Natural Image Statistics

Can a machine learn to perceive emotions as evoked by an artwork? Here we propose an emotion categorization system, trained by ground truth from psychology studies. The training data contains emotional valences scored by human subjects on the International Affective Picture System (IAPS), a standard emotion evoking image set in psychology. Our approach is based on the assessment of local image statistics which are learned per emotional category using support vector machines. We show results for our system on the IAPS dataset, and for a collection of masterpieces. Although the results are preliminary, they demonstrate the potential of machines to elicit realistic emotions when considering masterpieces.

Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) non-Gaussian 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.

Existing color constancy methods are all based on specific assumptions such as the spatial and spectral characteristics of images. As a consequence, no algorithm can be considered as universal. However, with the large variety of available methods, the question is how to select the method that performs best for a specific image. To achieve selection and combining of color constancy algorithms, in this paper, natural image statistics are used to identify the most important characteristics of color images. Then, based on these image characteristics, the proper color constancy algorithm (or best combination of algorithms) is selected for a specific image. To capture the image characteristics, the Weibull parameterization (e.g. grain size and contrast) is used. It is shown that the Weibull parameterization is related to the image attributes to which the used color constancy methods are sensitive to. A MoG-classifier is used to learn the correlation and weighting between the Weibull-parameters and the image attributes (number of edges, amount of texture and SNR). The output of the classifier is the selection of the best performing color constancy method for a certain image. Experimental results show a large improvement over state-of-the-art single algorithms. On a data set consisting of more than 11,000 images, an increase in color constancy performance up to 20% (median angular error) can be obtained compared to the best-performing single algorithm. Further, it is shown that for certain scene categories, one specific color constancy algorithm can be used instead of the classifier considering several algorithms.

Reduced-reference (RR) image quality assessment (IQA) has been recognized as an effective and efficient way to predict the visual quality of distorted images. The current standard is the wavelet-domain natural image statistics model (WNISM), which applies the Kullback-Leibler divergence between the marginal distributions of wavelet coefficients of the reference and distorted images to measure the image distortion. However, WNISM fails to consider the statistical correlations of wavelet coefficients in different subbands and the visual response characteristics of the mammalian cortical simple cells. In addition, wavelet transforms are optimal greedy approximations to extract singularity structures, so they fail to explicitly extract the image geometric information, e.g., lines and curves. Finally, wavelet coefficients are dense for smooth image edge contours. In this paper, to target the aforementioned problems in IQA, we develop a novel framework for IQA to mimic the human visual system (HVS) by incorporating the merits from multiscale geometric analysis (MGA), contrast sensitivity function (CSF), and the Weber's law of just noticeable difference (JND). In the proposed framework, MGA is utilized to decompose images and then extract features to mimic the multichannel structure of HVS. Additionally, MGA offers a series of transforms including wavelet, curvelet, bandelet, contourlet, wavelet-based contourlet transform (WBCT), and hybrid wavelets and directional filter banks (HWD), and different transforms capture different types of image geometric information. CSF is applied to weight coefficients obtained by MGA to simulate the appearance of images to observers by taking into account many of the nonlinearities inherent in HVS. JND is finally introduced to produce a noticeable variation in sensory experience. Thorough empirical studies are carried out upon the LIVE database against subjective mean opinion score (MOS) and demonstrate that 1) the proposed framework has good consistency with subjective perception values and the objective assessment results can well reflect the visual quality of images, 2) different transforms in MGA under the new framework perform better than the standard WNISM and some of them even perform better than the standard full-reference IQA model, i.e., the mean structural similarity index, and 3) HWD performs best among all transforms in MGA under the framework.

At scotopic luminance level, investigators reported that both contrast sensitivity and acuity are greatly reduced relative to photopic level. In this study, we investigated whether spatial frequency (SF) discrimination is similarly degraded at scotopic level. For this purpose, we measured SF discrimination at an eccentricity of 8 o in the temporal retina using high contrast spatially localized stimuli with 1 octave Fourier bandwidths (sixth derivative of spatial Gaussian Vimal 2 function). Data were collected at luminance of 27.5 cd/m 2 (photopic) and 6.3 x 10 -4 cd/m 2 (scotopic). Discrimination was measured over a range from 0.25 to 1.19 cpd in 0.25 octave steps because the scotopic acuity under these conditions was about 2 cpd. Results show that percent discrimination thresholds were slightly lower (on average) under photopic condition for two out of three subjects, but were about the same as scotopic thresholds for the third subject. However, photopic discrimination was generally worse than scotopic when photopic contrasts were scaled down so as to be the same factor above threshold as were the scotopic contrasts. These data led us to conclude that the scotopic (rod) visual system appears capable of processing spatial (hyperacuity) information over its restricted dynamic range with at least as much accuracy as the photopic (cone) system.

