3D image

As explained in Geometry for Programmers

A 3D image is a three-dimensional sampled representation of geometry or spatial data arranged as image-like values.

A 3D image extends a 2D raster picture into space. Like pixels, its basic units are voxels—volume pixels arranged as a regular three-dimensional grid. You can picture it as an array of 2D images, or as a perfect, aligned image stack. section 12.0

Figure 12.1 The same data (a) represented as an array of colors: a 2D 4×2 image made of pixels (b) and a 3D 2×2×2 image made of voxels (c)

Compare a 2D 4×2 pixel image with a 3D 2×2×2 voxel image to see how the same array-like idea gains a spatial dimension. section 12.0

Most 3D images are grayscale stacks produced by tomography rather than color photographs. Gray values encode measurements, such as information gathered from X-rays. Since raw intensities are awkward for geometric operations, segmentation extracts regions into image masks: equal-sized grids whose bits mark whether each voxel belongs to the selected part. section 12.0

Voxel representations are especially useful when:

• Boolean operations must be fast and reliable, provided the operands use the same voxel grid. section 12.8
• Erosion and dilation provide voxel analogues of offsets used with signed distance functions and boundary representations. section 12.8
• Image vectorization converts voxel data into other geometric representations, supporting workflows that move among voxels, signed distance functions, and boundary representations. section 12.8

How Geometry for Programmers covers it

How deep it goes

Defines pixels, voxels, image stacks, grayscale data, masks, segmentation, and operations, then connects them to representation conversion.

Examples

Uses grayscale tomography stacks, a 2D 4×2 image, and a 3D 2×2×2 voxel grid as concrete representations.

What it assumes

Assumes familiarity with 2D raster images while teaching the extension from pixels to voxels and from intensities to masks.

What you can do after

Operate on voxel models with Boolean, erosion, and dilation workflows, and choose conversions among geometric representations.

How it connects

Connects voxels with image masks, segmentation, tomography, erosion, dilation, signed distance functions, and boundary representations.

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Related concepts

• segmentation maskincludes · A segmentation mask is an image-shaped array that assigns each pixel or spatial element to a class, object, region, or corresponding segmentation value.
• computed tomographyproduced by · Computed tomography is an imaging technique that uses multiple X-ray measurements and computational reconstruction to produce cross-sectional or volumetric images.
• voxelhas part · A voxel is a discrete volumetric element, typically cubical, used to represent spatial data or occupancy in a three-dimensional grid.

This explainer was generated by Manning's knowledge graph from the text of Geometry for Programmers. The section links point to the parts of the book it draws on.