Marching cubes: A high resolution 3D surface construction algorithm

TLDR

The authors introduce the marching cubes algorithm, which generates triangle models of constant‑density surfaces from 3D medical data and includes enhancements that reduce processing time and enable solid modeling. Marching cubes uses a divide‑and‑conquer strategy to build inter‑slice connectivity, constructs a case table for triangle topology, processes data in scan‑line order with linear interpolation for vertices, and normalizes gradients for shading, while also incorporating speed‑up and solid‑modeling improvements. The algorithm preserves inter‑slice connectivity, surface data, and gradient information, producing highly detailed images that are validated across CT, MR, and SPECT modalities.

Abstract

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.