We develop a code length principle which is invariant to the choice of parameterization on the model distributions. An invariant approximation formula for easy computation of the marginal distribution is provided for gaussian likelihood models. We provide invariant estimators of the model parameters and formulate conditions under which these estimators are essentially posteriori unbiased for gaussian models. An upper bound on the coarseness of discretization on the model parameters is deduced. We introduce a discrimination measure between probability distributions and use it to construct probability distributions on model classes. The total code length is shown to be closely related to the NML code length of Rissanen when choosing Jeffreys prior distribution on the model parameters together with a uniform prior distribution on the model classes. Our model selection principle is applied to a gaussian estimation problem for data in a wavelet representation and its performance is tested and compared to alternative wavelet-based estimation methods in numerical experiments.

In order to account for the rapidity of visual processing, we explore visual coding strategies using a one-pass feed-forward spiking neural network. We based our model on the work of Van Rullen and Thorpe Neural Comput. 13 (6) (2001) 1255, which constructs a retinal representation using an orthogonal wavelet transform. This strategy provides a spike code, thanks to a rank order coding scheme which o ers an alternative to the classical spike frequency coding scheme. We extended this model to e cient representations in arbitrary linear generative models by implementing lateral interactions on top of this feed-forward model. This method uses a matching pursuit scheme-recursively detecting in the image the best match with the elements of a dictionary and then subtracting it-and which may similarly deÿne a visual spike code. In particular, this transform could be used with large and arbitrary dictionaries, so that we may deÿne an over-complete representation which may deÿne an e cient sparse spike coding scheme in arbitrary multi-layered architectures. We show here extensions of this method of computing with spike events, introducing an adaptive scheme leading to the emergence of V1-like receptive ÿelds and then a model of bottom-up saliency pursuit.

Statistical models of natural images provide an important tool for researchers in the fields of machine learning and computational neuroscience. The canonical measure to quantitatively assess and compare the performance of statistical models is given by the likelihood. One class of statistical models which has recently gained increasing popularity and has been applied to a variety of complex data is formed by deep belief networks. Analyses of these models, however, have often been limited to qualitative analyses based on samples due to the computationally intractable nature of their likelihood. Motivated by these circumstances, the present article introduces a consistent estimator for the likelihood of deep belief networks which is computationally tractable and simple to apply in practice. Using this estimator, we quantitatively investigate a deep belief network for natural image patches and compare its performance to the performance of other models for natural image patches. We find that the deep belief network is outperformed with respect to the likelihood even by very simple mixture models.

We develop a code length principle which is invariant to the choice of parameterization on the model distributions. An invariant approximation formula for easy computation of the marginal distribution is provided for gaussian likelihood models. We provide invariant estimators of the model parameters and formulate conditions under which these estimators are essentially posteriori unbiased for gaussian models. An upper bound on the coarseness of discretization on the model parameters is deduced. We introduce a discrimination measure between probability distributions and use it to construct probability distributions on model classes. The total code length is shown to equal the NML code length of Rissanen to within an additive constant when choosing Je#reys prior distribution on the model parameters together with a particular choice of prior distribution on the model classes. Our model selection principle is applied to a gaussian estimation problem for data in a wavelet representation a...

Recently, applied mathematicians have been pursuing the goal of sparse coding of certain mathematical models of images with edges. They have found by mathematical analysis that, instead of wavelets and Fourier methods, sparse coding leads towards new systems: ridgelets and curvelets. These new systems have elements distributed across a range of scales and locations, but also orientations. In fact they have highly direction-specific elements and exhibit increasing numbers of distinct directions as we go to successively finer scales.

