Higher-Order Clique Reduction without Auxiliary Variables

Ishikawa, Hiroshi

doi:10.1109/cvpr.2014.177

Cited by 25 publications

(28 citation statements)

References 28 publications

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“…Some algorithms to convert the function of any order to that of the first order have been proposed [5,7]. This enables us to use any higher-order energy to describe more complicated conditions.…”

Section: Higher-order Energymentioning

confidence: 99%

“…A class of the minimization problem can effectively solved by graph-cut based methods. Although the order of energy function in the class, which describes the degree of dependency among voxels, has been limited to 1, this limitation has been overcome in recent works [5,6,7] that convert a higher-order energy to the second-order one. A higher-order energy enables us to express complex constraints among multiple organs or widely spanning structure [8].…”

Section: Introductionmentioning

confidence: 99%

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Multi-organ segmentation by minimization of higher-order energy for CT boundary

Okagawa

Oyamada

Mochizuki

et al. 2015

2015 14th IAPR International Conference on Machine Vision Applications (MVA)

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In medical image analysis, segmentation of medical images such as Computed Tomography (CT) volumetric images is necessary for further medical image analysis and computer aided intervention. We propose a method for medical image segmentation by higherorder energy minimization. Specifically, we introduce a higher-order term that describes the continuity around the edge points of a CT image. The parameters of the energy terms are determined according to various conditional probabilities learned from sample data with the ground truth. Then we minimize the energy using graph cuts and evaluate the effectiveness of the introduction of the term into the traditional energy.

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Section: Higher-order Energymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-organ segmentation by minimization of higher-order energy for CT boundary

Okagawa

Oyamada

Mochizuki

et al. 2015

2015 14th IAPR International Conference on Machine Vision Applications (MVA)

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“…This allows reduction of higher order terms either by: A) addition of auxiliary variables (for example by reducing a triplet to three pairwise terms [11]; or B) by reconfiguration of the polynomial form of the MRF energy, until the high-order function can be replaced by a single quadratic [12]. We present results using the latter version, known as Excludable Local Configuration (ELC).…”

Section: Optimisationmentioning

confidence: 99%

“…In order to account for triplet terms we adopt the approach of [11,12]. This allows reduction of higher order terms either by: A) addition of auxiliary variables (for example by reducing a triplet to three pairwise terms [11]; or B) by reconfiguration of the polynomial form of the MRF energy, until the high-order function can be replaced by a single quadratic [12].…”

Section: Optimisationmentioning

confidence: 99%

Discrete Optimisation for Group-Wise Cortical Surface Atlasing

Glocker

Rajchl

Rueckert

2016

2016 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)

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This paper presents a novel method for cortical surface atlasing. Group-wise registration is performed through a discrete optimisation framework that seeks to simultaneously improve pairwise correspondences between surface feature sets, whilst minimising a global cost relating to the rank of the feature matrix. It is assumed that when fully aligned, features will be highly linearly correlated, and thus have low rank. The framework is regularised through use of multi-resolution control point grids and higher-order smoothness terms, calculated by considering deformation strain for displacements of triplets of points. Accordingly the discrete framework is solved through high-order clique reduction. The framework is tested on cortical folding based alignment, using data from the Human Connectome Project. Preliminary results indicate that group-wise alignment improves folding correspondences, relative to registration between all pair-wise combinations, and registration to a global average template.

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“…Further, it is not possible to optimally weight isotropic and anisotropic distortions. We therefore required a method for considering higher-order deformations, through comparing displacements of triplets of points; for this we implemented a method for higher-order discrete optimisation through clique reduction (Ishikawa, 2009(Ishikawa, , 2014, which has already been successfully applied to 2D registration in (Glocker et al, 2010) A prototype of this framework proved fundamental to the methods used during developed of the HCP's multi-modal parcellation (Glasser et al, 2016b,a). For (Glasser et al, 2016a), we proposed an triplet-based angular deviation penalty, that penalised change in the angles of each triangular mesh face.…”

Section: Introductionmentioning

confidence: 99%