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.

Abstract. In this paper, we use a level set based segmentation algorithm to extract the vascular tree from Magnetic Resonance Angiography (MRA) data sets. The classification approach depends on initializing the level sets in the 3D volume and, the level sets evolve with time to yield the blood vessels. This work introduces a high quality initialization for the level set functions, allowing extraction of the blood vessels in 3D and elimination of non-vessel tissues. A comparison between the 2D and 3D segmentation approaches is made. The results are validated using a phantom that simulates the MRA data and demonstrate good accuracy. 1.