Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models
Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models
复制标题
3D Procrustes 方法的推断：树干生长、秩亏扩散张量和扰动模型
DOI：
10.1111/j.1467-9469.2010.00724.x
复制
发表时间：
2010
影响因子：
1
通讯作者：
S. Huckemann
中科院分区：
文献类型：
--
作者：
S. Huckemann
摘要：将流形上外均值和内均值的中心极限定理推广到Fréchet均值的推广。 例子是3D肯德尔形状的Procrustes平均值以及Ziezold引入的平均值。这允许以前不可能的单样本测试，并在数值上评估扰动模型的“Procrustes平均值的不一致性”和最近提出的扩散张量成像模型中的“不一致性”。此外，它表明，CLT可以扩展到轻度秩亏扩散张量。应用到林业给出了时间演变的道格拉斯冷杉树干倾向于强烈的圆柱在早期年龄和倾向于增加竞争。
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.