Image Compression Back
to main page

Quantization
Quantization refers to the process of approximating
the continuous set of values in the image data with a
finite (preferably small) set of values. The input to a
quantizer is the original data, and the output is always
one among a finite number of levels. The quantizer is a
function whose set of output values are discrete, and
usually finite. Obviously, this is a process of
approximation, and a good quantizer is one which
represents the original signal with minimum loss or
distortion.
There are two types of quantization  Scalar
Quantization and Vector Quantization. In scalar
quantization, each input symbol is treated separately in
producing the output, while in vector quantization the
input symbols are clubbed together in groups called
vectors, and processed to give the output. This clubbing
of data and treating them as a single unit increases the
optimality of the vector quantizer, but at the cost of
increased computational complexity. Here, we'll take a
look at scalar quantization.
A quantizer can be specified by its
input partitions and output levels (also called
reproduction points). If the input range is divided into
levels of equal spacing, then the quantizer is termed as
a Uniform Quantizer, and if not, it is termed as a
NonUniform Quantizer. A uniform quantizer can be easily
specified by its lower bound and the step size. Also,
implementing a uniform quantizer is easier than a
nonuniform quantizer. Take a look at the uniform
quantizer shown below. If the input falls between n*r and
(n+1)*r, the quantizer outputs the symbol n.
Fig 1. A uniform quantizer
Just the same way a quantizer partitions its input and
outputs discrete levels, a Dequantizer is one which
receives the output levels of a quantizer and converts
them into normal data, by translating each level into a
'reproduction point' in the actual range of data. It can
be seen from literature, that the optimum quantizer
(encoder) and optimum dequantizer (decoder) must satisfy
the following conditions.
 Given the output levels or partitions of the
encoder, the best decoder is one that puts the
reproduction points x' on the centers of
mass of the partitions. This is known as centroid
condition.
 Given the reproduction points of the decoder, the
best encoder is one that puts the partition
boundaries exactly in the middle of the
reproduction points, i.e. each x is
translated to its nearest reproduction point.
This is known as nearest neighbour condition.
The quantization error (x  x') is used as a
measure of the optimality of the quantizer and
dequantizer.
Copyright (c) Satish Kumar. S 20012003. Last Modified  22 Oct 2001
Suggestions/Broken links/queries? Write to satish@debugmode.com
