| 1. |
- Fredriksson, Johan, et al.
(author)
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Tighter Relaxations for Higher-Order Models based on Generalized Roof Duality
- 2012
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In: Lecture Notes in Computer Science (Computer Vision - ECCV 2012. Workshops and Demonstrations, Florence, Italy, October 7-13, 2012, Proceedings, Part III). - Berlin, Heidelberg : Springer Berlin Heidelberg. - 1611-3349 .- 0302-9743. - 9783642338854 - 9783642338847 ; 7585, s. 273-282
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Conference paper (peer-reviewed)abstract
- Many problems in computer vision can be turned into a large-scale boolean optimization problem, which is in general NP-hard. In this paper, we further develop one of the most successful approaches, namely roof duality, for approximately solving such problems for higher-order models. Two new methods that can be applied independently or in combination are investigated. The first one is based on constructing relaxations using generators of the submodular function cone. In the second method, it is shown that the roof dual bound can be applied in an iterated way in order to obtain a tighter relaxation. We also provide experimental results that demonstrate better performance with respect to the state-of-the-art, both in terms of improved bounds and the number of optimally assigned variables.
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| 2. |
- Kahl, Fredrik, et al.
(author)
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Generalized roof duality
- 2012
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In: Discrete Applied Mathematics. - : Elsevier BV. - 1872-6771 .- 0166-218X. ; 160:16-17, s. 2419-2434
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Journal article (peer-reviewed)abstract
- The roof dual bound for quadratic unconstrained binary optimization is the basis for several methods for efficiently computing the solution to many hard combinatorial problems. It works by constructing the tightest possible lower-bounding submodular function, and instead of minimizing the original objective function, the relaxation is minimized. However, for higher-order problems the technique has been less successful. A standard technique is to first reduce the problem into a quadratic one by introducing auxiliary variables and then apply the quadratic roof dual bound, but this may lead to loose bounds. We generalize the roof duality technique to higher-order optimization problems. Similarly to the quadratic case, optimal relaxations are defined to be the ones that give the maximum lower bound. We show how submodular relaxations can efficiently be constructed in order to compute the generalized roof dual bound for general cubic and quartic pseudo-boolean functions. Further, we prove that important properties such as persistency still hold, which allows us to determine optimal values for some of the variables. From a practical point of view, we experimentally demonstrate that the technique outperforms the state of the art for a wide range of applications, both in terms of lower bounds and in the number of assigned variables. (C) 2012 Elsevier B.V. All rights reserved.
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| 3. |
- Strandmark, Petter
(author)
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Discrete Optimization in Early Vision - Model Tractability Versus Fidelity
- 2012
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Doctoral thesis (other academic/artistic)abstract
- Early vision is the process occurring before any semantic interpretation of an image takes place. Motion estimation, object segmentation and detection are all parts of early vision, but recognition is not. Some models in early vision are easy to perform inference with---they are tractable. Others describe the reality well---they have high fidelity. This thesis improves the tractability-fidelity trade-off of the current state of the art by introducing new discrete methods for image segmentation and other problems of early vision. The first part studies pseudo-boolean optimization, both from a theoretical perspective as well as a practical one by introducing new algorithms. The main result is the generalization of the roof duality concept to polynomials of higher degree than two. Another focus is parallelization; discrete optimization methods for multi-core processors, computer clusters, and graphical processing units are presented. Remaining in an image segmentation context, the second part studies parametric problems where a set of model parameters and a segmentation are estimated simultaneously. For a small number of parameters these problems can still be optimally solved. One application is an optimal method for solving the two-phase Mumford-Shah functional. The third part shifts the focus to curvature regularization---where the commonly used length and area penalization is replaced by curvature in two and three dimensions. These problems can be discretized over a mesh and special attention is given to the mesh geometry. Specifically, hexagonal meshes in the plane are compared to square ones and a method for generating adaptive meshes is introduced and evaluated. The framework is then extended to curvature regularization of surfaces. Finally, the thesis is concluded by three applications to early vision problems: cardiac MRI segmentation, image registration, and cell classification.
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| 4. |
- Strandmark, Petter, et al.
(author)
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HEp-2 Staining Pattern Classification
- 2012
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In: Pattern Recognition (ICPR), 2012 21st International Conference on. - 9781467322164
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Conference paper (peer-reviewed)abstract
- Classifying images of HEp-2 cells from indirect immunofluorescence has important clinical applications. We have developed an automatic method based on random forests that classifies an HEp-2 cell image into one of six classes. The method is applied to the data set of the ICPR 2012 contest. The previously obtained best accuracy is 79.3% for this data set, whereas we obtain an accuracy of 97.4%. The key to our result is due to carefully designed feature descriptors for multiple level sets of the image intensity. These features characterize both the appearance and the shape of the cell image in a robust manner.
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