Magnetic resonance and computed tomography produce sets of tomograms which are termed discrete 3D scenes. Usually, discrete 3D scenes are analyzed in two dimensions by observing each tomogram on a screen so that the three-dimensional information contained in the scene can be recovered only partially and qualitatively. The three-dimensional reconstruction of the shape of biological structures from discrete 3D scenes would allow a complete and quantitative recovery of the available information, but this task has proved hard for conventional processing techniques. In this paper we present a system architecture based on neural networks for the fully automated segmentation and recognition of structures of interest in discrete 3D scenes. The system includes a retina and two main processing modules, an Attention-Focuser System and a Region-Finder System, which have been implemented by using feed-forward nets trained with the back-propagation algorithm. This architecture has been tested on computer-simulated structures and has been applied to the reconstruction of the spinal cord and the brain from sets of tomograms.