Page 193 - DCAP303_MULTIMEDIA_SYSTEMS

Unit 11: Compression

Figs. 11.1 (e) and (f) show the respective autocorrelation coefficients computed along one line of notes
each image.
A ( n )∆
g(Dn) =
A()
0
where,
1
1 N−−∆ n
n)
(, )( ,
A(Dn) = ∑ fx yf xy + ∆ .
N − ∆ n y= 0
The scaling factor in equation above accounts for the varying number of sum terms that arise
for each integer value of Δn. Of course, Δn must be strictly less than N, the number of pixels on
a line. The variable x is the coordinate of the line used in the computation. Note the dramatic
difference between the shape of the functions shown in Figs. 11.1(e) and (f). Their shapes can be
qualitatively related to the structure in the images in Figs. 11.1(a) and (b). This relationship is
particularly noticeable in Fig. 11.1 (f), where the high correlation between pixels separated by 45
and 90 samples can be directly related to the spacing between the vertically oriented matches of
Fig. 11.1(b). In addition, the adjacent pixels of both images are highly correlated. When Δn is 1, γ
is 0.9922 and 0.9928 for the images of Figs. 11.1 (a) and (b), respectively. These values are typical
of most properly sampled television images.
These illustrations reflect another important form of data redundancy—one directly related to
the interpixel correlations within an image. Since the value of any given pixel can be reasonably
predicted from the value of its neighbours, the information carried by individual pixels is relatively
small. Much of the visual contribution of a single pixel to an image is redundant; it could have
been guessed on the basis of the values of its neighbours. A variety of names, including spatial
redundancy, geometric redundancy and interframe redundancy, have been coined to refer to these
interpixel dependencies. We use the term interpixel redundancy to encompass them all.
In order to reduce the interpixel redundancies in an image, the 2D pixel array normally used
for human viewing and interpretation must be transformed into a more efficient (but usually
“nonvisual”) format. For example, the differences between adjacent pixels can be used to represent
an image. Transformations of this type (that is, those that remove interpixel redundancy) are
referred to as mappings. They are called reversible mappings if the original image elements can
be reconstructed from the transformed data set.
11.4.3 psychovisual redundancy

The brightness of a region, as perceived by the eye, depends on factors other than simply the
light reflected by the region. For example, intensity variations (Mach bands) can be perceived in
an area of constant intensity. Such phenomena result from the fact that the eye does not respond
with equal sensitivity to all visual information. Certain information simply has less relative
importance than other information in normal visual processing. This information is said to be
psychovisually redundant. It can be eliminated without significantly impairing the quality of
image perception.
In general, an observer searches for distinguishing features such as edges or textural regions and
mentally combines them into recognizable groupings. The brain then correlates these groupings
with prior knowledge in order to complete the image interpretation process. Unlike coding and
interpixel redundancy, psychovisual redundancy is associated with real or quantifiable visual
information. Its elimination is possible only because the information itself is not essential for
normal visual processing. Since the elimination of psychovisually redundant data results in a
loss of quantitative information, it is commonly referred to as quantization.
This terminology is consistent with normal usage of the word, which generally means the mapping
of a broad range of input values to a limited number of output values. As it is an irreversible
operation (visual information is lost), quantization results in lossy data compression.

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