This module gives a basic image compression example.
We shall represent a monochrome (luminance) image by a matrix
whose elements are
, where
is the integer vector of row and column indexes. The
energy of
is
defined as
where the sum is performed over all
in
.
The basic block diagram of an image coding system.
shows the main blocks in
any image coding system. The decoder is the inverse of theencoder. The three encoder blocks perform the following tasks:
Energy compression - This is usually a
transformation or filtering process which aims toconcentrate a high proportion of the energy of the image
into as few
samples (coefficients) of
as
possible while preservingthe total energy of
in
. This
minimises the numberof non-zero samples of
which
need to be transmitted for a given level of distortion inthe reconstructed image
.
Quantisation - This represents the samples of
to a given
level of accuracy in the integer matrix
. The quantiser step size
controls the tradeoff between distortion and bit rate andmay be adapted to take account of human visual
sensitivities. The inverse quantiser reconstructs
, the best estimate of
from
.
Entropy coding - This encodes the integers in
into a serial
bit stream
, using
variable-length entropy codes which attempt to minimise thetotal number of bits in
,
based on the statistics (PDFs) of various classes of samplesin
.
The energy compression / reconstruction and the entropy coding /
decoding processes are normally all lossless. Only the quantiserintroduces loss and distortion:
is a distorted version of
, and hence
is a distorted version of
. In the absence of quantisation,
if
, then
.
