Discrimination of Volumetric Shapes Using Orthogonal Tensor Decomposition - Itoh, Hayato; Imiya, Atsushi (Shape in Medical Imaging, 2018)
Organs, cells and microstructures in cells dealt with in medical image analysis are volumetric data. Sampled values of volumetric data are expressed as three-way array data. For the quantitative discrimination of multiway forms from the viewpoint of principal component analysis (PCA)-based pattern recognition, distance metrics for subspaces of multiway data arrays are desired. The paper aims to extend pattern recognition methodologies based on PCA for vector spaces to those for multilinear data. First, we extend the canonical angle between linear subspaces for vector-based pattern recognition to the canonical angle between multilinear subspaces for tensor-based pattern recognition. Furthermore, using transportation between the Stiefel manifolds, we introduce a new metric for a collection of linear subspaces. Then, we extend the transportation of between Stiefel manifolds in vector space to the transportation of the Stiefel manifolds in multilinear spaces for the discrimination analysis of multiway array data.