Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors

By P. T. Fletcher, Sarang C. Joshi. ECCV Workshops CVAMIA and MMBIA, 2004

322 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/c53a49522e963e15a582408633d4c6d90ac083c5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Geometry and Topology

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements (2006, background): “In medical image analysis, selected applications cover the validation of the rigid registration accuracy [4, 66, 67], shape statistics [7] and more recently tensor computing, either for processing and analyzing diffusion tensor images [10, 8, 9, 11], or to model the brain variability [12].”
Multiclass Brain–Computer Interface Classification by Riemannian Geometry (2012, methodology): “An efficient iterative algorithm to compute the Riemannian mean of I SPD matrices is given in [7].”
A smeary central limit theorem for manifolds with application to high-dimensional spheres (2018, methodology): “(β) In other examples, P = Γ, the space of geodesics on Q is considered, in view of PCA-like dimension reduction methods (e.g. Fletcher and Joshi (2004); Huckemann and Ziezold (2006); Huckemann et al. (2010)), or (γ) P is a family of subspaces of Q, or even a space of nested subspheres in Jung et…”
Riemannian geometry for the statistical analysis of diffusion tensor data (2007, background): “This work is an expanded version of the material found in [12] and the first author’s thesis work [11].”
A Riemannian Framework for Tensor Computing (2005, methodology): “During the writing of this paper, we discovered that the invariant metric has been independently proposed by [F¨orstner and Moonen, 1999] to deal with covariance matrices, and very recently by [Fletcher and Joshi, 2004] for the analysis of principal modes of sets of diﬀusion tensors.”
Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models (2010, methodology): “Since their original definition by Fréchet (1948) for P =Q and =d , such means have found much interest.”
Transfer Learning for Brain–Computer Interfaces: A Euclidean Space Data Alignment Approach (2018, methodology): “A causal band-pass filter (50-order linear phase Hamming window FIR filter designed by Matlab function fir1, with 6 dB cut-off frequencies at [8, 30] Hz) was applied to remove muscle artifacts, line-noise contamination and DC drift.”