Multidimensional Images Given by Mappings:
Construction and Visualization
V.A.Bushenkov, O.L.Chernykh, G.K.Kamenev, and A.V.Lotov
Published: Pattern Recognition and Image Analysis,
Vol. 5, No 1, 1995, pp. 35-56.
The paper summarizes the studies the authors have carried on for
the past 20 years on the visualization of multidimensional (mainly, three-
to seven-dimensional) images given by mappings. The proposed approach has
come to be known as the
Generalized Reachable Sets (GRS) method. Among the matters considered
in the paper are the mathematical
foundations of the method, including application of convolution of polyhedral
sets introduced by Fourier, the polyhedral approximation of convex sets,
and the approximation of non-convex sets by coverings. An overview
of the method is given, as it applies to multicriteria decision making in
environmental protection, economy, and technology.