Multidimensional Reconstruction by Set-valued Approximations

Some generalizations of the notion of univariate data interpolationare presented, inducing the concept of set-valued interpolationin a general metric space. Consequently methods for univariateinterpolation or smoothing of multidimensional geometrical dataare suggested. In particular the application of these methodsto 3-D body recognition from cross-sectional data is discussed.Preliminary analysis of the interpolation process is presentedand the capability of reconstructing bodies of complex topologiesis exemplified.