Quantization (image processing): Difference between revisions
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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]], the quantized matrix can be much more efficiently stored than the non-quantized version.<ref name="wiseman"/> |
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]], the quantized matrix can be much more efficiently stored than the non-quantized version.<ref name="wiseman"/> |
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Revision as of 20:10, 6 November 2010
Quantization, involved in image processing, is a lossy compression technique achieved by compressing a range of values to a single quantum 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 makes it possible to reduce its file size. Specific applications include DCT data quantization in JPEG 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 octrees.
It is common to combine color quantization with dithering 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 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 than chrominance, further compression can be obtained by working in a non-RGB color space which separates the two (e.g. YCbCr), and quantizing the channels separately.[1]
Quantization matrices
A typical video codec works by breaking the picture into discreet blocks (8×8 pixels in the case of MPEG[1]). These blocks can then be subjected to discrete cosine transform (DCT) to separate out the low frequency and high frequency components in both the horizontal and vertical direction.[1] The resulting block (the same size as the original block) is then divided by the quantization matrix, and each entry rounded. The coefficients of quantization matrices are often specifically designed to keep certain frequencies in the source to avoid losing image quality. Many video encoders, such as MPEG-2, DivX, Xvid, 3ivx and H.264/AVC allow custom matrices to be used. Alternatively, the extent of the reduction may be varied by multiplying the quantizer matrix by a scaling factor, the quantizer scale code, prior to performing the division.[1]
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, the quantized matrix can be much more efficiently stored than the non-quantized version.[1]