Reconstruction in space and visualization of a planar image: a mathematical and computational introduction

Aim of this paper is to provide a short introduction to the fundamental mathematical ideas involved in tri-dimensional (3D) image reconstruction, in a basic way as to make such ideas available to a large audience. Particular attention is then given to the case in which the bi-dimensional (2D) input data are represented of very few images. A feasibility study is outlined for a 3D reconstruction of a human gland or organ, satisfying hypothesis of uniformity in the tissue and in the arterial distribution, spacial extension and density. The resulting method aims at obtaining functional information on the target organ, minimizing the number (and social cost) of possibly invasive imaging techniques by employing one or very few scintigraphic or echographic images.