Voxelization and the Marching Cube Algorithm

The surface reconstruction can also be performed by evaluating the volumetric space of a 3D object in the form of Voxels. A voxel is a basic volume element on a regular grid in 3D space. This is analogous to a pixel in 2D space. Voxels are frequently used in the visualization and analysis of medical and scientific data. Some 3D displays use voxels to describe their internal resolution.

Voxelization is the process of adding depth to a set of cross-sectional images represented in pixels on planar slices. The space between any two pixels in one

Fig. 8.19 Triangulation between two scan lines (Leu et al., 2005)

Fig. 8.21 Fifteen cases in the marching cube algorithm for surface rendering

slice is referred to as interpixel distance, and the distance between any two slices is referred to as interslice distance.

Lorensen and Cline (1987) invented a surface construction and visualization algorithm called the Marching Cube, which is a widely used technique for real-time visualization of 3D models represented in voxels. This algorithm can be applied for visualization of voxelized data generated from CT or MRI images. The marching

cube algorithm traverses all boundary cells of an entire volume and determines the triangulation within each cell based on the values of cell vertices, each having a value of 0 or 1, to represent whether the corresponding voxel is empty or occupied by the object. This method first partitions the entire volume into cells, each consisting of eight voxels. Then it decides the surface triangulation for each cell according to 15 possible configurations shown in Fig. 8.21.

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