (Jeulin, 1997; Lee et al., 2001) although there are important differences (see section 5.”