# Voxel

Image:Voxels.png
a series of voxels; an individual voxel is colored in gray

A voxel (a portmanteau of the words volumetric and pixel) is a volume element, representing a value on a regular grid in three dimensional space. This is analogous to a pixel, which represents 2D image data. Voxels are frequently used in the visualisation and analysis of medical and scientific data. Some true 3D displays use voxels to describe their resolution. For example, a display might be able to show 512×512×512 voxels.

As with pixels, voxels themselves typically do not contain their position in space (their coordinates) - but rather, it is inferred based on their position relative to other voxels (i.e. their position in the data structure that makes up a single volume image).

##  Voxel data

Image:Ribo-Voxels.png
a data set of voxels for a macromolecule

A voxel represents the sub-volume box with constant scalar/vector value inside which is equal to scalar/vector value of the corresponding grid/pixel of the original discrete representation of the volumetric data. The boundaries of a voxel are exactly in the middle between neighboring grids. Thus, the notion of “Voxel” is applicable only for nearest neighbor interpolation and it is not applicable for higher order of interpolation such as tri-linear, tri-cubic... etc; these cases can be represented through Cell volume subdivision.

The value of a voxel may represent various properties. In CT scans, the values are Hounsfield units, giving the opacity of material to X-rays. Different types of value are acquired from MRI or ultrasound.

Voxels can contain multiple scalar values what essentially is a vector data; in the case of ultrasound scans with B-mode and Doppler data, density, and volumetric flow rate are captured as separate channels of data relating to the same voxel positions.

Other values may be useful for immediate 3D rendering, such as a surface normal vector and color.

There are different kind of voxels, one is to see voxel as a way to represent volumetric object as 3D bitmaps instead of vectors (by opposition, polygonal objects are made of vectors). Another popular one is Voxel terrain which is generally used in games and simulations.

##  Uses

###  Visualization

A volume containing voxels can be visualised either by direct volume rendering or by the extraction of polygon iso-surfaces which follow the contours of given threshold values. The marching cubes algorithm is often used for iso-surface extraction, however other methods exist as well.

##  Trivia

In the minimalist webcomic Pixel, in which pixels inside a computer are the main characters, one 'race' of supporting characters are the voxels, who have the "supernatural" power of moving in three dimensions.