3. Image Sampling & Quantisation
3.1 Basic Concepts
•To create a digital image, we need to
convert continuous sensed data into
digital form.
•This involves two processes: sampling
and quantisation
•The basic idea behind sampling and
quantization is illustrated in Fig. 3.1.
• Figure 3.1(a) shows a continuous image,
f (x, y), that we want to convert to digital
form.
• To convert it to digital form, we have to
sample the function in both coordinates
and in amplitude.
• An image may be continuous with respect
to the x- and y-coordinates and also in
amplitude.
• Digitizing the coordinate values is called
sampling.
• Digitizing the amplitude values is called
quantization.
Fig 3.1 Generating a digital image (a) Continuous image. (b) A scan line from
A to B in the continuous image. (c) Sampling & quantisation. (d) Digital scan
line.
• The one-dimensional function shown in
Fig. 3.1(b) is a plot of amplitute (gray level)
values of the continuous image along the
line segment AB in Fig. 3.1(a).
• To sample this function, we take equally
spaced samples along line AB, as shown
in Fig. 3.1(c).
• Location of each sample is given by a
vertical tick mark in the bottom part of the
figure.
• The samples are shown as small white
squares superimposed on the function.
The set of these discrete locations gives
the sampled function.
• However, the values of the samples still
span (vertically) a continuous range of
gray-level values.
• In order to form a digital function, the
gray-level values also must be converted
(quantized) into discrete quantities.
• The right side of Fig. 3.1(c) shows the
gray-level scale divided into eight discrete
levels, ranging from black to white.
• The vertical tick marks indicate the specific
value assigned to each of eight gray
levels.
• The continuous gray levels are quantized
simply by assigning one of the eight
discrete gray levels to each sample.
• The assignment is made depending on the
vertical proximity of a sample to a vertical
tick mark.
• The digital samples resulting from both
sampling and quantization are shown in
Fig. 3.1(d) and Fig 3.2 (b).
Fig. 3.2 (a) Continuous image projected onto a sensor array.
(b) Result of image sampling and quantisation
3.2 Representing Digital Images
• The result of sampling and quantisation is
a matrix of real numbers as shown in
Fig.3.3, Fig.3.4. and Fig 3.5.
• The values of the coordinates at the origin
are (x,y) = (0,0).
• The next coordinate values along the first
row are (x,y) = (0,1).
• The notation (0,1) is used to signify the 2nd
sample along the 1st row.
Fig. 3.3. Coordinate convention used to represent
digital images
Fig. 3.4. A digital image of size M x N
• It is advantageous to use a more
traditional matrix notation to denote a
digital image and its elements.
Fig. 3.5 A digital image
• The number of bits required to store a
digitised image is
•
b=MxNxk
Where M & N are the number of rows and
columns, respectively.
• The number of gray levels is an integer
power of 2:
•
L = 2k where k =1,2,…24
• It is common practice to refer to the image
as a “k-bit image”
• The spatial resolution of an image is the
physical size of a pixel in that image; i.e.,
the area in the scene that is represented
by a single pixel in that image.
• Dense sampling will produce a high
resolution image in which there are many
pixels, each of which represents of a small
part of the scene.
• Coarse sampling, will produce a low
resolution image in which there are a few
pixels, each of which represents of a
relatively large part of the scene.
Fig. 3.6 Effect of resolution on image interpretation (a) 8x8
image. (b) 32x32 image © 256x256 image
Fig.3.7 Effect of quantisation on image interpretation. (a) 4
levels. (b) 16 levels. (c) 256 levels