Statistical models of natural images provide an important tool for researchers in the fields of machine learning and computational neuroscience. The canonical measure to quantitatively assess and compare the performance of statistical models is given by the likelihood. One class of statistical models which has recently gained increasing popularity and has been applied to a variety of complex data is formed by deep belief networks. Analyses of these models, however, have often been limited to qualitative analyses based ...

s Abstract It has long been assumed that sensory neurons are adapted, through both evolutionary and developmental processes, to the statistical properties of the signals to which they are exposed. and proposed that information theory could provide a link between environmental statistics and neural responses through the concept of coding efficiency. Recent developments in statistical modeling, along with powerful computational tools, have enabled researchers to study more sophisticated statistical models for visual images, to validate these models empirically against large sets of data, and to begin experimentally testing the efficient coding hypothesis for both individual neurons and populations of neurons.

Recently Arnold (2011) asked “Why is binocular rivalry uncommon?”. He answered in an entertainingly written, provocative article, for which I thank and congratulate him. However, I will argue that Arnold’s answer falls short in two respects and his assumption that rivalry is uncommon is correct for two reasons other than the one he discusses.

To understand possible strategies of temporal spike coding in the central nervous system, we study functional neuromimetic models of visual processing for static images. We will first present the retinal model which was introduced by Van Rullen and Thorpe [1] and which represents the multi-scale contrast values of the image using an orthonormal wavelet transform. These analog values activate a set of spiking neurons which each fire once to produce an asynchronous wave of spikes. According to this model, the image may be progressively reconstructed from this spike wave thanks to regularities in the statistics of the coefficients determined with natural images. Here, we study mathematically how the quality of information transmission carried by this temporal representation varies over time. In particular, we study how these regularities can be used to optimize information transmission by using a form of temporal cooperation of neurons to code analog values. The original model used wavelet transforms that are close to orthogonal. However, the selectivity of realistic neurons overlap, and we propose an extension of the previous model by adding a spatial cooperation between filters. This model extends the previous scheme for arbitrary -and possibly non-orthogonalrepresentations of features in the images. In particular, we compared the performance of increasingly over-complete representations in the retina. Results show that this algorithm provides an efficient spike coding strategy for low-level visual processing which may adapt to the complexity of the visual input. ), M. Samuelides with DTIM/ONERA, France and S. Thorpe with CerCo/CNRS

As an alternative to classical representations in machine learning algorithms, we explore coding strategies using events as is observed for spiking neurons in the central nervous system. Focusing on visual processing, we have previously shown that we may define a sparse spike coding scheme by implementing accordingly lateral interactions . This class of algorithms is both compatible with biological constraints and also to neurophysiological observations and provides a possible algorithm to explain the speed of visual processing despite the relatively slow time of response of single neurons. We explore here learning mechanisms to unsupervisely derive a overcomplete set of filters which provide a sparse representation of the input. We first based this work on previous work of and the results leads to similar results on the same architecture, suggesting that this provide a neural implementation to Blind Source Separation. However, this neuromimetic algorithm may be more easily extended to realistic architectures of cortical columns in the primary visual cortex. We show results for simple models of cortical colums but also for a strategy of higher-order representation.

According to Marr's paradigm of computational vision the first process is an extraction of relevant features. The goal of this paper is to quantify and characterize the information carried by features using imagestructure measured at feature-points to reconstruct images. In this way, we indirectly evaluate the concept of feature-based image analysis. The main conclusions are that (i) a reasonably low number of features characterize the image to such a high degree, that visually appealing reconstructions are possible, (ii) different feature-types complement each other and all carry important information. The strategy is to define metamery classes of images and examine the information content of a canonical least informative representative of this class. Algorithms for identifying these are given. Finally, feature detectors localizing the most informative points relative to different complexity measures derived from models of natural image statistics, are given.

Perceptual grouping of the complete boundaries of objects in natural images remains an unsolved problem in computer vision. The computational complexity of the problem and difficulties capturing global constraints limit the performance of current algorithms. In this paper we develop a coarse-to-fine Bayesian algorithm which addresses these constraints. Candidate contours are extracted at a coarse scale and then used to generate spatial priors on the location of possible contours at finer scales. In this way, a rough estimate of the shape of an object is progressively refined. The coarse estimate provides robustness to texture and clutter while the refinement process allows for the extraction of detailed object contours. The grouping algorithm is probabilistic and uses multiple grouping cues derived from natural scene statistics. We present a quantitative evaluation of grouping performance on the Berkeley Segmentation Database, and show that the multi-scale approach outperforms several single-scale contour extraction algorithms.

