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Reconstruction of a 3D object from a finite number of its 1D parallel cross-sections

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ASC - Approximation, sampling and compression in data science

The problem of reconstruction of a 3D object from its parallel 2D cross sections has been
considered by many researchers. In some previous works we suggested to regard the problem as an approximation of a set-valued function from a finite number of its samples, which are 2D sets. We used approximation methods for single-valued functions by applying operations between sets instead of operations between numbers.
Since 2D sets are much more complicated than 1D sets, we suggest here to regard 3D objects as bivariate  functions  with 1D sets as samples, and to use the analogue of piecewise linear interpolation on a triangulation as the approximation method.
In this talk we present our method, and discuss the properties of the resulting interpolants, including continuity and approximation rates. Few examples will be presented.



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