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Concept of Sampling
Conversion of analog signal to digital signal:
Most image sensors output analog signals, which cannot be
stored and thus processed digitally
...
An analog signal has to be converted into a digital one
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The procedure consists of two phases
...
But first, we'll talk a little bit about the differences
between the two, and why these two processes are necessary
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Sampling is the process of digitizing coordinates since a picture
is continuous not only in its co-ordinates (x axis), but also in its
amplitude (y axis)
...
Sampling
...
But we are going to discuss
here more
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The term sampling refers to take samples
We digitize x axis in sampling
It is done on independent variable
In case of equation y = sin(x), it is done on x variable
It is further divided into two parts , up sampling and down
sampling
You can observe that the signal has some arbitrary changes if you
look at the above figure
...
By obtaining samples during sampling, we can lower this noise
...
But unless you also sample the y-axis, a process known as
quantization, the signal is not converted to digital format if you
sample only the x axis
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Relation ship with pixels
Since a pixel is a smallest element in an image
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Lets say we have total of 25 pixels, that means we have a square
image of 5 X 5
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So it means that
of our continuous signal, we have taken 25 samples on x axis
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This leads to another conclusion that since pixel is also the
smallest division of a CCD array
...
Relationship with CCD array
A CCD array's number of sensors and number of pixels are
identical
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Oversampling
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Which is up sampling and down
sampling
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The oversampling has a very deep application in image
processing which is known as Zooming
...
Zooming refers to increase the quantity of pixels, so that when
you zoom an image, you will see more detail
...
The one way to zoom is, or to increase samples, is
to zoom optically, through the motor movement of the lens and
then capture the image
...
There is a difference between zooming and sampling
The concept is same, which is, to increase samples
...
Pixel Resolution
Before we define pixel resolution, it is necessary to define a pixel
...
We also defined that a pixel can store a value
proportional to the light intensity at that particular location
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Resolution
The resolution can be defined in many ways
...
Out of which we are going to discuss pixel resolution
...
t
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For example
...
If we define resolution as the total number of pixels, then pixel
resolution can be defined with set of two numbers
...
We can say that the higher is the pixel resolution, the higher is
the quality of the image
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Megapixels
We can calculate mega pixels of a camera using pixel resolution
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The size of an image can be defined by its pixel resolution
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Its pixel resolution = 2500 * 3192 = 7982350 bytes
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9 = 8 mega pixel (approximately)
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Aspect ratio is the ratio between width of an image and the
height of an image
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This ratio differs in different images,
and in different screens
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33:1, 1
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43:1, 1
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56:1, 1
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75:1, 1
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85:1, 2
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t
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It does not let the image to get
distorted when aspect ratio is increased
...
If
we wish to make is smaller, and the condition is that the quality
remains the same or in other way the image does not get
distorted, here how it happens
...
Result
Smaller image, but with same balance
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Finding the dimensions of the image from aspect ratio:
Aspect ratio tells us many things
...
For example
If you are given an image with aspect ratio of 6:2 of an image of
pixel resolution of 480000 pixels given the image is an gray scale
image
...
•
•
Resolve pixel resolution to calculate the dimensions of
image
Calculate the size of the image
Solution:
Given:
Aspect ratio: c:r = 6:2
Pixel resolution: c * r = 480000
Bits per pixel: grayscale image = 8bpp
Find:
Number of rows = ?
Number of cols = ?
Solving first part:
Solving 2nd part:
Size = rows * cols * bpp
Size of image in bits = 400 * 1200 * 8 = 3840000 bits
Size of image in bytes = 480000 bytes
Size of image in kilo bytes = 48 kb (approx)
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Zooming
Zooming simply means enlarging a picture in a sense that the
details in the image became more visible and clear
...
t
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For example
is zoomed into
You can zoom something at two different steps
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This is known as pre processing zoom
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The second step is to zoom once an image has been captured
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We will discuss them in detail in the next tutorial
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Optical Zoom:
The optical zoom is achieved using the movement of the lens of
your camera
...
