A Log-Euclidean Framework for Statistics on Diffeomorphisms

Arsigny, Vincent; Commowick, Olivier; Pennec, Xavier; Ayache, Nicholas

doi:10.1007/11866565_113

Cited by 358 publications

(436 citation statements)

References 13 publications

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“…However, the computation of a displacement field requires the numerical integration of a time-varying ODE (Trouvé, 1998). In (Arsigny et al, 2006) the authors proposed a practical approximation of such a Lie group structure on diffeomorphisms by using stationary speed vector fields only. This has the significant advantage of yielding very fast computations of exponentials.…”

Section: Newton Methods For Diffeomorphic Registrationmentioning

confidence: 99%

“…This has the significant advantage of yielding very fast computations of exponentials. It becomes indeed possible to use the scaling and squaring method and compute the exponential with just a few compositions of spatial transformations (Arsigny et al, 2006).…”

Section: Newton Methods For Diffeomorphic Registrationmentioning

confidence: 99%

“…Finally, diffeomorphisms are considered to be a good working framework when no additional information about the spatial transformation is available. The main contribution of this paper, in Section 3, is to show that the alternate optimization scheme of the demons algorithm can be used in combination with the Lie group structure on diffeomorphic transformations of (Arsigny et al, 2006). In contrast to many diffeomorphic registration schemes, our diffeomorphic demons algorithm, which we initially proposed in (Vercauteren et al, 2007c), is computationally efficient.…”

Section: Introductionmentioning

confidence: 99%

“…Diffeomorphisms are also considered to be a good working framework when no additional information about the spatial transformation is available. With the development of computational anatomy and in the absence of a justified physical model of inter-subject variability, statistics on diffeomorphisms also become an important topic (Arsigny et al, 2006;Lepore et al, 2008;Vaillant et al, 2004;Xue et al, 2006). Diffeomorphic registration algorithms are at the core of this research field since they often provide the input data.…”

Section: Introducing Diffeomorphisms Into the Demonsmentioning

confidence: 99%

“…The main idea of our algorithm is to adapt this optimization procedure to a space of diffeomorphic transformations. We show that a Lie group structure on diffeomorphic transformations that has recently been proposed in (Arsigny et al, 2006) can be used in combination with optimization tools on Lie groups to derive our diffeomorphic image registration algorithm.…”

Section: Introducing Diffeomorphisms Into the Demonsmentioning

confidence: 99%

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Diffeomorphic demons: Efficient non-parametric image registration

et al. 2009

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We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. In the first part of this paper, we show that Thirion's demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.

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Section: Newton Methods For Diffeomorphic Registrationmentioning

confidence: 99%

Section: Newton Methods For Diffeomorphic Registrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introducing Diffeomorphisms Into the Demonsmentioning

confidence: 99%

Section: Introducing Diffeomorphisms Into the Demonsmentioning

confidence: 99%

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Diffeomorphic demons: Efficient non-parametric image registration

et al. 2009

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Complementary cortical gray and white matter developmental patterns in healthy, preterm neonates

Rajagopalan¹,

Scott

Liu

et al. 2017

Hum. Brain Mapp.

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Preterm birth is associated with brain injury and altered cognitive development. However, the consequences of extra-uterine development are not clearly distinguished from perinatal brain injury. Therefore, we characterized cortical growth patterns from 30 to 46 post menstrual weeks (PMW) in 27 preterm neonates (25 – 32 PMW at birth) without detectable brain injury on magnetic resonance imaging. We introduce surface-based morphometric descriptors that quantify radial (thickness) and tangential (area) change rates. Within a tensor-based morphometry framework, we use a temporally weighted formulation of regression to simultaneously model local age-related changes in cortical gray matter (GM) and underlying white matter (WM) mapped onto the cortical surface. The spatiotemporal pattern of GM and WM development corresponded to the expected gyrification timecourse of primary sulcal deepening and branching. In primary gyri, surface area and thickness rates were below average along sulcal pits and above average on gyral banks and crests in both GM and WM. Above average surface area rates in GM corresponded to emergence of secondary and tertiary folds. These findings map the development of neonatal cortical morphometry in the context of extra-uterine brain development using a novel approach. Future studies may compare this developmental trajectory to preterm populations with brain injury.

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Fast three‐dimensional image generation for healthy brain aging using diffeomorphic registration

Tzortzakakis

Barroso

et al. 2022

Human Brain Mapping

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Predicting brain aging can help in the early detection and prognosis of neurodegenerative diseases. Longitudinal cohorts of healthy subjects scanned through magnetic resonance imaging (MRI) have been essential to understand the structural brain changes due to aging. However, these cohorts suffer from missing data due to logistic issues in the recruitment of subjects. This paper proposes a methodology for filling up missing data in longitudinal cohorts with anatomically plausible images that capture the subject‐specific aging process. The proposed methodology is developed within the framework of diffeomorphic registration. First, two novel modules are introduced within Synthmorph, a fast, state‐of‐the‐art deep learning‐based diffeomorphic registration method, to simulate the aging process between the first and last available MRI scan for each subject in three‐dimensional (3D). The use of image registration also makes the generated images plausible by construction. Second, we used six image similarity measurements to rearrange the generated images to the specific age range. Finally, we estimated the age of every generated image by using the assumption of linear brain decay in healthy subjects. The methodology was evaluated on 2662 T1‐weighted MRI scans from 796 healthy participants from 3 different longitudinal cohorts: Alzheimer's Disease Neuroimaging Initiative, Open Access Series of Imaging Studies‐3, and Group of Neuropsychological Studies of the Canary Islands (GENIC). In total, we generated 7548 images to simulate the access of a scan per subject every 6 months in these cohorts. We evaluated the quality of the synthetic images using six quantitative measurements and a qualitative assessment by an experienced neuroradiologist with state‐of‐the‐art results. The assumption of linear brain decay was accurate in these cohorts ( R 2 ∈ [.924, .940]). The experimental results show that the proposed methodology can produce anatomically plausible aging predictions that can be used to enhance longitudinal datasets. Compared to deep learning‐based generative methods, diffeomorphic registration is more likely to preserve the anatomy of the different structures of the brain, which makes it more appropriate for its use in clinical applications. The proposed methodology is able to efficiently simulate anatomically plausible 3D MRI scans of brain aging of healthy subjects from two images scanned at two different time points.

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A Log-Euclidean Framework for Statistics on Diffeomorphisms

Cited by 358 publications

References 13 publications

Diffeomorphic demons: Efficient non-parametric image registration

Diffeomorphic demons: Efficient non-parametric image registration

Complementary cortical gray and white matter developmental patterns in healthy, preterm neonates

Fast three‐dimensional image generation for healthy brain aging using diffeomorphic registration

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