Mipmap

In 3D computer graphics texture filtering, MIP maps (also mipmaps) are pre-calculated, optimized collections of images that accompany a main texture, intended to increase rendering speed and reduce aliasing artifacts. They are widely used in 3D computer games, flight simulators and other 3D imaging systems. The technique is known as mipmapping. The letters "MIP" in the name are an acronym of the Latin phrase multum in parvo, meaning "much in little". Mipmaps need more space in memory. They also form the basis of wavelet compression.

Origin

Mipmapping was invented by Lance Williams in 1983 and is described in his paper Pyramidal parametrics. From the abstract: "This paper advances a 'pyramidal parametric' prefiltering and sampling geometry which minimizes aliasing effects and assures continuity within and between target images." The "pyramid" can be imagined as the set of mipmaps stacked on top of each other.

How it works

An example of mipmap image storage: the principal image on the left is accompanied by filtered copies of reduced size.

Each bitmap image of the mipmap set is a version of the main texture, but at a certain reduced level of detail. Although the main texture would still be used when the view is sufficient to render it in full detail, the renderer will switch to a suitable mipmap image (or in fact, interpolate between the two nearest, if trilinear filtering is activated) when the texture is viewed from a distance or at a small size. Rendering speed increases since the number of texture pixels ("texels") being processed can be much lower than with simple textures. Artifacts are reduced since the mipmap images are effectively already anti-aliased, taking some of the burden off the real-time renderer. Scaling down and up is made more efficient with mipmaps as well.

If the texture has a basic size of 256 by 256 pixels, then the associated mipmap set may contain a series of 8 images, each one-fourth the total area of the previous one: 128×128 pixels, 64×64, 32×32, 16×16, 8×8, 4×4, 2×2, 1×1 (a single pixel). If, for example, a scene is rendering this texture in a space of 40×40 pixels, then either a scaled up version of the 32×32 (without trilinear interpolation) or an interpolation of the 64×64 and the 32×32 mipmaps (with trilinear interpolation) would be used. The simplest way to generate these textures is by successive averaging; however, more sophisticated algorithms (perhaps based on signal processing and Fourier transforms) can also be used.

The increase in storage space required for all of these mipmaps is a third of the original texture, because the sum of the areas 1/4 + 1/16 + 1/64 + 1/256 + · · · converges to 1/3. In the case of an RGB image with three channels stored as separate planes, the total mipmap can be visualized as fitting neatly into a square area twice as large as the dimensions of the original image on each side (four times the original area - one square for each channel, then increase subtotal that by a third). This is the inspiration for the tag "multum in parvo".

In many instances, the filtering should not be uniform in each direction (it should be anisotropic, as opposed to isotropic), and a compromise resolution is used. If a higher resolution is used, the cache coherence goes down, and the aliasing is increased in one direction, but the image tends to be clearer. If a lower resolution is used, the cache coherence is improved, but the image is overly blurry, to the point where it becomes difficult to identify.

To help with this problem, nonuniform mipmaps (also known as rip-maps) are sometimes used, although there is no direct support for this method on modern graphics hardware. With a 16×16 base texture map, the rip-map resolutions would be 16×8, 16×4, 16×2, 16×1, 8×16, 8×8, 8×4, 8×2, 8×1, 4×16, 4×8, 4×4, 4×2, 4×1, 2×16, 2×8, 2×4, 2×2, 2×1, 1×16, 1×8, 1×4, 1×2 and 1×1. In the general case, for a 2ⁿ×2ⁿ base texture map, the rip-map resolutions would be 2ⁱ×2^j for i, j in 0,1,2,...,n.

A trade off : anisotropic mip-mapping

Mipmaps require 33% more memory than a single texture. To reduce the memory requirement, and simultaneously give more resolutions to work with, summed-area tables were conceived. However, this approach tends to exhibit poor cache behavior. Also, a summed-area table needs to have wider types to store the partial sums than the word size used to store the texture. For these reasons, there isn't any hardware that implements summed-area tables today.

A compromise has been reached today, called anisotropic mip-mapping. In the case where an anisotropic filter is needed, a higher resolution mipmap is used, and several texels are averaged in one direction to get more filtering in that direction. This has a somewhat detrimental effect on the cache, but greatly improves image quality.

See also

• Anti-aliasing
• Anisotropic filtering
• Hierarchical modulation – similar technique in broadcasting
• Scale space