Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models
By Stephan F. Huckemann. 2010
55 citations recorded by the source corpus.
Abstract. The Central Limit Theorem (CLT) for extrinsic and intrinsic means on manifolds is extended to a generalization of Fréchet means. Examples are the Procrustes mean for 3D Kendall shapes as well as a mean introduced by Ziezold. This allows for one‐sample tests previously not possible, and to numerically assess the ‘inconsistency of the Procrustes mean’ for a perturbation model and ‘inconsistency’ within a model recently proposed for diffusion tensor imaging. Also it is shown that the CLT can be extended to mildly rank deficient diffusion tensors. An application to forestry gives the temporal evolution of Douglas fir tree stems tending strongly towards cylinders at early ages and tending away with increased competition.
Subfields: Geometry and Topology, Mechanical Engineering, Nature and Landscape Conservation
View Paper: https://www.semanticscholar.org/paper/3a301753d9886d0bbd2c435dec6eef4911eaf028
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In Geometry and Topology
- Stephan F. Huckemann
- Benjamin Eltzner
- Huiling Le
- Vic Patrangenaru
- Thomas Hotz
- James Stephen Marron
- Jonathan C. Mattingly
- Ezra Miller
In Mechanical Engineering
In Nature and Landscape Conservation
Citations in the corpus
- A smeary central limit theorem for manifolds with application to high-dimensional spheres (2018, methodology): “…sample means on manifolds by Bhattacharya and Patrangenaru (2005), and many subsequent generalizations (e.g. Bhattacharya and Bhattacharya (2008); Huckemann (2011a); Bhattacharya and Patrangenaru (2013); Ellingson et al. (2013); Patrangenaru and Ellingson (2015); Bhattacharya and Lin (2017)),…”
- Sticky central limit theorems on open books (2012, background): “this intuition has been made rigorous when M is a manifold [5, 12, 14, 15], it can fail when M has certain types of singularities, as we demonstrate here for an open book O: a space obtained by gluing disjoint copies of a half-space along their boundary hyperplanes; see Section 1 for precise definit”