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34
On Advances in Statistical Modeling of Natural Images
, 2003
"... Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeli ..."
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Cited by 145 (7 self)
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Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeling of natural images that attempt to explain these patterns. Two categories of results are considered: (i) studies of probability models of images or image decompositions (such as Fourier or wavelet decompositions), and (ii) discoveries of underlying image manifolds while restricting to natural images. Applications of these models in areas such as texture analysis, image classification, compression, and denoising are also considered.
Occlusion models for natural images: a statistical study of a scale invariant dead leaves model
 International Journal of Computer Vision
"... Abstract. We develop a scaleinvariant 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 empiric ..."
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Cited by 90 (0 self)
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Abstract. We develop a scaleinvariant 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 cooccurrence statistics of two pixels, and the joint statistics of pairs of Haar wavelet responses. natural images, stochastic image model, nonGaussian statistics, scaling, dead leaves model, occluKeywords: sions, clutter 1.
Efficient construction of reversible jump markov chain monte carlo proposal distributions
 Journal of the Royal Statistical Society: Series B (Statistical Methodology
"... Summary. The major implementational problem for reversible jump Markov chain Monte Carlo methods is that there is commonly no natural way to choose jump proposals since there is no Euclidean structure in the parameter space to guide our choice. We consider mechanisms for guiding the choice of propos ..."
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Cited by 63 (2 self)
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Summary. The major implementational problem for reversible jump Markov chain Monte Carlo methods is that there is commonly no natural way to choose jump proposals since there is no Euclidean structure in the parameter space to guide our choice. We consider mechanisms for guiding the choice of proposal. The first group of methods is based on an analysis of acceptance probabilities for jumps. Essentially, these methods involve a Taylor series expansion of the acceptance probability around certain canonical jumps and turn out to have close connections to Langevin algorithms.The second group of methods generalizes the reversible jump algorithm by using the socalled saturated space approach. These allow the chain to retain some degree of memory so that, when proposing to move from a smaller to a larger model, information is borrowed from the last time that the reverse move was performed. The main motivation for this paper is that, in complex problems, the probability that the Markov chain moves between such spaces may be prohibitively small, as the probability mass can be very thinly spread across the space. Therefore, finding reasonable jump proposals becomes extremely important. We illustrate the procedure by using several examples of reversible jump Markov chain Monte Carlo applications including the analysis of autoregressive time series, graphical Gaussian modelling and mixture modelling.
Extension of Fill’s perfect rejection sampling algorithm to general chains (extended abstract
 Pages 37–52 in Monte Carlo Methods
, 2000
"... By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite general state spaces, and describe how use of bounding processes can ease computational burden. Along th ..."
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Cited by 47 (14 self)
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By developing and applying a broad framework for rejection sampling using auxiliary randomness, we provide an extension of the perfect sampling algorithm of Fill (1998) to general chains on quite general state spaces, and describe how use of bounding processes can ease computational burden. Along the way, we unearth a simple connection between the Coupling From The Past (CFTP) algorithm originated by Propp and Wilson (1996) and our extension of Fill’s algorithm. Key words and phrases. Fill’s algorithm, Markov chain Monte Carlo, perfect sampling, exact sampling, rejection sampling, interruptibility, coupling from the past, readonce coupling from the past, monotone transition rule, realizable monotonicity, stochastic monotonicity, partially ordered set, coalescence, imputation,
How to Couple from the Past Using a ReadOnce Source of Randomness
, 1999
"... We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related ..."
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Cited by 40 (1 self)
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We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related to an idea known as PASTA (Poisson arrivals see time averages) in the operations research literature. Because the new algorithm can be run using a readonce stream of randomness, we call it readonce CFTP. The memory and time requirements of readonce CFTP are on par with the requirements of the usual form of CFTP, and for a variety of applications the requirements may be noticeably less. Some perfect sampling algorithms for point processes are based on an extension of CFTP known as coupling into and from the past; for completeness, we give a readonce version of coupling into and from the past, but it remains unpractical. For these point process applications, we give an alternative...
Downlink Admission/Congestion Control and Maximal Load in CDMA Networks
 In Proceedings of the IEEE Conference on Computer Communications (INFOCOM ’03), March 30 – April 3
, 2003
"... This paper is focused on the influence of geometry on the combination of intercell and intracell interferences in the downlink of large cdma networks. We use an exact representation of the geometry of the downlink channels to define scalable admission and congestion control schemes, namely schemes ..."
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Cited by 33 (13 self)
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This paper is focused on the influence of geometry on the combination of intercell and intracell interferences in the downlink of large cdma networks. We use an exact representation of the geometry of the downlink channels to define scalable admission and congestion control schemes, namely schemes that allow each base station to decide independently of the others what set of voice users to serve and/or what bit rates to offer to elastic traffic users competing for bandwidth. We then study the load of these schemes when the size of the network tends to infinity using stochastic geometry tools. By load, we mean here the distribution of the number of voice users that each base station can serve and that of the bit rate offered to each elastic traffic user.
Markov Chain Monte Carlo for Statistical Inference
 University of Washington, Center for
, 2000
"... These notes provide an introduction to Markov chain Monte Carlo methods that are useful in both Bayesian and frequent... ..."
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Cited by 29 (0 self)
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These notes provide an introduction to Markov chain Monte Carlo methods that are useful in both Bayesian and frequent...
Perfect slice samplers
 In preparation
, 1999
"... Perfect sampling allows exact simulation of random variables from the stationary measure of a Markov chain. By exploiting monotonicity properties of the slice sampler we show that a perfect version of the algorithm can be easily implemented, at least when the target distribution is bounded. Various ..."
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Cited by 27 (9 self)
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Perfect sampling allows exact simulation of random variables from the stationary measure of a Markov chain. By exploiting monotonicity properties of the slice sampler we show that a perfect version of the algorithm can be easily implemented, at least when the target distribution is bounded. Various extensions, including perfect product slice samplers, and examples of applications are discussed.
Spatial Averages of Coverage Characteristics in Large CDMA Networks
, 2001
"... The aim of the present paper is to show that stochastic geometry provides an efficient computational framework allowing one to predict geometrical characteristics of large CDMA networks such as coverage or softhandoff level. The general idea consists in representing the location of antennas and/or ..."
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Cited by 25 (3 self)
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The aim of the present paper is to show that stochastic geometry provides an efficient computational framework allowing one to predict geometrical characteristics of large CDMA networks such as coverage or softhandoff level. The general idea consists in representing the location of antennas and/or mobile stations as realizations of stochastic point processes in the plane within a simple parametric class, which takes into account the irregularities of antenna/mobile patterns in a statistical way. This approach leads to new formulas and simulation schemes allowing one to compute/estimate the spatial averages of these local characteristics in function of the model parameters (density of antennas or mobiles, law of emission power, fading law etc.) and to perform various parametric optimizations.