Voxel

A voxel (short for "volume element") is a single cubic cell in a regular 3D grid that partitions space into equal intervals. Just as a pixel is the smallest unit of a 2D image, a voxel is the smallest unit of a 3D volume. Each voxel can store attributes such as density, color, material type, or occupancy probability.

Voxel resolution is determined by the grid subdivision. A 256x256x256 voxel grid contains approximately 16.7 million cells. Increasing resolution improves representational accuracy but memory consumption grows cubically (doubling resolution requires 8x memory). To address this, sparse representations using Octrees (recursive subdivision only where detail exists) are widely employed.

• Medical imaging: CT and MRI volume data are inherently voxel-based, with stacked 2D slices forming a 3D grid. Each voxel stores tissue density (CT values in Hounsfield units), enabling 3D rendering, organ segmentation, and surgical planning
• Point cloud voxelization: Converting irregular point clouds into regular voxel grids. The Voxel Grid Filter replaces all points within each voxel with their centroid, uniformly reducing data volume while preserving spatial structure
• Deep learning: 3D convolutional networks (3D CNNs) process voxelized inputs directly. VoxNet performs 3D object recognition on 32x32x32 grids. In Neural Radiance Fields (NeRF), voxel grids store pre-computed radiance values to accelerate rendering from hours to real-time

In gaming, Minecraft popularized voxel-based world construction. Industrial applications include architectural BIM (Building Information Modeling), geological modeling, and computational fluid dynamics. Beyond Octrees, hash-based sparse voxel structures and neural implicit representations are active research areas for improving memory efficiency while maintaining high-fidelity 3D representations.