On the metrics and euler-lagrange equations of computational anatomy.

By Michael I. Miller, Alain Trouv'e, Laurent Younes. Annual Review of Biomedical Engineering, 2002

510 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9dcbf08c04976adc0e1279d8302b562536e34b24

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In Computational Mechanics

In Computer Vision and Pattern Recognition

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Citations in the corpus

Shape deformation analysis from the optimal control viewpoint (2014, methodology): “This framework has led to the development of a family of registration algorithms called Large Deformation Diffeomorphic Metric Mapping (LDDMM), in which the correspondence between two shapes comes from the minimization of an objective functional defined as a sum of two terms [6, 7, 19, 22, 23].”
Geodesic Shooting for Computational Anatomy (2006, unknown): “sional analogue, the more general diffeomorphisms [7, 11, 16, 22, 23, 36].”
A Review of Geometric Transformations for Nonrigid Body Registration (2008, background): “This is mapping is related to the displacement field by Φ(x, 1) = x+ u(x) and satisfies the following [142]:”
Matrix-valued kernels for shape deformation analysis (2013, background): “…be applied for performing registration and computing distances in diﬀerent kinds of “shape spaces”, such as the manifolds curves [26, 41], surfaces [60], images [6, 42, 43], vector ﬁelds [14], diﬀusion tensor images [13], measures [25, 27], and labeled feature points, or landmarks [28, 33, 38, 43].”
A Reproducible Evaluation of ANTs Similarity Metric Performance in Brain Image Registration (2010, background): “The corresponding symmetric Euler–Lagrange equations are similar to (Miller et al., 2002).”
Medical image registration: a review (2014, background): “A study on this subject can be found in Miller et al. (2002).”
Surface Matching via Currents (2005, background): “Indeed, for a variationvt, = vt + ṽt of the vector fieldvt, the corresponding variation of xj1 = φ1(x ) is (see [19])”
Gromov–Wasserstein Distances and the Metric Approach to Object Matching (2011, background): “These developments have led to building Riemannian structures on many shape spaces [82–84, 115].”
Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain (2008, methodology): “Current developments in large deformation computational anatomy by Miller, Trouve and Younes extended the methods to include photometric variation and to use Euler–Lagrange equations (Miller et al., 2002).”
Brain templates and atlases (2012, unknown): “…et al., 2005; Christensen et al., 1997; Chung et al., 2001; Grenander and Miller, 2007; Guo et al., 2005; Lian and Davatzikos, 2011; Miller, 2004; Miller et al., 1993, 2002, 2006; Thompson and Toga, 1996, 1999; Thompson et al., 2000a,b; Wang et al., 2005; Yeo et al., 2010a; Yushkevich et al.,…”
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms (2005, background): “…et al. (1996), it provides large deformation coordinate system transformation and (2) as shown in Miller and Younes (2001), Trouvé (1995) and Miller et al. (2002), in contrast to Christensen et al. (1996), the length of the shortest path inf 1 0 v t V dt connecting images I 0 to I 1 defines…”
Deformable Medical Image Registration: A Survey (2013, background): “The distance between these elements is defined as a geodesic, according to a metric, that connects them and can be used for studies of anatomical variability [70].”
Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation (2003, result): “This smoothness property for the LAE-α equations was shown by Shkoller [1998] for regions with no boundary and for regions with boundary (for various boundary conditions), it was shown in Marsden, Ratiu and Shkoller [2000].”
Unbiased diffeomorphic atlas construction for computational anatomy. (2004, background): “These groups vary in dimensionality from simple global translations (R(3)) and rigid rotations (SO(3)) to the infinite dimensional group of diffeomorphisms (H) (Miller et al., 2002).”
Population Shape Regression from Random Design Data (2007, methodology): “It has been shown using the calculus of variations (Miller et al. 2002) that the solution to (19) satisfies”