The increasing photorealism for computer graphics has made computer graphics a convincing form of image forgery. Therefore, classifying photographic images and photorealistic computer graphics has become an important problem for image forgery detection. In this paper, we propose a new geometrybased image model, motivated by the physical image generation process, to tackle the above-mentioned problem. The proposed model reveals certain physical differences between the two image categories, such as the gamma correction in photographic images and the sharp structures in computer graphics. For the problem of image forgery detection, we propose two levels of image authenticity definition, i.e., imaging-process authenticity and scene authenticity, and analyze our technique against these definitions. Such definition is important for making the concept of image authenticity computable. Apart from offering physical insights, our technique with a classification accuracy of 83.5% outperforms those in the prior work, i.e., wavelet features at 80.3% and cartoon features at 71.0%. We also consider a recapturing attack scenario and propose a counter-attack measure. In addition, we constructed a publicly available benchmark dataset with images of diverse content and computer graphics of high photorealism.

The visual appearance of natural scenes is governed by a surprisingly simple hidden structure. The distributions of contrast values in natural images generally follow a Weibull distribution, with beta and gamma as free parameters. Beta and gamma seem to structure the space of natural images in an ecologically meaningful way, in particular with respect to the fragmentation and texture similarity within an image. Since it is often assumed that the brain exploits structural regularities in natural image statistics to efficiently encode and analyze visual input, we here ask ourselves whether the brain approximates the beta and gamma values underlying the contrast distributions of natural images. We present a model that shows that beta and gamma can be easily estimated from the outputs of X-cells and Y-cells. In addition, we covaried the EEG responses of subjects viewing natural images with the beta and gamma values of those images. We show that beta and gamma explain up to 71% of the variance of the early ERP signal, substantially outperforming other tested contrast measurements. This suggests that the brain is strongly tuned to the image's beta and gamma values, potentially providing the visual system with an efficient way to rapidly classify incoming images on the basis of omnipresent low-level natural image statistics.

We develop a code length principle which is invariant to the choice of parameterization on the model distributions. An invariant approximation formula for easy computation of the marginal distribution is provided for gaussian likelihood models. We provide invariant estimators of the model parameters and formulate conditions under which these estimators are essentially posteriori unbiased for gaussian models. An upper bound on the coarseness of discretization on the model parameters is deduced. We introduce a discrimination measure between probability distributions and use it to construct probability distributions on model classes. The total code length is shown to be closely related to the NML code length of Rissanen when choosing Jeffreys prior distribution on the model parameters together with a uniform prior distribution on the model classes. Our model selection principle is applied to a gaussian estimation problem for data in a wavelet representation and its performance is tested and compared to alternative wavelet-based estimation methods in numerical experiments.

Among the denoising methods studied, those operating in the wavelet domain are the VII basis of the study presented in this Thesis. In addition, two methods such as the Wiener filter and the non local means filter NLM, operating in the image domain, are used as a reference to compare the wavelet filters.

In order to account for the rapidity of visual processing, we explore visual coding strategies using a one-pass feed-forward spiking neural network. We based our model on the work of Van Rullen and Thorpe Neural Comput. 13 (6) (2001) 1255, which constructs a retinal representation using an orthogonal wavelet transform. This strategy provides a spike code, thanks to a rank order coding scheme which o ers an alternative to the classical spike frequency coding scheme. We extended this model to e cient representations in arbitrary linear generative models by implementing lateral interactions on top of this feed-forward model. This method uses a matching pursuit scheme-recursively detecting in the image the best match with the elements of a dictionary and then subtracting it-and which may similarly deÿne a visual spike code. In particular, this transform could be used with large and arbitrary dictionaries, so that we may deÿne an over-complete representation which may deÿne an e cient sparse spike coding scheme in arbitrary multi-layered architectures. We show here extensions of this method of computing with spike events, introducing an adaptive scheme leading to the emergence of V1-like receptive ÿelds and then a model of bottom-up saliency pursuit.

