Discrimination of Volumetric Shapes Using Orthogonal Tensor Decomposition

• Published in: Shape in Medical Imaging Vol. 11167; pp. 277 - 290
• Main Authors: Itoh, Hayato, Imiya, Atsushi
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2018; Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 9783030047467; 3030047466
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-04747-4_26

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.