Quantization, involved in
image processing
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
, is a
lossy compression
In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size ...
technique achieved by compressing a range of values to a single quantum (discrete) value. When the number of discrete symbols in a given stream is reduced, the stream becomes more compressible. For example, reducing the number of colors required to represent a digital
image
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
makes it possible to reduce its file size. Specific applications include
DCT data quantization in
JPEG
JPEG ( ) is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography. The degree of compression can be adjusted, allowing a selectable tradeoff between storage size and imag ...
and
DWT data quantization in
JPEG 2000.
Color quantization
Color quantization reduces the number of colors used in an image; this is important for displaying images on devices that support a limited number of colors and for efficiently compressing certain kinds of images. Most bitmap editors and many operating systems have built-in support for color quantization. Popular modern color quantization algorithms include the nearest color algorithm (for fixed palettes), the
median cut algorithm, and an algorithm based on
octree
An octree is a tree data structure in which each internal node has exactly eight children. Octrees are most often used to partition a three-dimensional space by recursively subdividing it into eight octants. Octrees are the three-dimensional ana ...
s.
It is common to combine color quantization with
dither
Dither is an intentionally applied form of image noise, noise used to randomize quantization error, preventing large-scale patterns such as color banding in images. Dither is routinely used in processing of both digital audio and digital vide ...
ing to create an impression of a larger number of colors and eliminate
banding artifacts.
Frequency quantization for image compression
The human eye is fairly good at seeing small differences in
brightness
Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminance, ...
over a relatively large area, but not so good at distinguishing the exact strength of a high frequency (rapidly varying) brightness variation. This fact allows one to reduce the amount of information required by ignoring the high frequency components. This is done by simply dividing each component in the frequency domain by a constant for that component, and then rounding to the nearest integer. This is the main lossy operation in the whole process. As a result of this, it is typically the case that many of the higher frequency components are rounded to zero, and many of the rest become small positive or negative numbers.
As human vision is also more sensitive to
luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls withi ...
than
chrominance
Chrominance (''chroma'' or ''C'' for short) is the signal used in video systems to convey the color information of the picture (see YUV color model), separately from the accompanying luma signal (or Y' for short). Chrominance is usually represente ...
, further compression can be obtained by working in a non-RGB color space which separates the two (e.g.,
YCbCr
YCbCr, Y′CbCr, or Y Pb/Cb Pr/Cr, also written as YCBCR or Y′CBCR, is a family of color spaces used as a part of the color image pipeline in video and digital photography systems. Y′ is the luma component and CB and CR are the blue-diff ...
), and quantizing the channels separately.
[John Wiseman, ''An Introduction to MPEG Video Compression'', https://web.archive.org/web/20111115004238/http://www.john-wiseman.com/technical/MPEG_tutorial.htm]
Quantization matrices
A typical video codec works by breaking the picture into discrete blocks (8×8 pixels in the case of MPEG
). These blocks can then be subjected to
discrete cosine transform (DCT) to calculate the frequency components, both horizontally and vertically.
The resulting block (the same size as the original block) is then pre-multiplied by the quantisation scale code and divided element-wise by the quantization matrix, and rounding each resultant element. The quantization matrix is designed to provide more resolution to more perceivable frequency components over less perceivable components (usually lower frequencies over high frequencies) in addition to transforming as many components to 0, which can be encoded with greatest efficiency. Many video encoders (such as
DivX,
Xvid
Xvid (formerly "XviD") is a video codec library following the MPEG-4 video coding standard, specifically MPEG-4 Part 2 Advanced Simple Profile (ASP). It uses ASP features such as b-frames, global and quarter pixel motion compensation, lumi mas ...
, and
3ivx) and compression standards (such as
MPEG-2
MPEG-2 (a.k.a. H.222/H.262 as was defined by the ITU) is a standard for "the generic video coding format, coding of moving pictures and associated audio information". It describes a combination of Lossy compression, lossy video compression and ...
and
H.264/AVC) allow custom matrices to be used. The extent of the reduction may be varied by changing the quantizer scale code, taking up much less bandwidth than a full quantizer matrix.
This is an example of DCT coefficient matrix:
:
A common quantization matrix is:
:
Dividing the DCT coefficient matrix element-wise with this quantization matrix, and rounding to integers results in:
:
For example, using −415 (the DC coefficient) and rounding to the nearest integer
:
Typically this process will result in matrices with values primarily in the upper left (low frequency) corner. By using a zig-zag ordering to group the non-zero entries and
run length encoding
Run-length encoding (RLE) is a form of lossless data compression in which ''runs'' of data (sequences in which the same data value occurs in many consecutive data elements) are stored as a single data value and count, rather than as the original ...
, the quantized matrix can be much more efficiently stored than the non-quantized version.
See also
*
Image segmentation
In digital image processing and computer vision, image segmentation is the process of partitioning a digital image into multiple image segments, also known as image regions or image objects ( sets of pixels). The goal of segmentation is to simpli ...
*
Image-based meshing Image-based meshing is the automated process of creating computer models for computational fluid dynamics (CFD) and finite element analysis (FEA) from 3D image data (such as magnetic resonance imaging (MRI), computed tomography (CT) or microtomogra ...
*
Range segmentation Range segmentation is the task of segmenting (dividing) a '' range image'', an image containing depth information for each pixel, into segments (regions), so that all the points of the same surface belong to the same region, there is no overlap b ...
References
{{DEFAULTSORT:Quantization (Image Processing)
Lossy compression algorithms
Image compression