A Log-Euclidean Framework for Statistics on Diffeomorphisms

By Vincent Arsigny, O. Commowick, Xavier Pennec, Nicholas Ayache. International Conference on Medical Image Computing and Computer-Assisted Intervention, 2006

563 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e08c258a4a48da5517be80012d77b5eae17ba834

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Citations in the corpus

Diffeomorphic demons: Efficient non-parametric image registration (2009, methodology): “…in the ﬁnite dimensional case between one-parameter subgroups and the exponential map, the exponential exp( u ) of a smooth vector ﬁeld is deﬁned in (Arsigny et al., 2006) as the ﬂow at time one of the stationary ODE, From the properties of one-parameters subgroups ( t 7→ exp( t u ) ), we know…”
SynthStrip: skull-stripping for any brain image (2022, methodology): “This random displacement ﬁeld is vector-integrated, using ﬁve scaling and squaring steps to encourage a diﬀeomor-phic warp (Arsigny et al., 2006; Dalca et al., 2019), and Table 1.”
SVF-Net: Learning Deformable Image Registration Using Shape Matching (2017, methodology): “The SVFs are extracted by using an iterative log-approximation scheme with the scaling and squaring approach [1] starting with the displacement field u.”
Non-parametric Diffeomorphic Image Registration with the Demons Algorithm (2007, methodology): “In Section 3, we show that a Lie group structure on diffeomorphic transformations that has recently been proposed in [1] can be used in combination with some optimization tools on Lie groups to derive our diffeomorphic image registration algorithm.”
A fast diffeomorphic image registration algorithm (2007, methodology): “For example, with eight time steps, the Euler integration method is equivalent to If the number of time steps is a power of two, then the solution can be determined by a scaling and squaring approach (Moler and Van Loan, 2003; Arsigny et al., 2006b,a).”
Deformable Medical Image Registration: A Survey (2013, methodology): “Stationary velocity fields [96] have been used towards this direction.”
A Generative Model for Image Segmentation Based on Label Fusion (2010, unknown): “The gap between the Semi-local ( ) TABLE II AVERAGE RUN-TIME (IN CPU HOURS ON A MODERN MACHINE -INTEL XEON 3 GHZ WITH A 32 GB RAM-) TO SEGMENT ONE TEST SUBJECT.”
Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration (2018, methodology): “We compute the integration numerically using scaling and squaring [1], which we briefly review here.”
Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks (2020, methodology): “We follow [1,5] to integrate the (smooth) stationary velocity field v over unit time using the scaling and squaring method with time step T = 7 to obtain the time 1 deformation field φ such that φ is approximated to exp(v), which is a member of the Lie group.”
TransMorph: Transformer for unsupervised medical image registration (2021, unknown): “Such a transformation can be achieved via the time-integration of time-dependent (Beg et al., 2005; Avants et al., 2008) or time-stationary velocity fields (SVFs) (Arsigny et al., 2006; Ashburner, 2007; Ver-cauteren et al., 2009; Hernandez et al., 2009).”
MRF-Based Deformable Registration and Ventilation Estimation of Lung CT (2013, methodology): “In our approach, we first allow for displacements larger than this theoretical limit, and afterwards obtain a diffeomorphic mapping by applying the scaling and squaring method [28].”
Scalable High Performance Image Registration Framework by Unsupervised Deep Feature Representations Learning (2015, methodology): “Intensity-based feature selection methods are widely used in medical image registration [6]–[11]; however, two image”
Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces (2019, methodology): “In addition, we implemented the integration of the velocity field using Tensorflow ODE solvers and using standard quadrature, but found that these required significantly more runtime compared to the scaling and squaring strategy, consistent with literature findings [4, 5, 50].”
Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration (2009, methodology): “However, we follow the convention of [3], [4], [66] who call their transformation diffeomorphic even though they are homeomorphic.”
Diffeomorphic registration using geodesic shooting and Gauss–Newton optimisation (2011, unknown): “The first of these involved parameterising with a one-parameter subgroup, which allows diffeomorphic mappings to be constructed via a scaling and squaring procedure (Arsigny et al., 2006; Ashburner, 2007; Arsigny et al., 2009).”
Residual Networks as Flows of Diffeomorphisms (2019, methodology): “In this work, we deepen this analogy between ResNets and deformation flows to relate ResNet and registration problems [27], especially diffeomorphic registration [30,5,3,2].”
An unsupervised convolutional neural network-based algorithm for deformable image registration (2018, background): “Many intensity based feature selection algorithms that aim to distinguish a good set of candidate regions with correspondingly strong features have been implemented for medical image registration (Arsigny et al 2006, Ashburner 2007, Rueckert and Aljabar 2015).”