Locating Fréchet means with application to shape spaces

By Huiling Le. Advances in Applied Probability, 2001

151 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b337dfa7cdc282aea0baaaa06553276b96dba598

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In Geometry and Topology

Citations in the corpus

Nonparametric statistics on manifolds with applications to shape spaces (2008, background): “, Le [24] and Bhattacharya and Patrangenaru [6–8]) is significantly relaxed, thereby substantially enhancing the applicability of the tests.”
Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces (2006, background): “[16]) or in our special case with the algorithm introduced below.”
Distances and inference for covariance operators (2014, methodology): “The recordings of people speaking different Romance languages are registered using the procedure by Tang and Müller (2008), having pronounced words in each language.”
Riemannian Lp center of mass: existence, uniqueness, and convexity (2011, background): “Le in [15] uses a rather similar argument to show that in a general (i.”
Fréchet means and Procrustes analysis in Wasserstein space (2017, methodology): “[1]) or Procrustes algorithms (Le [52], Groisser [39]) do not apply here, since the Fréchet functional may very well fail to be twice differentiable.”
Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models (2010, background): “Intrinsic means are unique if the underlying random elements are sufficiently concentrated (cf. Le (2001) for the elaborate proof).”
A smeary central limit theorem for manifolds with application to high-dimensional spheres (2018, background): “…Riemannian manifolds, uniqueness for intrinsic means has been shown if the support is sufficiently concentrated (cf. Karcher (1977); Kendall (1990); Le (2001); Groisser (2005); Afsari (2011)) and intrinsic sample means are unique a.s. if from a distribution absolutely continous w.r.t. Riemannian…”
Analysis of planar shapes using geodesic paths on shape spaces (2004, methodology): “A similar algorithm and convergence results for a landmark-based representation of shapes are described in [18].”
Rotation Averaging (2013, methodology): “intersect at a single point. Hence, in general, two rotation pairs are sufficient to give a unique solution, unless the rotations Ri are about the same axis. Alignment of Rotation Axes. As we shall see, the solution to the conjugate rotation averaging problem is closely related to alignment of the a”
Limit theorems for empirical Fr\'echet means of independent and non-identically distributed manifold-valued random variables (2011, methodology): “Ziezold (1989)’s application of Fréchet means to statistical shape theory has been taken up by several workers [see, e.g., Le (2001, 2004); also the recent survey by Kendall and Le (2010)].”
INTRINSIC SHAPE ANALYSIS: GEODESIC PCA FOR RIEMANNIAN MANIFOLDS MODULO ISOMETRIC LIE GROUP ACTIONS (2007, methodology): “Moreover, if gp1 is in optimal position to p2 then g p2 is in optimal position to p1, and gp1 and p2 are called registered. Note that in general, optimally positioned points will not be uniquely determined. Moreover, the relation being in optimal position may not be transitive, see Ziezold ((1977), ”
LARGE SAMPLE THEORY OF INTRINSIC AND EXTRINSIC SAMPLE MEANS ON MANIFOLDS—II (2003, background): “(a) It is known that under the given assumptions, there is a local minimum μI , say, of the Fréchet function F which belongs to Br and that this minimum is also the unique minimum in B2r [30, 34, 40].”