The result
of the optical zoom is far better then that of digital zoom
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In optical zoom the lens is physically extend to zoom or magnify
an object
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During a digital zoom, the center of the image is magnified and
the edges of the picture got crop out
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During a digital zoom, the pixels got expand , due to which the
quality of the image is compromised
...
The following picture is the result of digital zoom done through
one of the following methods given below in the zooming
methods
...
Rather we will focus on the methods, that enable to
zoom a digital image
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They are listed below
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Zooming Methods
In this tutorial we are going to formally introduce three methods
of zooming that were introduced in the tutorial of Introduction
to zooming
...
We will start by discussing pixel replication
...
As its name
suggest, in this method, we just replicate the neighboring pixels
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This
algorithm works on the same principle
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Each pixel is replicated in this method n times row wise
and column wise and you got a zoomed image
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For example:
if you have an image of 2 rows and 2 columns and you want to
zoom it twice or 2 times using pixel replication, here how it can
be done
...
1
2
3
4
The above image has two rows and two columns, we will first
zoom it row wise
...
Here how it would be done
...
Column size zooming:
The next step is to replicate each of the pixel column wise, that
we will simply copy the column pixel to its adjacent new column
or simply below it
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1
1
2
2
1
1
2
2
3
3
4
4
3
3
4
4
New image size:
As it can be seen from the above example, that an original image
of 2 rows and 2 columns has been converted into 4 rows and 4
columns after zooming
...
You just have to copy the pixels and nothing else
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And as the zooming factor increased,
the image got more and more blurred
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Method 2: Zero order hold
Introduction
Zero order hold method is another method of zooming
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Because it can only zoom twice
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Working
In zero order hold method, we pick two adjacent elements from
the rows respectively and then we add them and divide the
result by two, and place their result in between those two
elements
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For example
Lets take an image of the dimensions of 2 rows and 2 columns
and zoom it twice using zero order hold
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Row wise zooming
1
1
2
3
3
4
As we take the first two numbers : (2 + 1) = 3 and then we divide
it by 2, we get 1
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The same method
is applied in the row 2
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We
add them and got 4
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The same method is applied in all the
columns
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So it means that
the dimensions of the new image are based on the following
formula
(2(number of rows) minus 1) X (2(number of columns) minus 1)
Advantages and disadvantage
...
But it also has a disadvantage that it can
only run on the power of 2
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Reason behind twice zooming:
Consider the above image of 2 rows and 2 columns
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As the formula shows us this
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Even if you try to zoom it, you can not
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Then
you will zoom it again and you will get dimensions equal to 5 x 5
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Whereas according to the formula of yours the answer should be
11x11
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Method 3: K-Times zooming
Introduction:
K times is the third zooming method we are going to discuss
...
It
caters the challenges of both twice zooming and pixel
replication
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Working:
It works like this way
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Then you have to subtract the smaller from the
greater one
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Divide the output(OP) with the zooming factor(K)
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Add the value OP again to the value you just put and place it
again next to the previous putted value
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Repeat the same step for all the rows and the columns , and you
get a zoomed images
...
And you have to zoom it thrice or three times
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K = 3
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Row wise zooming
Take the first two adjacent pixels
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Subtract 15 from 30
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Divide 15 by k
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We call it OP
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15 + OP = 15 + 5 = 20
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20 + OP = 20 + 5 = 25
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Now repeat this step for the next two adjacent pixels
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After inserting the values, you have to sort the inserted values in
ascending order, so there remains a symmetry between them
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15
20
25
30
20
25
15
30
20
25
15
20
25
30
Table 2
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The
procedure include taking the two adjacent pixel values, and then
subtracting the smaller from the bigger one
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Store the result as OP
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Insert the new values
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15
20
25
30
25
20
15
20
21
21
25
21
21
20
25
22
22
20
22
22
25
30
25
20
15
20
25
30
New image size
The best way to calculate the formula for the dimensions of a
new image is to compare the dimensions of the original image
and the final image
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And the dimensions of the new image are 4 x 7
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So hence It comprises the power of the two algorithms
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