A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors

Szeliski, Richard; Zabih, Ramin; Scharstein, Daniel; Veksler, Olga; Kolmogorov, Vladimir; Agarwala, Aseem; Tappen, Marshall F.; Rother, Carsten

doi:10.1109/tpami.2007.70844

Cited by 875 publications

(677 citation statements)

References 55 publications

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“…In [7], the secondorder MRF is converted to a pairwise one and then the TRW-S algorithm [8] is utilized to infer the MRF variables. Unfortunately, no running time is provided, but it is assumed to be much higher [9] than for the method proposed in [6] which uses the FastPD algorithm [10,11] (based on iterative graph-cuts).…”

Section: Introductionmentioning

confidence: 99%

Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs

Glocker

Komodakis

Paragios

et al. 2009

Advances in Visual Computing

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Abstract. Labeling of discrete Markov Random Fields (MRFs) has become an attractive approach for solving the problem of non-rigid image registration. Here, regularization plays an important role in order to obtain smooth deformations for the inherent ill-posed problem. Smoothness is achieved by penalizing the derivatives of the displacement field. However, efficient optimization strategies (based on iterative graph-cuts) are only available for first-order MRFs which contain cliques of size up to two. Higher-order cliques require graph modifications and insertion of auxiliary nodes, while pairwise interactions actually allow only regularization based on the first-order derivatives. In this paper, we propose an approximated curvature penalty using second-order derivatives defined on the MRF pairwise potentials. In our experiments, we demonstrate that our approximated term has similar properties as higher-order approaches (invariance to linear transformations), while the computational efficiency of pairwise models is preserved.

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Section: Introductionmentioning

confidence: 99%

Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs

Glocker

Komodakis

Paragios

et al. 2009

Advances in Visual Computing

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“…( Blaschke, 2010), MRF(Markov random fields) (Sui et al, 2012;Szeliski et al, 2008). MRF (i,j) (Fig.…”

Section: Salt and Pepper 오류 제거mentioning

confidence: 99%

Automatic Extraction of Initial Training Data Using National Land Cover Map and Unsupervised Classification and Updating Land Cover Map

이승기¹,

최석근²,

노신택³

et al. 2015

Journal of the Korean Society of Surveying, Geodesy, Photogramm

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Those land cover maps have widely been used in various fields, such as environmental studies, military strategies as well as in decision-makings. This study proposes a method to extract training data, automatically and classify the cover using ingle satellite images and national land cover maps, provided by the Ministry of Environment. For this purpose, as the initial training data, those three were used; the unsupervised classification, the ISODATA, and the existing land cover maps. The class was classified and named automatically using the class information in the existing land cover maps to overcome the difficulty in selecting classification by each class and in naming class by the unsupervised classification; so as achieve difficulty in selecting the training data in supervised classification. The extracted initial training data were utilized as the training data of MLC for the land cover classification of target satellite images, which increase the accuracy of unsupervised classification. Finally, the land cover maps could be extracted from updated training data that has been applied by an iterative method. Also, in order to reduce salt and pepper occurring in the pixel classification method, the MRF was applied in each repeated phase to enhance the accuracy of classification. It was verified quantitatively and visually that the proposed method could effectively generate the land cover maps. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http:// creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Keywords

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“…for two neighboring pixels and the labels a, b ∈ L. In practice, approximate optimization methods are proposed [21,29] for minimizing the energy in (1). Iterated Conditional Modes (ICM) [2], Simulated Annealing [10] and Highest Confidence First (HCF) [4] are among the oldest such methods.…”

Section: Map Inference -Discrete Mrfmentioning

confidence: 99%

Efficient Loopy Belief Propagation Using the Four Color Theorem

Timofte

Gool

2013

Advanced Topics in Computer Vision

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Summary. Recent work on early vision such as image segmentation, image denoising, stereo matching, and optical flow uses Markov Random Fields. Although this formulation yields an NP-hard energy minimization problem, good heuristics have been developed based on graph cuts and belief propagation. Nevertheless both approaches still require tens of seconds to solve stereo problems on recent PCs. Such running times are impractical for optical flow and many image segmentation and denoising problems and we review recent techniques for speeding them up. Moreover, we show how to reduce the computational complexity of belief propagation by applying the Four Color Theorem to limit the maximum number of labels in the underlying image segmentation to at most four. We show that this provides substantial speed improvements for large inputs, and this for a variety of vision problems, while maintaining competitive result quality.

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A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors

Cited by 875 publications

References 55 publications

Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs

Approximated Curvature Penalty in Non-rigid Registration Using Pairwise MRFs

Automatic Extraction of Initial Training Data Using National Land Cover Map and Unsupervised Classification and Updating Land Cover Map

Efficient Loopy Belief Propagation Using the Four Color Theorem

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