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.
Abstract 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.