Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms

By Mirza Faisal Beg, Michael I. Miller, Alain Trouv'e, Laurent Younes. International Journal of Computer Vision, 2005

1,941 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/ede22f3682bc33b361f5c67a17476a46ea3d3f4c

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Citations in the corpus

A Log-Euclidean Framework for Statistics on Diffeomorphisms (2006, methodology): “To fully take into account the group structure of diffeomorphisms, it has been proposed to parameterize dense deformations with Hilbert spaces of time-varying speed vector fields, which yield geometrical deformations via the integration of an Ordinary Differential Equation (ODE) during one unit of t”
Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces (2019, methodology): “Diffeomorphic transforms have seen extensive methodological development, yielding state-of-the-art tools, such as Large Diffeomorphic Distance Metric Mapping (LDDMM) [10, 12, 13, 28, 33, 42, 47, 59], DARTEL [3], diffeomorphic Demons [56], and symmetric normalization (SyN) [5].”
CycleMorph: Cycle Consistent Unsupervised Deformable Image Registration (2020, methodology): “A diffeomorphic deformation ensures certain desirable properties between two image volumes like continuous, differentiable, and preserving topology [6], [7], [21].”
Statistical analysis of trajectories on Riemannian manifolds: Bird migration, hurricane tracking and video surveillance (2014, methodology): “One can also draw solutions from problems in image registration where 2D and 3D images are registered to each other using a spatial warping instead of a temporal warping [see, e.g., LDDMM technique, Beg et al. (2005)].”
Survey of Medical Image Registration (2013, methodology): “For example, the LDDMM (large deformation diffeomorphic metric mapping) algorithm [85], does not fix the deformation parameters once they have been estimated.”
Multi-Contrast Human Neonatal Brain Atlas: Application to Normal Neonate Development Analysis (2011, positive): “test the feasibility of the atlas-based analysis to detect the diffusion properties of the infant brain using the JHUneonate-SS and LDDMM, we measured FA and MD of 20 white matter structures and four deep gray structures of the 33 DTIs normalized to the JHU-neonate-SS.”
Dreaming More Data: Class-dependent Distributions over Diffeomorphisms for Learned Data Augmentation (2015, background): “…is, however, not limited to MNIST: • Image alignment is a routine task in many medical imaging tasks, such as the analysis of magnetic resonance images (MRI) [7, 13, 37], X-ray Computed Tomography (CT) [34, 41], Positron Emission Tomography (PET) [45, 46] and mam-Class-dependent mograms [24, 38].”
Survey of Non-Rigid Registration Tools in Medicine (2017, methodology): “A tool developed by Schwarz [54], the Fast and Flexible Image Registration Toolbox, developed by the SAFIR research group at the University of Lübeck [55], and the Large Deformation Diffeomorphic Metric Mapping (LDDMM) [56] tool, developed by the Center for Imaging Science (CIS) at Johns Hopkins Uni”
Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration (2009, methodology): “An alternative interpretation of the smoothing implementation of Christensen’s algorithm comes from choosing a different metric for computing the gradient from the derivatives [9].”
Fast Predictive Image Registration (2016, background): “Image registration is typically cast as an optimization problem, which can be especially computationally demanding for non-parametric diﬀusive, elastic, or ﬂuid models [10] such as LDDMM [1].”
Image Similarity and Tissue Overlaps as Surrogates for Image Registration Accuracy: Widely Used but Unreliable (2011, background): “On the other hand, many regularized algorithms adjust the degree of regularization using a parameter such as a constraint weight factor (e.g., [30]) or the width of a smoothing kernel (e.g., [31], [32]).”
Population Shape Regression from Random Design Data (2007, methodology): “We apply the theory of large deformation diffeomorphisms [1,9,18,30] to generate deformations φ that are solutions to the Lagrangian ODEs d dsφs(x) = vs(φs(x)) for a”
SVF-Net: Learning Deformable Image Registration Using Shape Matching (2017, methodology): “We use Stationary Velocity Fields (SVF) [1] but the method could also be adapted to other choices of diffeomorphic parametrization such as time-varying velocity fields [2] and B-splines.”
elastix: A Toolbox for Intensity-Based Medical Image Registration (2010, methodology): “Nonparametric registration methods, such as [34], [35], [38], [39],”