Image Processing Reference
In-Depth Information
(
a
)
(
b
)
Fig. 2.1.
Sampling of a 2D image (
•
: Sample point; solid and broken lines: pixel):
(
a
) Sampling with a square pixel (or a square lattice); (
b
) sampling with a hexagonal
pixel (or a triangular lattice).
(b)
Quantization
: The density value at each pixel (or sampling point) is as-
signed to one of the finite set of integers selected as suitable. This process is
called
quantization
. Quantization is in principle the same as that of a uni-
variate function, such as a time-varying signal transmitted in the commu-
nication system. Typically, a set of integers
0
,
1
,
2
,...,
2
m
,m
=
5
12
is employed to represent the density values of a digitized image. A digi-
tized image defined in this way takes only integer density values. This is
almost always true in applications in which only the finite number of bits
are available. It is not so convenient, however, for the theoretical analysis
of image processing, because in many image operations such as smooth-
ing, differentiation and spatial frequency enhancement, density values of
an output image may in principle take on an arbitrary real value. There-
fore, we assume that a digitized image can take arbitrary real values as
its density values unless stated otherwise.
∼
The size of an image is always finite in practical cases. In the theoretical
considerations in this topic, we treat both an image of the finite size and that
of the infinite size. From now on we will consider that a digitized image is
sampled at the square lattice or is divided into square pixels unless stated
otherwise. An image is called
binary image
if the density at any pixel assumes
only two values. We assign
0
and
1
to the densities of a digitized binary
image unless defined otherwise. Pixels of a binary image with values
0
and
1
are called 0-
pixels
and 1-
pixels
, respectively. An image that may take various
different density values is called
gray-tone image
.
Let (
i, j
) denote a pixel location in the
i
-throwandthe
j
-th column, and
F
denote a digitized image in which the value of the density at a
pixel (
i, j
)isgivenby
f
ij
. We represent an arbitrary pixel in the way such as
apixelP,apointP,apixelP=(
i, j
), and a pixel
=
{
f
ij
}
x
.
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