Riemannian metric optimization on surfaces (RMOS) for intrinsic brain mapping in the Laplace–Beltrami embedding space

Gahm, Jin Kyu; Shi, Yonggang

doi:10.1016/j.media.2018.03.004

Cited by 15 publications

(7 citation statements)

References 56 publications

(74 reference statements)

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“…As discussed previously, little work is present in surface data augmentation as this requires the encoding of surface deformation into a tractable feature space as well as efficient computation to draw samples from that space. Although non-parametrization-based surface registration is appealing such as particle shape correspondence ( Datar et al, 2013 ; Oguz et al, 2009 ) or spectral alignment ( Gahm et al, 2018 ; Lombaert et al, 2013 ; Wright et al, 2015 ), these methods would need explicit encoding of deformation trajectories in the context of surface data augmentation, which can be explored in future work.…”

Section: Discussionmentioning

confidence: 99%

Labeling lateral prefrontal sulci using spherical data augmentation and context-aware training

et al. 2021

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The inference of cortical sulcal labels often focuses on deep (primary and secondary) sulcal regions, whereas shallow (tertiary) sulcal regions are largely overlooked in the literature due to the scarcity of manual/well-defined annotations and their large neuroanatomical variability. In this paper, we present an automated framework for regional labeling of both primary/secondary and tertiary sulci of the dorsal portion of lateral prefrontal cortex (LPFC) using spherical convolutional neural networks. We propose two core components that enhance the inference of sulcal labels to overcome such large neuroanatomical variability: (1) surface data augmentation and (2) context-aware training. (1) To take into account neuroanatomical variability, we synthesize training data from the proposed feature space that embeds intermediate deformation trajectories of spherical data in a rigid to non-rigid fashion, which bridges an augmentation gap in conventional rotation data augmentation. (2) Moreover, we design a two-stage training process to improve labeling accuracy of tertiary sulci by informing the biological associations in neuroanatomy: inference of primary/secondary sulci and then their spatial likelihood to guide the definition of tertiary sulci. In the experiments, we evaluate our method on 13 deep and shallow sulci of human LPFC in two independent data sets with different age ranges: pediatric ( N = 60) and adult ( N = 36) cohorts. We compare the proposed method with a conventional multi-atlas approach and spherical convolutional neural networks without/with rotation data augmentation. In both cohorts, the proposed data augmentation improves labeling accuracy of deep and shallow sulci over the baselines, and the proposed context-aware training offers further improvement in the labeling of shallow sulci over the proposed data augmentation. We share our tools with the field and discuss applications of our results for understanding neuroanatomical-functional organization of LPFC and the rest of cortex ( https://github.com/ilwoolyu/SphericalLabeling ).

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Section: Discussionmentioning

confidence: 99%

Labeling lateral prefrontal sulci using spherical data augmentation and context-aware training

et al. 2021

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“…Each individual triangulated mesh was then registered to our constructed cerebellar template mesh using the novel curvature-driven surface mapping algorithm, Riemannian metric optimization on surfaces (RMOS), which incorporated both geometric and anatomical features to guide surface mapping in the LB embedding space ( Gahm et al, 2018 ). For the cerebellum, the mean curvature feature was used to drive the surface mapping process.…”

Section: Methodsmentioning

confidence: 99%

“…For each triangular mesh, the Riemannian metric was denoted as a set of weights defined on all edges and fully determined the heat kernel on the mesh ( Zeng et al, 2012 ; Goes et al, 2014 ). The RMOS approach can be used to iteratively optimize the Riemannian metric to match the curvature feature and realize surface mapping in the LB embedding space ( Gahm et al, 2018 ). As a result, all surfaces were represented with the same triangulation, and the vertices were in one-to-one correspondence.…”

