Lecture # 02:
Basic Concepts of an Image.
What is an Image?
 An Image is a projection of 3D objects on 2D surface.
OR
 An Image is a 2D light intensity function of form f(x,y).
 Where x & y denotes the spatial co-ordinates and the
value of f @ (x,y) is brightness of the image at that
point.
What is an Image?
 As Image is light Intensity function, so
0<f(x,y)<∞
Light Energy cannot be –ve
Light Energy cannot be Infinite
 An image consists of two components, namely
Illumination and Reflectance, i:e
f(x,y)=i(x,y) * r(x,y)
0<i(x,y)<∞
0<r(x,y)<1
What is an Image?

Illumination is the amount of light falling on the object, and ,
this is property of light source.

Reflectance is the light reflected back from object and this
remains between 0 & 1.
Reflectance=0 (Transparent objects)
Reflectance=1 (Opaque objects)
Digital Image:

A digital image is an image f(x,y) that has been “discritized”
both in spatial & in brightness.

A 2D matrix whose rows & columns identify a unique point in
the image.

The corresponding matrix element value identifies the
brightness level at that point.

The elements of such a digital array are called image elements
,picture elements , pixels or pel.
Digital Image:
Gray Scale:

The Intensity value of any Pixel is called as Gray Level Value,
and it is denoted by ‘ L ’.

The value of ‘L’ lies in a certain range, and this is called as
Gray Scale.

[Lmin , Lmax] is the Gray Scale, such that Lmin <L< Lmax .

For Binary Images, the Gray scale used is [0,1].

For color Images, the Gray scale is [0,255]
Gray Scale:

The interval between the L min and L
0 to 1 (for Binary Images).

We generally have the following conventions:
[0, 7 ]
8-levels
[0, 15 ]
16-levels
[0, 31 ]
32-levels
[0, 255]
256-levels



max
is usually taken from
The Low value represents BLACK.
The high value represent WHITE.
Intermediate Values gives different shades.
Digitization:
 A process of converting Analog Images in to Digital.
 Constitutes of Two steps.
 Sampling
 Digitization of spatial coordinates.
 Quantization
 Digitization of Amplitude Values.
Sampling:

Digitization of spatial coordinates (x, y ) referred to as Image
Sampling.

How much samples are required to extract the enough
information from Analog Image?

Decision is made by using famous “Sampling” Theorem.

Digitization process requires that a decision be made on the
number of discrete grey levels allowed for each pixel.
Quantization:

Amplitude Digitization is called Gray-level Quantization.


In Digital Image Processing let these quantities be integer
powers of two; that is,
N = 2n
and
G = 2m

Where G denotes number of Gray level and Discrete levels are
equally spaced between 0-L
Digital Image Approximation:

Suppose that a continuous Image f(x,y) is approximated by
equally spaced samples to form a N*N array, such that:
 f(x,y)=
f(0,0)
f(1,0)
f(2,0)
.
.
.
f(N-1,0)
f(0,1)
f(1,1)
f(2,1)
.
.
.
f(N-1,1)
f(0,2)
f(1,2)
f(2,2)
.
.
.
f(N-1,2)
f(0,N-1)
f(1,N-1)
f(2,N-1)
.
.
.
f(N-1,N-1)
Digitization:
Analog Image
Digital Image
Quantization
Sampling
Image Representation:

So, a Binary Image stored in computer can be shown as:
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
Memory Representation
for a Digital Image
Image Displayed
Resolution:

It may be defined as the degree of discrete details of an image
which is strongly dependent on both n and m.

The more these parameters are increased, the closer the
digitized array will approximate the original image.

By reducing the number of samples an image is distorted (less
information is available).

By decreasing the number of gray levels we get imperceptible
image and is called False Contouring.
Storage Requirements:

The storage capacity for a digital Image depends upon:
 The Detail Available in Image.
 The Gray Scale being used.

The detail available is represented in terms of the Resolution
(rows * Cols)

The gray scale is represented in terms of encoded bits.
Storage Requirements:

The formula used for calculating “bits” required, is given by:
B=M*N*k
Where M=
N=
K=
Number of Rows
Number of Columns
Bits required to encode
the used Gray scale.

For encoding a gray scale of [0,7] ,that is 8 different gray
values, we need 3 bits.

In case of Square Images (M=N), this becomes:
B=N2*k
Storage Requirements:

Example:
 Find bits required to store a 4*4 digital Image ,when
we are using 64 different gray levels?

Solution:




Resolution=4*4
Gray scale=[0,63]
Encoded bits =6 (coz 26 =64)
So bits required are:



B=M*N*k
B=4*4*6
=96 bits
Answer
Storage Requirements:
N/k
1
2
3
4
5
6
7
8
32
1024
2048
3072
4096
5120
6144
7168
8192
64
4096
8192
12288
16384
20480
24576
28672
32768
128
16384
32768
49152
65536
81920
98304
11468
8
13107
2
256
65536
13107
2
19660
8
26214
4
32768
0
39321
6
45875
2
52428
8
512
262144
52428
8
78643
2
10485
76
13107
20
15728
64
18350
08
20971
52
Table showing Bits required for some typical values of N (N2k)