A Comparative Study of Energy Minimization Methods for Markov Random Fields

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

doi:10.1007/11744047_2

Cited by 292 publications

(257 citation statements)

References 34 publications

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“…We use the graph cut package 7 provided by [13]. The solution for a 50 × 50 image and 73 possible colors is obtained by graph cuts in a fraction of second and is generally already very satisfying.…”

Section: Global Coherency Via Graph Cutsmentioning

confidence: 99%

Automatic Image Colorization Via Multimodal Predictions

Charpiat

Hofmann

Schölkopf

2008

Lecture Notes in Computer Science

191

177

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Abstract. We aim to color greyscale images automatically, without any manual intervention. The color proposition could then be interactively corrected by user-provided color landmarks if necessary. Automatic colorization is nontrivial since there is usually no one-to-one correspondence between color and local texture. The contribution of our framework is that we deal directly with multimodality and estimate, for each pixel of the image to be colored, the probability distribution of all possible colors, instead of choosing the most probable color at the local level. We also predict the expected variation of color at each pixel, thus defining a nonuniform spatial coherency criterion. We then use graph cuts to maximize the probability of the whole colored image at the global level. We work in the L-a-b color space in order to approximate the human perception of distances between colors, and we use machine learning tools to extract as much information as possible from a dataset of colored examples. The resulting algorithm is fast, designed to be more robust to texture noise, and is above all able to deal with ambiguity, in contrary to previous approaches.

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Section: Global Coherency Via Graph Cutsmentioning

confidence: 99%

Automatic Image Colorization Via Multimodal Predictions

Charpiat

Hofmann

Schölkopf

2008

Lecture Notes in Computer Science

191

177

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“…We used a graph cutbased a-expansion algorithm for the energy minimization of the MRF with the implementation accompanying Szeliski et al (2006). The selection of the value of L is based on data's temporal resolution.…”

Section: Results For Spatiotemporal Mrf Model Event Detectionmentioning

confidence: 99%

Extreme anomaly event detection in biosphere using linear regression and a spatiotemporal MRF model

et al. 2018

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Detecting abnormal events within time series is crucial for analyzing and understanding the dynamics of the system in many research areas. In this paper, we propose a methodology to detect these anomalies in multivariate environmental data. Five biosphere variables from a preliminary version of the Earth System Data Cube have been used in this study: Gross Primary Productivity, Latent Energy, Net Ecosystem Exchange, Sensible Heat and Terrestrial Ecosystem Respiration. To tackle the spatiotemporal dependencies of the biosphere variables, the proposed methodology after preprocessing the data is divided into two steps: a feature extraction step applied to each time series in the grid independently, followed by a spatiotemporal event detection step applied to the obtained novelty scores over the entire study area. The first step is based on the assumption that the time series of each variable can be represented by an autoregressive moving average (ARMA) process, and the anomalies are those time instances that are not well represented by the estimated ARMA model. The Mahalanobis distance of the ARMA models' multivariate residuals is used as a novelty score. In the second step, the obtained novelty scores of the entire study are treated as time series of images. Markov random fields (MRFs) provide an effective and theoretically well-established methodology for integrating spatiotemporal dependency into the classification of image time series. In this study, the classification of the novelty score images into three classes, intense anomaly, possible anomaly, and normal, is performed using unsupervised K-means clustering followed by multi-temporal MRF segmentation applied recursively on the images of each consecutive L ! 1 time steps. The proposed methodology was applied to an area covering Europe and Africa. Experimental results and validation based on known historic events show that the method is able to detect historic events and also provides a useful tool to define sensitive regions.

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“…Figure 1 illustrates the steps behind a single expansion move. Because a graph cut finds the best move from an exponential number of possibilities, the α-expansion algorithm is a very large-scale neighbourhood search (VLSN) technique (Ahuja et al, 2002) and is very competitive in practice (Szeliski et al, 2006). With respect to some current labelingf , the full set of possible expansion moves is M(f ) = ∪ α∈L M α (f ).…”

Section: How α-Expansion Workmentioning

confidence: 99%

Minimizing Energies with Hierarchical Costs

et al. 2012

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Computer vision is full of problems elegantly expressed in terms of energy minimization. We characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm. Hierarchical costs are natural for modeling an array of difficult problems. For example, in semantic segmentation one could rule out unlikely object combinations via hierarchical context. In geometric model estimation, one could penalize the number of unique model families in a solution, not just the number of models-a kind of hierarchical MDL criterion. Hierarchical fusion uses the well-known α-expansion algorithm as a subroutine, and offers a much better approximation bound in important cases.

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A Comparative Study of Energy Minimization Methods for Markov Random Fields

Cited by 292 publications

References 34 publications

Automatic Image Colorization Via Multimodal Predictions

Automatic Image Colorization Via Multimodal Predictions

Extreme anomaly event detection in biosphere using linear regression and a spatiotemporal MRF model

Minimizing Energies with Hierarchical Costs

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