Marching cubes: A high resolution 3D surface construction algorithm

By William E. Lorensen, Harvey E. Cline. 1987

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.

Subfields: Computer Graphics and Computer-Aided Design

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Citations in the corpus

Occupancy Networks: Learning 3D Reconstruction in Function Space (2018, methodology): “Liao et al. [43] proposed an end-to-end learnable version of the marching cubes algorithm [44].”
Features and development of Coot (2010, neutral): “Electron-density maps are displayed using a three-dimensional mesh to visualize the surface of electron-density regions higher than a chosen electron-density value using a ‘marching-cubes’-type algorithm (Lorensen & Cline, 1987).”
Deep Level Sets: Implicit Surface Representations for 3D Shape Inference (2019, methodology): “1 Correspondingly, surface representations can be extracted from occupancy grids by means of the Marching Cubes algorithm [23].”
DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation (2019, methodology): “A view of this implicit surface can be rendered through raycasting or rasterization of a mesh obtained with, for example, Marching Cubes [35].”
Learning Implicit Fields for Generative Shape Modeling (2018, methodology): “A shape is represented by all points assigned to a specific value and is typically rendered via iso-surface extraction such as Marching Cubes.”
Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images (2018, methodology): “To compare the quality of mesh model, we convert volumetric and point cloud to mesh using standard approaches [21, 1].”
OctNetFusion: Learning Depth Fusion from Data (2017, methodology): “We apply this architecture to the depth map fusion problem and formulate the task as the prediction of truncated signed distance fields which can be meshed using standard techniques [27].”
Hierarchical Surface Prediction for 3D Object Reconstruction (2017, methodology): “The meshes are extracted with marching cubes [24] using the same thresholds as for the”
The Replica Dataset: A Digital Replica of Indoor Spaces (2019, methodology): “Meshes are extracted using the standard Marching Cubes [20] algorithm, simpliﬁed via Instant Meshes [15] and textured with a PTex-like system [5].”
Discrete optimization of ray potentials for semantic 3D reconstruction (2015, methodology): “To extract mesh out of voxelized solution we used Marching cubes algorithm [19].”
A survey of the marching cubes algorithm (2006, methodology): “The 15 basic intersection topologies (using the numbering of [2]).”
Learning Semantic Deformation Flows with 3D Convolutional Networks (2016, methodology): “We then use marching cubes [27] for reconstructing a surface mesh representation for the deformed shape.”
Meso-scale FE analyses of textile composite reinforcement deformation based on X-ray computed tomography (2014, methodology): “9) by triangularizing the external surface of each phase (i.e. each colour) with triangles using the marching cubes algorithm [44].”
DoubleFusion: Real-Time Capture of Human Performances with Inner Body Shapes from a Single Depth Sensor (2018, methodology): “We extract a triangle mesh from the volume using Marching Cube algorithm [25] and sample additional far-body nodes.”
Visualization of image data from cells to organisms (2010, unknown): “These models are often generated using isosurface approaches such as the marching cubes algorithm 24 .”