Fields of Experts: A Framework for Learning Image Priors

Roth, Stefan; Black, Michael J.

doi:10.1109/cvpr.2005.160

Cited by 829 publications

(739 citation statements)

References 24 publications

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“…The pairwise MRFs employed here are very similar to models that have been popular for a long time [10]; the higher-order MRFs follow the recently proposed Fields-of-Experts (FoE) approach [9]. Richer models of natural images have also been proposed on the basis of MRFs with multiple pairwise pixel interactions [11,12].…”

Section: Learning Markov Random Field Models Of Imagesmentioning

confidence: 99%

“…The Fields-of-Experts framework [9] used in the higher-order MRF case models the clique potentials using a so-called Product of Experts (PoE) [14]. The idea behind the PoE is to model complex distributions as the product of several simpler expert distributions that each work on a low-dimensional subspace, in this case a linear 1D subspace.…”

Section: Learning Markov Random Field Models Of Imagesmentioning

confidence: 99%

“…Such approaches have lacked the representational power needed to capture the rich statistics of natural scenes. The second line of research involves improving the expressive power of MRFs with higher-order models that are learned from data [7,8,9]. These approaches better capture the rich statistics of the natural world and…”

Section: Introductionmentioning

confidence: 99%

“…Throughout the paper we develop and test our solutions in the context of image denoising to illustrate the power of learned MRFs and the applicability of BP to these models. In particular, we exploit the recently proposed Field-of-Experts (FoE) model for learning MRFs from example data [9]. We start with the case of pairwise MRFs, where previous work on efficient inference schemes has relied on ad hoc potentials such as the Potts model [1] or the truncated quadratic [4].…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, following [9] we take the experts to be Student t-distributions. Assuming that we use K experts, we can write the prior probability of an image under the FoE model as…”

Section: Learning Markov Random Field Models Of Imagesmentioning

confidence: 99%

See 4 more Smart Citations

Efficient Belief Propagation with Learned Higher-Order Markov Random Fields

Lan

Roth

Huttenlocher

et al. 2006

Lecture Notes in Computer Science

165

167

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Abstract. Belief propagation (BP) has become widely used for low-level vision problems and various inference techniques have been proposed for loopy graphs. These methods typically rely on ad hoc spatial priors such as the Potts model. In this paper we investigate the use of learned models of image structure, and demonstrate the improvements obtained over previous ad hoc models for the image denoising problem. In particular, we show how both pairwise and higher-order Markov random fields with learned clique potentials capture rich image structures that better represent the properties of natural images. These models are learned using the recently proposed Fields-of-Experts framework. For such models, however, traditional BP is computationally expensive. Consequently we propose some approximation methods that make BP with learned potentials practical. In the case of pairwise models we propose a novel approximation of robust potentials using a finite family of quadratics. In the case of higher order MRFs, with 2 × 2 cliques, we use an adaptive state space to handle the increased complexity. Extensive experiments demonstrate the power of learned models, the benefits of higher-order MRFs and the practicality of BP for these problems with the use of simple principled approximations.

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Section: Learning Markov Random Field Models Of Imagesmentioning

confidence: 99%

Section: Learning Markov Random Field Models Of Imagesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Consequently, following [9] we take the experts to be Student t-distributions. Assuming that we use K experts, we can write the prior probability of an image under the FoE model as…”

Section: Learning Markov Random Field Models Of Imagesmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Belief Propagation with Learned Higher-Order Markov Random Fields

Lan

Roth

Huttenlocher

et al. 2006

Lecture Notes in Computer Science

165

167

View full text Add to dashboard Cite

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Robustness and exploration of variational and machine learning approaches to inverse problems: An overview

Auras,

Gandikota,

Droege

et al. 2024

GAMM-Mitteilungen

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This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one‐dimensional toy problem are provided, showing the robustness of different approaches and empirically verifying theoretical guarantees. Another focus of this review is the exploration of the subspace of data‐consistent solutions through explicit guidance to satisfy specific semantic or textural properties.

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Neural‐network‐based regularization methods for inverse problems in imaging

Habring,

Holler

2024

GAMM-Mitteilungen

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This review provides an introduction to—and overview of—the current state of the art in neural‐network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for regularizing inverse problems in imaging. Distinguishing features of this review are, among others, an easily accessible introduction to learned generators and learned priors, in particular diffusion models, for inverse problems, and a section focusing explicitly on existing results in function space analysis of neural‐network‐based approaches in this context.

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Fields of Experts: A Framework for Learning Image Priors

Abstract: We develop a framework for learning generic

Cited by 829 publications

References 24 publications

Efficient Belief Propagation with Learned Higher-Order Markov Random Fields

Efficient Belief Propagation with Learned Higher-Order Markov Random Fields

Robustness and exploration of variational and machine learning approaches to inverse problems: An overview

Neural‐network‐based regularization methods for inverse problems in imaging

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