Image analysis in the visual system is well adapted to the statistics of natural scenes. Investigations of natural image statistics have so far mainly focused on static features. We present a method to investigate the statistics of natural optic flow fields related to self-motion within natural scenes and present first results of a statistical analysis.

People can recognize the meaning or gist of a scene from a single glance, and a few recent studies have begun to examine the sorts of information that contribute to scene gist recognition. The authors of the present study used visual masking coupled with image manipulations (randomizing phase while maintaining the Fourier amplitude spectrum; random image structure evolution [RISE]; J. Sadr & P. Sinha, 2004) to explore whether and when unlocalized Fourier amplitude information contributes to gist perception. In 4 experiments, the authors found that differences between scene categories in the Fourier amplitude spectrum are insufficient for gist recognition or gist masking. Whereas the global 1/f spatial frequency amplitude spectra of scenes plays a role in gist masking, local phase information is necessary for gist recognition and for the strongest gist masking. Moreover, the ability to recognize the gist of a target image was influenced by mask recognizability, suggesting that conceptual masking occurs even at the earliest stages of scene processing.

Adaptive data-driven dictionaries for sparse approximations provide superior performance compared to predefined dictionaries in applications involving representation and classification of data. In this paper, we propose a novel algorithm for learning global dictionaries particularly suited to the sparse representation of natural images. The proposed algorithm uses a hierarchical energy based learning approach to learn a multilevel dictionary. The atoms that contribute the most energy to the representation are learned in the first level and those that contribute lesser energies are learned in the subsequent levels. The learned multilevel dictionary is compared to a dictionary learned using the K-SVD algorithm. Reconstruction results using a small number of non-zero coefficients demonstrate the advantage of exploiting energy hierarchy using multilevel dictionaries, pointing to potential applications in low bit-rate image compression. Superior performance in compressed sensing using optimized sensing matrices with small number of measurements is also demonstrated.

The visual appearance of natural scenes is governed by a surprisingly simple hidden structure. The distributions of contrast values in natural images generally follow a Weibull distribution, with beta and gamma as free parameters. Beta and gamma seem to structure the space of natural images in an ecologically meaningful way, in particular with respect to the fragmentation and texture similarity within an image. Since it is often assumed that the brain exploits structural regularities in natural image statistics to efficiently encode and analyze visual input, we here ask ourselves whether the brain approximates the beta and gamma values underlying the contrast distributions of natural images. We present a model that shows that beta and gamma can be easily estimated from the outputs of X-cells and Y-cells. In addition, we covaried the EEG responses of subjects viewing natural images with the beta and gamma values of those images. We show that beta and gamma explain up to 71% of the variance of the early ERP signal, substantially outperforming other tested contrast measurements. This suggests that the brain is strongly tuned to the image's beta and gamma values, potentially providing the visual system with an efficient way to rapidly classify incoming images on the basis of omnipresent low-level natural image statistics.

We present a generic and robust approach for scene categorization. A complex scene is described by proto-concepts like vegetation, water, fire, sky etc. These proto-concepts are represented by low level features, where we use natural images statistics to compactly represent color invariant texture information by a Weibull distribution. We introduce the notion of contextures which preserve the context of textures in a visual scene with an occurrence histogram (context) of similarities to proto-concept descriptors (texture). In contrast to a codebook approach, we use the similarity to all vocabulary elements to generalize beyond the code words. Visual descriptors are attained by combining different types of contexts with different texture parameters. The visual scene descriptors are generalized to visual categories by training a support vector machine. We evaluate our approach on 3 different datasets: 1) 50 categories for the TRECVID video dataset; 2) the Caltech 101-object images; 3) 89 categories being the intersection of the Corel photo stock with the Art Explosion photo stock. Results show that our approach is robust over different datasets, while maintaining competitive performance.

Perceptual grouping of the complete boundaries of objects in natural images remains an unsolved problem in computer vision. The computational complexity of the problem and difficulties capturing global constraints limit the performance of current algorithms. In this paper we develop a coarse-to-fine Bayesian algorithm which addresses these constraints. Candidate contours are extracted at a coarse scale and then used to generate spatial priors on the location of possible contours at finer scales. In this way, a rough estimate of the shape of an object is progressively refined. The coarse estimate provides robustness to texture and clutter while the refinement process allows for the extraction of detailed object contours. The grouping algorithm is probabilistic and uses multiple grouping cues derived from natural scene statistics. We present a quantitative evaluation of grouping performance on the Berkeley Segmentation Database, and show that the multi-scale approach outperforms several single-scale contour extraction algorithms.

