Group Actions, Homeomorphisms, and Matching: A General Framework

By Michael I. Miller, Laurent Younes. International Journal of Computer Vision, 2004

365 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/91044fc4d287ea69ad8a5ae1635d5e2e54821ea9

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In Computer Vision and Pattern Recognition

Citations in the corpus

Deformable Medical Image Registration: A Survey (2013, background): “A number of theoretical aspects of this framework and especially the ones related with computational analysis were further developed in [71]–[75].”
Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups (2013, neutral): “This formalism was developed in particular by Grenander and Miller [31, 48] based on advanced mathematical tools to compute on inﬁnite dimensional groups of diﬀeomorphisms [64, 70].”
On the metrics and euler-lagrange equations of computational anatomy. (2002, methodology): “between two images I and I ′ is performed by minimizing over all paths satisfying v(x, t)= 0, t∈ [0, 1], x∈ ∂X, andJ(0)= I, J(1)= I ′ as in Reference (71); see algorithm in Supplemental Material link in the online version of this chapter or at http://www.”
Statistical shape analysis: clustering, learning, and testing (2005, background): “On the other hand, in Grenander’s formulation [10] shapes are considered as points on infinite-dimensional differentiable manifolds, and the variations between the shapes are modeled by the action of Lie groups (diffeomorphisms) on these manifolds[ 23 , 11].”
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].”
Unbiased diffeomorphic atlas construction for computational anatomy. (2004, methodology): “Following the greedy fluid algorithm of propagating templates described in Miller and Younes (2001), we approximate the solution to the minimization problem in Eq.”
Population Shape Regression from Random Design Data (2007, methodology): “We apply the theory of large deformation diffeomorphisms (Beg et al. 2005; Dupuis and Grenander 1998; Joshi and Miller 2000; Miller and Younes 2001) to generate deformations φ that are solutions to the Lagrangian ODEs d ds φs(x) = vs(φs(x)) for a simulated time parameter s ∈ [0,1].”
Content-Based Image Retrieval in Radiology: Current Status and Future Directions (2010, background): “In fact, approaches based on continuous (and even diffeomorphic) mappings are becoming increasingly popular in the medical domain.(49,63) Yet, elastic matching methods are more suitable for cases of abnormalities of overall size and/or shape of an organ, which limits their applicability to some exte”
On Advances in Statistical Modeling of Natural Images (2004, background): “As described in [34, 59], occurrences of physical objects in 3D system are modeled as the orbits of groups acting on the configurations of objects in the scenes.”
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].”
Geodesic Shooting for Computational Anatomy (2006, background): “We do not detail numerical algorithms in this paper, but the reader can refer to [4, 5, 17, 23] for examples of choices of K.”
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms (2005, background): “The following construction (Dupuis et al., 1998; Miller and Younes, 2001; Trouvé, 1995). ρ G (ϕ 0 , ϕ 1 ) .”