An Efficient Optimization Framework for Multi-Region Segmentation Based on Lagrangian Duality

Ulén, Johannes; Strandmark, Petter; Kahl, Fredrik

doi:10.1109/tmi.2012.2218117

Cited by 29 publications

(35 citation statements)

References 30 publications

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“…However, optimization problem (4) is NP-hard even for unary metrics 5 . One can solve Lagrangian dual of (4) by iterative sequence of graph cuts as in [23], but the corresponding duality gap may be large and the optimum for (4) is not guaranteed.…”

Section: Lsa-trmentioning

confidence: 99%

Submodularization for Binary Pairwise Energies

Gorelick

Boykov

Veksler

et al. 2014

2014 IEEE Conference on Computer Vision and Pattern Recognition

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Many computer vision problems require optimization of binary non-submodular energies. We propose a general optimization framework based on local submodular approximations (LSA). Unlike standard LP relaxation methods that linearize the whole energy globally, our approach iteratively approximates the energies locally. On the other hand, unlike standard local optimization methods (e.g. gradient descent or projection techniques) we use non-linear submodular approximations and optimize them without leaving the domain of integer solutions. We discuss two specific LSA algorithms based on trust region and auxiliary function principles, LSA-TR and LSA-AUX. These methods obtain state-of-the-art results on a wide range of applications outperforming many standard techniques such as LBP, QPBO, and TRWS. While our paper is focused on pairwise energies, our ideas extend to higher-order problems. The code is available online 1 .

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Section: Lsa-trmentioning

confidence: 99%

Submodularization for Binary Pairwise Energies

Gorelick

Boykov

Veksler

et al. 2014

2014 IEEE Conference on Computer Vision and Pattern Recognition

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“…Given that it was formulated using polar coordinates, their method could only handle star-shaped objects. Delong and Boykov [18] and Ulén et al [61] encoded geometric interactions (including containment and exclusion) between distinct regions into a graph-cut framework. Both these methods have been proposed in the discrete domain and hence tend to exhibit a grid bias (metrication error) as well as large memory usage.…”

Section: A Related Workmentioning

confidence: 99%

“…Schmidt et al [56] modified [18] by adding the Hausdorff distance prior to the MRF-based segmentation framework to impose maximum distance constraint. Inspired by [18], [61], Nosrati et al [45] proposed a method to encode containment and detachment, between different regions with a specified minimum distance between their boundaries in the continuous domain. Their approach guarantees the global optimal solution using functional lifting technique.…”

Section: A Related Workmentioning

confidence: 99%

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Local Optimization Based Segmentation of Spatially-Recurring, Multi-Region Objects With Part Configuration Constraints

Nosrati

Hamarneh

2014

IEEE Trans. Med. Imaging

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The level set framework has been a popular medical image segmentation technique for many years due to its several advantages, such as parametrization independence, ease of implementation , extendibility from a curve in 2D to higher dimensions , and automatic handling of topological changes. However, existence of noise, low contrast and objects complexity in medical images cause many segmentation algorithms (including level set-based methods) to fail. Incorporating prior knowledge into image segmentation algorithms has proven useful for obtaining more accurate and plausible results. Two important constraints, containment and exclusion of regions, have gained attention in recent years mainly due to their descriptive power and intuitive definitions. In this paper, we augment the level set framework with the ability to handle these two intuitive geometric relationships, containment and exclusion, along with a distance constraint between boundaries of multi-region objects. Level set's important property of automatically handling topological changes of evolving contours/surfaces enables us to segment spatially-recurring objects (e.g. multiple instances of multi-region cells in a large microscopy image) while satisfying the two aforementioned constraints. In addition, the level set approach gives us a very simple and natural way to compute the distance between contours/surfaces and impose constraints on it. The downside, however, is a local optimization framework in which the final segmentation solution depends on the initialization. In fact, here, we sacrifice the optimizibility (local instead of global solution) in exchange for lower space complexity (less memory usage) and faster runtime (especially for large microscopic images) as well as no grid artifacts. Nevertheless, the result from validating our method on synthetic and several biomedical applications, mainly on multi-region cell segmentation in microscopy images and cardiac segmentation in MR images, showed the utility and advantages of this augmented level set framework (even with fully automatic or rough initialization that is distant from the desired boundaries). We also compared our framework with its counterpart methods in the discrete domain and reported the pros and cons of each of these methods in terms of metrication error and efficiency in memory usage and runtime.

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“…In the discrete domain, Li et al [16] proposed a method to segment nested objects, but their method is limited to star-shaped objects. Delong and Boykov [11] and Ulén et al [24] proposed segmentation methods that encode geometric constraints (including containment) between distinct regions into a graph cut framework. Our work can be viewed as a continuous analogue to these works, providing several advantages, as noted earlier and as will demonstrated in Section 4.…”

Section: Previous Workmentioning

confidence: 99%

Bounded Labeling Function for Global Segmentation of Multi-part Objects with Geometric Constraints

Nosrati

Andrews

Hamarneh

2013

2013 IEEE International Conference on Computer Vision

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The inclusion of shape and appearance priors have proven useful for obtaining more accurate and plausible segmentations, especially for complex objects with multiple parts. In this paper, we augment the popular MumfordShah model to incorporate two important geometrical constraints, termed containment and detachment, between different regions with a specified minimum distance between their boundaries. Our method is able to handle multiple instances of multi-part objects defined by these geometrical constraints using a single labeling function while maintaining global optimality. We demonstrate the utility and advantages of these two constraints and show that the proposed convex continuous method is superior to other state-of-theart methods, including its discrete counterpart, in terms of memory usage, and metrication errors.

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An Efficient Optimization Framework for Multi-Region Segmentation Based on Lagrangian Duality

Cited by 29 publications

References 30 publications

Submodularization for Binary Pairwise Energies

Submodularization for Binary Pairwise Energies

Local Optimization Based Segmentation of Spatially-Recurring, Multi-Region Objects With Part Configuration Constraints

Bounded Labeling Function for Global Segmentation of Multi-part Objects with Geometric Constraints

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