We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

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. 0 1992 Academic Press. Inc.