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168
Fields of experts: A framework for learning image priors
 In CVPR
, 2005
"... We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov Random Field (MRF) models by learning potential functions over extended pixel neighborhood ..."
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Cited by 277 (4 self)
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We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach extends traditional Markov Random Field (MRF) models by learning potential functions over extended pixel neighborhoods. Field potentials are modeled using a ProductsofExperts framework that exploits nonlinear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field of Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with and even outperform specialized techniques. 1.
Sparse representation for color image restoration
 the IEEE Trans. on Image Processing
, 2007
"... Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted ..."
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Cited by 172 (26 self)
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Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted dictionaries for images has been a major challenge. The KSVD has been recently proposed for this task [1], and shown to perform very well for various grayscale image processing tasks. In this paper we address the problem of learning dictionaries for color images and extend the KSVDbased grayscale image denoising algorithm that appears in [2]. This work puts forward ways for handling nonhomogeneous noise and missing information, paving the way to stateoftheart results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper. EDICS Category: COLCOLR (Color processing) I.
On Advances in Statistical Modeling of Natural Images
 Journal of Mathematical Imaging and Vision
, 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 modelin ..."
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Cited by 133 (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.
Minimizing nonsubmodular functions with graph cuts  a review
 TPAMI
, 2007
"... Optimization techniques based on graph cuts have become a standard tool for many vision applications. These techniques allow to minimize efficiently certain energy functions corresponding to pairwise Markov Random Fields (MRFs). Currently, there is an accepted view within the computer vision communi ..."
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Cited by 132 (8 self)
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Optimization techniques based on graph cuts have become a standard tool for many vision applications. These techniques allow to minimize efficiently certain energy functions corresponding to pairwise Markov Random Fields (MRFs). Currently, there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of MRF energies (e.g. submodular functions). In this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions (in particular, nonsubmodular functions). While these results are wellknown in the optimization community, to our knowledge they were not used in the context of computer vision and MRF optimization. We demonstrate the relevance of these results to vision on the problem of binary texture restoration.
Diffusion snakes: introducing statistical shape knowledge into the MumfordShah functional
 J. OF COMPUTER VISION
, 2002
"... We present a modification of the MumfordShah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneit ..."
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Cited by 123 (15 self)
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We present a modification of the MumfordShah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes. We propose a closedform, parameterfree solution for incorporating invariance with respect to similarity transformations in the variational framework. We show segmentation results on artificial and realworld images with and without prior shape information. In the cases of noise, occlusion or strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by a level set implementation of geodesic active contours.
On the Spatial Statistics of Optical Flow
 In ICCV
, 2005
"... We develop a method for learning the spatial statistics of optical flow fields from a novel training database. Training flow fields are constructed using range images of natural scenes and 3D camera motions recovered from handheld and carmounted video sequences. A detailed analysis of optical flow ..."
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Cited by 97 (8 self)
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We develop a method for learning the spatial statistics of optical flow fields from a novel training database. Training flow fields are constructed using range images of natural scenes and 3D camera motions recovered from handheld and carmounted video sequences. A detailed analysis of optical flow statistics in natural scenes is presented and machine learning methods are developed to learn a Markov random field model of optical flow. The prior probability of a flow field is formulated as a FieldofExperts model that captures the higher order spatial statistics in overlapping patches and is trained using contrastive divergence. This new optical flow prior is compared with previous robust priors and is incorporated into a recent, accurate algorithm for dense optical flow computation. Experiments with natural and synthetic sequences illustrate how the learned optical flow prior quantitatively improves flow accuracy and how it captures the rich spatial structure found in natural scene motion.
Advances and Challenges in SuperResolution
 International Journal of Imaging Systems and Technology
, 2004
"... Superresolution reconstruction produces one or a set of highresolution images from a sequence of lowresolution frames. This paper reviews a variety of superresolution methods proposed in the last twenty years, and provides some insight to, and a summary of, our recent contributions to the gen ..."
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Cited by 88 (14 self)
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Superresolution reconstruction produces one or a set of highresolution images from a sequence of lowresolution frames. This paper reviews a variety of superresolution methods proposed in the last twenty years, and provides some insight to, and a summary of, our recent contributions to the general superresolution problem. In the process, a detailed study of several very important aspects of superresolution, often ignored in the literature, is presented. Specifically, we discuss robustness, treatment of color, and dynamic operation modes. Novel methods for addressing these issues are accompanied by experimental results on simulated and real data. Finally, some future challenges in superresolution are outlined and discussed.
Statistical edge detection: learning and evaluating edge cues
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... We formulate edge detection as statistical inference. This statistical edge detection is data driven, unlike standard methods for edge detection which are model based. For any set of edge detection filters (implementing local edge cues) we use presegmented images to learn the probability distributi ..."
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Cited by 86 (10 self)
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We formulate edge detection as statistical inference. This statistical edge detection is data driven, unlike standard methods for edge detection which are model based. For any set of edge detection filters (implementing local edge cues) we use presegmented images to learn the probability distributions of filter responses conditioned on whether they are evaluated on or off an edge. Edge detection is formulated as a discrimination task specified by a likelihood ratio test on the filter responses. This approach emphasizes the necessity of modeling the image background (the offedges). We represent the conditional probability distributions nonparametrically and learn them on two different datasets of 100 (Sowerby) and 50 (South Florida) images. Multiple edges cues, including chrominance and multiplescale, are combined by using their joint distributions. Hence this cue combination is optimal in the statistical sense. We evaluate the effectiveness of different visual cues using the Chernoff information and Receiver Operator Characteristic (ROC) curves. This shows that our approach gives quantitatively better results than the Canny edge detector when the image background contains significant clutter. In addition, it enables us to determine the effectiveness of different edge cues and gives quantitative measures for the advantages of multilevel processing, for the use of chrominance, and for the relative effectiveness of different detectors. Furthermore, we show that we can learn these conditional distributions on one dataset and adapt them to the other with only slight degradation of performance without knowing the ground truth on the second dataset. This shows that our results are not purely domain specific. We apply the same approach to the spatial grouping of edge cues and obtain analogies to nonmaximal suppression and hysteresis.
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 85 (1 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.
What makes a good model of natural images
 in: CVPR 2007: Proceedings of the 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Computer Society
, 2007
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