The main goals of “Efficient Global Minimization Methods for Sparsity and Regularity Promoting Optimization Problems in Imaging and Vision, 2014” are design and analysis of regularity/sparsity promoting energy minimization models in image processing, computer vision and compressed sensing, and design and analysis of efficient numerical methods that can produce global or nearly global solutions of the resulting optimization problems. Imaging and vision are some of the core emerging technologies that are shaping our society. This can partly be explained by progressively better physical sensing devices for acquiring image data. Another important reason is the development of image processing and computer vision software for restoring, analyzing, simplifying and interpreting the image information. Energy minimization has been established as one of the most important paradigms for formulating problems in image processing and computer vision in a mathematical language. The problems can elegantly be formulated as finding the minimal state of some energy potential, which typically encodes the underlying assumption that the image data is regular/sparse, i.e. values at different image pixels are correlated. More recently, it has been realized that the expensive acquisition process can be greatly improved by incorporating the same assumption in an energy minimization framework, a field known as compressed sensing. A major challenge is to solve the resulting optimization problems efficiently. The most desirable models are often the most difficult to handle from an optimization perspective. Continuous optimization problems may be non-convex and contain many inferior local minima. Discrete optimization problems may be NP-hard, which means an algorithm is unlikely to exist which can always compute an exact solution without an unreasonable amount of effort. Even though the underlying problems are NP-hard, computational methods will be constructed that produce global solutions for practical input data, and otherwise close approximations.

The data are presented in various articles.

"Efficient Global Minimization Methods for Sparsity and Regularity Promoting Optimization Problems in Imaging and Vision, 2014"

NSD2253

Name | Affiliation |
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Bae, Egil | Department of Mathematics, University of Bergen |

Name | Affiliation | Abbreviation | Role |
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Bae, Egil | Department of Mathematics, University of Bergen | UiB | Principal Investigator |

Copyright (C) 2015 Egil Bae, Department of Mathematics, UiB

Name | Abbreviation | Role | Grant |
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The Research Council of Norway | RCN | 214889 |

Name | Affiliation | Abbreviation |
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NSD - Norwegian Centre for Research Data | NSD |

Date: 2015-11-15

Original data from Egil Bae, Department of Mathematics, UiB are documented and prepared, first NSD-version.

"Efficient Global Minimization Methods for Sparsity and Regularity Promoting Optimization Problems in Imaging and Vision, 2014". Data collected by Egil Bae, Department of Mathematics, UiB. First NSD edition, Bergen 2015.

- Mathematical models
- Modelling
- Information processing
- Technology
- Research and development
- Scientific development

Start | End | Cycle |
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2012-12-31 | 2014-12-31 |

Start | End | Cycle |
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2012-12-31 | 2014-12-31 |

Other

Other

Cross-sectional survey

Other

The data are presented in various articles.

Bae E., Yuan J., Tai X.C., Boykov Y. (2014) A Fast Continuous Max-Flow Approach to Non-convex Multi-labeling Problems. In Efficient Algorithms for Global Optimization Methods in Computer Vision (pp. 134-154). Springer Berlin Heidelberg, Heidelberg.

Duggana N., Bae E., Jonesa E., Glavina M., Veseb L. (2014) A simple boundary reinforcement technique for segmentation without prior. Pattern Recognition Letters, 46, 27-35.

Yuan J., Bae E., Tai X.C., Boykov Y. (2014) A spatially continuous max-flow and min-cut framework for binary labeling problems. Numerische Mathematik, 126(3), 559-587.

Duggan N., Bae E., Shen S., Hsu W., Bui A., Jones E., Glavin M., Vese L. (2015) A Technique for Lung Nodule Candidate Detection in CT Using Global Minimization Methods. In Energy Minimization Methods in Computer Vision and Pattern Recognition (pp. 478-491). Springer International Publishing, Switzerland.

Bae E., Lellmann J., Tai X.C. (2013) Convex Relaxations for a Generalized Chan-Vese Model. In Energy Minimization Methods in Computer Vision and Pattern Recognition (pp. 223-236). Springer Berlin Heidelberg, Heidelberg.

Bae E., Tai X.C. (2015) Efficient Global Minimization Methods for Image Segmentation Models with Four Regions. Journal of Mathematical Imaging and Vision, 51(1), 71-97.

Merkurjev E., Bae E., Bertozzi A.L., Tai X.C. (2015) Global Binary Optimization on Graphs for Classification of High-Dimensional Data. Journal of Mathematical Imaging and Vision, 52(3), 414-435.

Bae E., Tai X.C., Yuan J. (2015) Maximizing Flows with Message-Passing: Computing Spatially Continuous Min-Cuts. In Energy Minimization Methods in Computer Vision and Pattern Recognition (pp. 15-28). Springer International Publishing, Switzerland.

Wan M., Wang Y., Bae, E., Tai X.C., Wang D. (2013) Reconstructing Open Surfaces via Graph-Cuts. Visualization and Computer Graphics, IEEE Transactions on, 19(2), 306-318.

Bae, E., Yuan J., Tai X.C. (2013) Simultaneous Convex Optimization of Regions and Region Parameters in Image Segmentation Models. In Innovations for Shape Analysis (pp. 421-438). Springer Berlin Heidelberg, Heidelberg.

Rajchl M., Baxter J.S.H., Bae E., Tai X.C., Fenster A., Peters T.M., Yuan J. (2015) Variational Time-Implicit Multiphase Level-Sets. In Energy Minimization Methods in Computer Vision and Pattern Recognition (pp. 278-291). Springer International Publishing, Switzerland.

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