Advances in our understanding of natural image statistics and of gain control within the retinal circuitry are leading to new insights into the classic problem of retinal light adaptation. Here we review what we know about how rapid adaptation occurs during active exploration of the visual scene. Adaptational mechanisms must balance the competing demands of adapting quickly, locally, and reliably, and this balance must be maintained as lighting conditions change. Multiple adaptational mechanisms in different locations within the retina act in concert to accomplish this task, with lighting conditions dictating which mechanisms dominate.

We consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent (also known as factorial). A widely studied family of solutions, generally known as independent components analysis (ICA), exists for the case when the signal is generated as a linear transformation of independent non-Gaussian sources. Here, we examine a complementary case, in which the signal density is non-Gaussian but elliptically symmetric. In this case, no linear transform suffices to properly decompose the signal into independent components, and thus, the ICA methodology fails. We show that a simple nonlinear transformation, which we call radial Gaussianization (RG), provides an exact solution for this case. We then examine this methodology in the context of natural image statistics, demonstrating that joint statistics of spatially proximal coefficients in a multi-scale image representation are better described as elliptical than factorial. We quantify this by showing that reduction in dependency achieved by RG is far greater than that achieved by ICA, for local spatial neighborhoods. We also show that the RG transformation may be closely approximated by divisive normalization transformations that have been used to model the nonlinear response properties of visual neurons, and that have been shown to reduce dependences between multi-scale image coefficients.

Computer graphics as well as related disciplines often benefit from
understanding the human visual system and its input. In this paper,
we study statistical regularities of both conventional as well as
high dynamic range images, and find that several commonly held
wisdoms regarding natural image statistics do not directly apply to
high dynamic range data. These results have implications for both
the study of human vision, as well as for the design of algorithms in
computer graphics and computer vision that rely on such statistical
regularities.

Viewers can recognize the gist of a scene (i.e., its holistic semantic representation, such as its category) in less time than a single fixation, and backward masking has traditionally been employed as a means to determine that time course. The masks used in those paradigms are often characterized by either specific amplitude spectra only, or amplitude and phase spectra-defined structural properties. However, it remains unclear whether there would be a differential contribution of amplitude only or amplitude + phase defined image statistics to the effective backward masking of rapid scene categorization. The current study addresses this issue. Experiments 1–3 explored amplitude spectra defined contributions to category masking and revealed that the slope of the amplitude spectrum was more important for modulating scene category masking strength than amplitude orientation. Further, the masking effects followed an “amplitude spectrum slope similarity principle” whereby the more similar the amplitude spectrum slope of the mask was to the target's amplitude spectrum slope, the stronger the masking. Experiment 5 showed that, when holding mask amplitude spectrum slope approximately constant, both categorically specific unrecognizable amplitude only and amplitude + phase statistical regularities disrupted rapid scene categorization. Specifically, the masking effects observed in Experiment 5 followed a target-mask categorical dissimilarity principle whereby the more dissimilar the mask category is to the target image category, the stronger the masking. Overall, the results support the notion that amplitude only or amplitude + phase-defined image statistics differentially contribute to the effective backward masking of rapid scene gist recognition.

Computer graphics as well as related disciplines often benefit from understanding the human visual system and its input. In this paper, we study statistical regularities of both conventional as well as high dynamic range images, and find that several commonly held wisdoms regarding natural image statistics do not directly apply to high dynamic range data. These results have implications for both the study of human vision, as well as for the design of algorithms in computer graphics and computer vision that rely on such statistical regularities.

We present a probabilistic model for natural images that is based on mixtures of Gaussian scale mixtures and a simple multiscale representation. We show that it is able to generate images with interesting higher-order correlations when trained on natural images or samples from an occlusion-based model. More importantly, our multiscale model allows for a principled evaluation. While it is easy to generate visually appealing images, we demonstrate that our model also yields the best performance reported to date when evaluated with respect to the cross-entropy rate, a measure tightly linked to the average log-likelihood. The ability to quantitatively evaluate our model differentiates it from other multiscale models, for which evaluation of these kinds of measures is usually intractable.