Sampled values of volumetric data are expressed as three-way array data, which is expressed as tensors. We are required to process and analyse volumetric data without embedding into higher-dimensional vector space from the viewpoints of object oriented data analysis. Multi-way forms of volumetric data require quantitative methods for the discrimination of multi-way forms. Therefore, we define a distance metric for subspaces of multi-way data arrays using transportation between the Stiefel manifolds constructed by subspaces of multi-way data arrays.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 firstname.lastname@example.org
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 email@example.com