Section: Methodsmentioning

confidence: 99%

“…The absolute and relative volumes of the cerebellum were both calculated to describe its developmental trajectory. Shape analysis was performed using our novel curvature-driven surface mapping algorithm, the Riemannian metric optimization on surfaces (RMOS) method ( Gahm et al, 2018 ), to characterize the regional growth patterns of the fetal cerebellum. These results may be helpful for understanding the development of the cerebellum during the early second trimester and provide an anatomical reference for future cerebellar studies.…”

Section: Introductionmentioning

confidence: 99%

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Morphometric development of the human fetal cerebellum during the early second trimester

Shi

et al. 2020

NeuroImage

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The protracted nature of development makes the cerebellum vulnerable to a broad spectrum of pathologic conditions, especially during the early fetal period. This study aims to characterize normal cerebellar growth in human fetuses during the early second trimester. We manually segmented the fetal cerebellum using 7.0-T high-resolution MR images obtained in 35 specimens with gestational ages ranging from 15 to 22 weeks. Volume measurements and shape analysis were performed to quantitatively evaluate global and regional cerebellar growth. The absolute volume of the fetal cerebellum showed a quadratic growth with increasing gestational age, while the pattern of relative volume changes revealed that the cerebellum grew at a greater pace than the cerebrum after 17 gestational weeks. Shape analysis was used to examine the distinctive development of subregions of the cerebellum. The extreme lateral portions of both cerebellar hemispheres showed the lowest rate of growth. The anterior lobe grew faster than most of the posterior lobe. These findings expand our understanding of the early growth pattern of the human cerebellum and could be further used to assess the developmental conditions of the fetal brain.

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“…In particular, the structural details of the cortical and subcortical regions of the brain have been typically represented using surfaces that were reconstructed from three-dimensional (3D) MR volumes. Moreover, surfacebased analysis plays an important role in the local tracking of disease based on surface registration in clinical and research settings [1], [2]. Therefore, high-resolution (HR) MRI is needed to achieve accurate surface reconstruction to aid in diagnostic decisions [3].…”

Section: Introductionmentioning

confidence: 99%

Super-Resolution of 3D Brain MRI With Filter Learning Using Tensor Feature Clustering

Park

Gahm

2022

IEEE Access

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Surface-based analysis of magnetic resonance imaging (MRI) data of the brain plays an important role in clinical and research applications. To achieve accurate three-dimensional (3D) surface reconstruction, high-resolution (HR) MR image acquisition is needed. However, HR image acquisition is hindered by hardware limitations that result in long acquisition time and low spatial coverage. Single image super-resolution (SISR) can alleviate these problems by converting a low-resolution (LR) image to an HR image. However, unlike 2D SISR methods, conventional 3D methods incur a large computational cost and require abundant data. Further, 3D boundaries for surface reconstruction based on MR images have not been sufficiently investigated. We herein propose a cost-efficient novel regression-based framework for full 3D super-resolution imaging that directly analyzes 3D features by introducing a tensor using gradient information. We initially cluster features using tensors to create labels for both the training and testing stages. In the training stage, for each label, we collect LR patches and corresponding HR intensities to compute filters. In the testing stage, for each voxel, we construct a tensor to obtain a feature and predict the HR intensity using trained filters. We also propose a patch span reduction method by limiting patch orientation to reduce the orientation span and increase shape variety. Using only 30 masked T1-weighted brain MR volumes from the Human Connectome Project (HCP) 900 dataset, the proposed algorithm exhibited superior performance in terms of HR boundary recovery in the cerebral cortex as well as improved overall quality compared to conventional methods.

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Riemannian metric optimization on surfaces (RMOS) for intrinsic brain mapping in the Laplace–Beltrami embedding space

Cited by 15 publications

References 56 publications

Labeling lateral prefrontal sulci using spherical data augmentation and context-aware training

Labeling lateral prefrontal sulci using spherical data augmentation and context-aware training

Morphometric development of the human fetal cerebellum during the early second trimester

Super-Resolution of 3D Brain MRI With Filter Learning Using Tensor Feature Clustering

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