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A trainable filter-based higher-order Markov Random Fields (MRFs) model - the so called Fields of Experts (FoE), has proved a highly effective image prior model for many classic image restoration problems. Generally, two options are…

Computer Vision and Pattern Recognition · Computer Science 2015-10-27 Yunjin Chen

Consider $n$ random variables forming a Markov random field (MRF). The true model of the MRF is unknown, and it is assumed to belong to a binary set. The objective is to sequentially sample the random variables (one-at-a-time) such that the…

Methodology · Statistics 2020-08-04 Javad Heydari , Ali Tajer , H. Vincent Poor

Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming…

Machine Learning · Computer Science 2021-05-04 Chirag Pabbaraju , Po-Wei Wang , J. Zico Kolter

It is now well known that Markov random fields (MRFs) are particularly effective for modeling image priors in low-level vision. Recent years have seen the emergence of two main approaches for learning the parameters in MRFs: (1)…

Computer Vision and Pattern Recognition · Computer Science 2014-01-17 Yunjin Chen , Thomas Pock , René Ranftl , Horst Bischof

Semantic segmentation tasks can be well modeled by Markov Random Field (MRF). This paper addresses semantic segmentation by incorporating high-order relations and mixture of label contexts into MRF. Unlike previous works that optimized MRFs…

Computer Vision and Pattern Recognition · Computer Science 2017-08-09 Ziwei Liu , Xiaoxiao Li , Ping Luo , Chen Change Loy , Xiaoou Tang

The Fields of Experts (FoE) image prior model, a filter-based higher-order Markov Random Fields (MRF) model, has been shown to be effective for many image restoration problems. Motivated by the successes of FoE-based approaches, in this…

Computer Vision and Pattern Recognition · Computer Science 2015-06-19 Yunjin Chen , Wensen Feng , René Ranftl , Hong Qiao , Thomas Pock

In this paper, we study the problem of inferring time-varying Markov random fields (MRF), where the underlying graphical model is both sparse and changes sparsely over time. Most of the existing methods for the inference of time-varying…

Machine Learning · Computer Science 2021-02-09 Salar Fattahi , Andres Gomez

In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…

Emerging Technologies · Computer Science 2025-01-03 Timothe Presles , Cyrille Enderli , Gilles Burel , El Houssain Baghious

A large number of problems in computer vision can be modelled as energy minimization problems in a Markov Random Field (MRF) or Conditional Random Field (CRF) framework. Graph-cuts based $\alpha$-expansion is a standard move-making method…

Computer Vision and Pattern Recognition · Computer Science 2014-03-26 Vibhav Vineet , Jonathan Warrell , Philip H. S. Torr

Stereo matching is a core task for many computer vision and robotics applications. Despite their dominance in traditional stereo methods, the hand-crafted Markov Random Field (MRF) models lack sufficient modeling accuracy compared to…

Computer Vision and Pattern Recognition · Computer Science 2024-10-24 Tongfan Guan , Chen Wang , Yun-Hui Liu

Dense conditional random fields (CRFs) have become a popular framework for modelling several problems in computer vision such as stereo correspondence and multi-class semantic segmentation. By modelling long-range interactions, dense CRFs…

Computer Vision and Pattern Recognition · Computer Science 2018-10-29 Thomas Joy , Alban Desmaison , Thalaiyasingam Ajanthan , Rudy Bunel , Mathieu Salzmann , Pushmeet Kohli , Philip H. S. Torr , M. Pawan Kumar

Recent Large Reasoning Models (LRMs) have achieved remarkable performance in solving complex problems via supervised fine-tuning (SFT) and reinforcement learning (RL). Although existing RL algorithms significantly enhance model accuracy,…

Artificial Intelligence · Computer Science 2025-10-20 Zezhong Tan , Hang Gao , Xinhong Ma , Feng Zhang , Ziqiang Dong

This paper addresses semantic image segmentation by incorporating rich information into Markov Random Field (MRF), including high-order relations and mixture of label contexts. Unlike previous works that optimized MRFs using iterative…

Computer Vision and Pattern Recognition · Computer Science 2015-09-25 Ziwei Liu , Xiaoxiao Li , Ping Luo , Chen Change Loy , Xiaoou Tang

In modern astrophysics, the machine learning has increasingly gained more popularity with its incredibly powerful ability to make predictions or calculated suggestions for large amounts of data. We describe an application of the supervised…

Astrophysics of Galaxies · Physics 2018-12-26 Yu Bai , JiFeng Liu , Song Wang , Fan Yang

We propose a general and versatile framework that significantly speeds-up graphical model optimization while maintaining an excellent solution accuracy. The proposed approach relies on a multi-scale pruning scheme that is able to…

Computer Vision and Pattern Recognition · Computer Science 2014-09-16 B. Conejo , N. Komodakis , S. Leprince , J. P. Avouac

While the literature has been fairly dense in the areas of scene understanding and semantic labeling there have been few works that make use of motion cues to embellish semantic performance and vice versa. In this paper, we address the…

Computer Vision and Pattern Recognition · Computer Science 2015-04-27 N. Dinesh Reddy , Prateek Singhal , K. Madhava Krishna

Incremental methods for structure learning of pairwise Markov random fields (MRFs), such as grafting, improve scalability by avoiding inference over the entire feature space in each optimization step. Instead, inference is performed over an…

Machine Learning · Computer Science 2018-05-22 Walid Chaabene , Bert Huang

Extreme classification seeks to assign each data point, the most relevant labels from a universe of a million or more labels. This task is faced with the dual challenge of high precision and scalability, with millisecond level prediction…

Machine Learning · Computer Science 2019-05-29 Ankit Jalan , Purushottam Kar

This paper introduces a novel algorithm for transductive inference in higher-order MRFs, where the unary energies are parameterized by a variable classifier. The considered task is posed as a joint optimization problem in the continuous…

Many problems in real-world applications involve predicting several random variables which are statistically related. Markov random fields (MRFs) are a great mathematical tool to encode such relationships. The goal of this paper is to…

Machine Learning · Computer Science 2015-04-29 Liang-Chieh Chen , Alexander G. Schwing , Alan L. Yuille , Raquel Urtasun
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