Abstract 3D reconstruction is a branch of computer vision with a broad range of applications like computer aided design, animation, medicine and many others. In this talk we use continuous linear functionals for characterizing different kinds of 3D data. These problems can be tackled in the framework of Reproducing Kernel Hilbert Spaces and regularization of inverse problems. It can be said that 3D reconstruction is the general problem of estimating or finding functional dependencies from a three‐dimensional data set. The origin of these data covers a wide range that includes tomography, surface reconstruction from point clouds or image and signal processing. Usually the problem of reconstruction has a very close relationship with scientific visualization and computer graphics. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)