Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

Spatial Resolution
Image resolution
There are numerous ways to define image resolution
...

We'll define spatial resolution as a different form of resolution in
this tutorial
...
An image's pixel count is
not important
...
(Digital Image
Processing, Second Edition, Gonzalez, Woods)
Alternatively, the number of distinct pixel values per inch can be
used to determine spatial resolution
...

If we want to identify which photo is clearer or has a greater
spatial resolution, we must compare two images of the same
size
...


Even if the same individual appears in both photographs, that is
not the circumstance we are evaluating
...
The image on
the right side, in contrast, is zoomed and measures 980 x 749
pixels
...
Keep in mind that in this situation, the zoom factor is
irrelevant; the only thing that counts is that these two images
are not equal
...


Now you can compare these two pictures
...
Now when you
compare them, you will see that the picture on the left side has
more spatial resolution or it is more clear then the picture on the
right side
...

Measuring spatial resolution
Since the spatial resolution refers to clarity, so for different
devices, different measure has been made to measure it
...

Dots per inch
Dots per inch or DPI is usually used in monitors
...

Pixel per inch
Pixel per inch or PPI is measure for different devices such as
tablets , Mobile phones e
...
c
...
Now we are formally going to
discuss all of them
...

The higher is the PPI, the higher is the quality
...
Lets calculate the PPI of a
mobile phone
...
But how
does it is calculated?
First of all we will Pythagoras theorem to calculate the diagonal
resolution in pixels
...

For Samsung galaxy s4, it is 1080 x 1920 pixels
...
90717
Now we will calculate PPI
PPI = c / diagonal size in inches
The diagonal size in inches of Samsung galaxy s4 is 5
...

PPI = 2202
...
0
PPI = 440
...

Dots per inch
...
Dots per inch, or DPI, is a
measurement of a printer's spatial resolution
...


Keep in mind that not every pixel per inch must be printed with
one dot per inch
...
The majority of color
printers employ the CMYK model, which is the cause of this
...
In contrast to the hundreds of
thousands of colors available on a computer, the printer must
choose from these colors to create the color of each pixel
...

Usually some of the laser printers have dpi of 300 and some have
600 or more
...
The resolution of halftone screen is measured in
lines per inch
...

Printer

LPI

Screen printing

45-65 lpi

Laser printer (300 dpi)

65 lpi

Laser printer (600 dpi)

85-105 lpi

Offset Press (newsprint paper) 85 lpi

Offset Press (coated paper)

85-185 lpi

Gray Level Resolution
Image resolution
A resolution can be defined as the total number of pixels in an
image
...
And we have
also discussed, that clarity of an image does not depends on
number of pixels, but on the spatial resolution of the image
...
Here we are going
to discuss another type of resolution which is called gray level
resolution
...

In short gray level resolution is equal to the number of bits per
pixel
...
We will define bpp
here briefly
...


Mathematically
The mathematical relation that can be established between gray
level resolution and bits per pixel can be given as
...
It can also be
defined as the shades of gray
...
So the 2 raise to the power of bits per pixel is equal to the
gray level resolution
...
Means it is
an image with 8 bits per pixel or 8bpp
...


It means it gray level resolution is 256
...

The more is the bits per pixel of an image, the more is its gray
level resolution
...
We can also define it in terms of bits
per pixel
...
There are two answers to that question
...

The second answer is 4 bits
...
For this, we just have to twist the formula a little
...


This formula finds the levels
...

K = log base 2(L) Equation (2)
Because in the first equation the relationship between Levels (L
) and bits per pixel (k) is exponentional
...

Lets take an example to find bits per pixel from gray level
resolution
...
What is the bits per pixel
required for it
...

K = log base 2 ( 256)
K = 8
...

Gray level resolution and quantization:
The quantization will be formally introduced in the next tutorial,
but here we are just going to explain the relation ship between
gray level resolution and quantization
...
In the
tutorial of Introduction to signals and system, we have studied

that digitizing a an analog signal requires two steps
...


Sampling is done on x axis
...

So that means digitizing the gray level resolution of an image is
done in quantization
...
We are formally going to relate it with digital images in
this tutorial
...

Digitizing a signal
As we have seen in the previous tutorials, that digitizing an
analog signal into a digital, requires two basic steps
...
Sampling is done on x axis
...

The below figure shows sampling of a signal
...
The more
samples you take, the more pixels, you get
...
This has been discussed under
sampling and zooming tutorial
...

What is quantization
Quantization is opposite to sampling
...
When
you are quantizing an image, you are actually dividing a signal
into quanta(partitions)
...
So digitizing the amplitudes is known
as Quantization
...
That means that when we sample an
image, we actually gather a lot of values, and in quantization, we
set levels to these values
...


In the figure shown in sampling, although the samples has been
taken, but they were still spanning vertically to a continuous

range of gray level values
...
Ranging from 0 black to 4 white
...

The relation of quantization with gray levels has been further
discussed below
...

It means that the image formed from this signal, would only have
5 different colors
...
Now if you were to make the
quality of the image more better, there is one thing you can do
here
...

If you increase this level to 256, it means you have an gray scale
image
...

Now 256, or 5 or what ever level you choose is called gray level
...

Which were these two
...
(k in the
equation)
Gray level = number of levels per pixel
...
If we have to
calculate the number of bits, we would simply put the values in
the equation
...

Reducing the gray level
Now we will reduce the gray levels of the image to see the effect
on the image
...

It is a grayscale image and the image looks something like this
...
We will first reduce
the gray levels from 256 to 128
...
Lets decrease some more
...

32 Gray Levels

Surprised to see, that there is still some little effect
...

16 Gray Levels

Boom here, we go, the image finally reveals, that it is effected by
the levels
...
Now we will reduce it to 2 levels, which is nothing but a
simple black and white level
...

2 Gray Levels

Thats the last level we can achieve, because if reduce it further,
it would be simply a black image, which can not be interpreted
...
This effect is known as Contouring
...
They are discussed in our next tutorial of
Contouring and Iso preference curves

---