A Basic Image Compression Example2.42003/03/262003/04/28NickKingsburyngk10@cam.ac.ukLiqunWangliqun@rice.eduNickKingsburyngk10@cam.ac.ukEnergy CompressionEntropy CodingImage CompressionQuantisationThis module gives a basic image compression example.
We shall represent a monochrome (luminance) image by a matrix
x whose elements are
xn, where
nn1n2 is the integer vector of row and column indexes. The
energy of x is
defined as
Energy of xnxn2
where the sum is performed over all
n in x.
The basic block diagram of an image coding system.
shows the main blocks in
any image coding system. The decoder is the inverse of the
encoder. The three encoder blocks perform the following tasks:
Energy compression - This is usually a
transformation or filtering process which aims to
concentrate a high proportion of the energy of the image
x into as few
samples (coefficients) of y as
possible while preserving
the total energy of x in
y. This
minimises the number
of non-zero samples of y which
need to be transmitted for a given level of distortion in
the reconstructed image
x^.
Quantisation - This represents the samples of
y to a given
level of accuracy in the integer matrix q. The quantiser step size
controls the tradeoff between distortion and bit rate and
may be adapted to take account of human visual
sensitivities. The inverse quantiser reconstructs
y^, the best estimate of
y from q.
Entropy coding - This encodes the integers in
q into a serial
bit stream d, using
variable-length entropy codes which attempt to minimise the
total number of bits in d,
based on the statistics (PDFs) of various classes of samples
in q.
The energy compression / reconstruction and the entropy coding /
decoding processes are normally all lossless. Only the quantiser
introduces loss and distortion:
y^ is a distorted version of
y, and hence
x^ is a distorted version of x. In the absence of quantisation,
if
y^y, then
x^x.