Digital Image Processing Unit-3

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Department: ELECTRONICS &COMMU

Unit: III

Topic name: Image Enhancement P

Books referred: 01. Digital Image P02. www.wikipedi

03. www.google.c

Image Enhancement:

The aim of image enha

information in images for human

processing techniques.

Image enhancement techniques ca

1. Spatial domain methods, which

2. Frequency domain methods, whi

Unfortunately, there is no

is when it comes to human pe

enhancement techniques are use

then quantitative measures can de

Spatial Domain Methods:

The value of a pixel wit

performing some operation on the

Neighborhoods can be any

Grey scale manipulation:

The simplest form of opera

in the input image that is F (x, y

transformation or mapping.The simplest case is thres

active at a chosen threshold value.

input image gets mapped to 0 in th

Other grey scale transform

Faculty/Date:

Page 1 of4

L

TEACHING NOTES

NICATION ENGINEERING

Date:

oint Processing No. of marks allotted by JNT

rocessing by R C Gonzalez and R E Woodsa.org

om

cement is to improve the interpretability or

iewers, or to provide better input for other aut

n be divided into two broad categories:

perate directly on pixels, and

ch operate on the Fourier transform of an image.

general theory for determining what `good image

ception. If it looks good, it is good! However

as pre-processing tools for other image processi

ermine which techniques are most appropriate.

coordinates (x, y) in the enhanced image F is

pixels in the neighborhood of (x, y) in the input ima

shape, but usually they are rectangular.

tion is when the operator T acts only on a 11 pixel

) depends on the value of F only at (x, y). This

hold where the intensity profile is replaced by a

In this case any pixel with a grey level below the t

e output image. Other pixels are mapped to 255.

ations are outlined in figure-1 below.

HOD/Date:

CE/7.5.1/RC 01

K:

perception of

omated image

enhancement

when image

ng techniques,

the result of

ge, F.

neighborhood

is a grey scale

step function,

reshold in the

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LCE/7.5.1/RC 01

TEACHING NOTES

Department: ELECTRONICS &COMMUNICATION ENGINEERING

Unit: III Date:

Topic name: Histogram Processing No. of marks allotted by JNTUK:

Books referred: 01. Digital Image Processing by R C Gonzalez and R E Woods02. www.wikipedia.org

03. www.google.com

Histogram Processing:

Histogram equalization is a common technique for enhancing the appearance of images.

Suppose we have an image which is predominantly dark. Then its histogram would be skewed

towards the lower end of the grey scale and all the image detail is compressed into the dark end of

the histogram. If we could stretch out the grey levels at the dark end to produce a more uniformly

distributed histogram then the image would become much cleaner.

Histogram equalization involves finding a grey scale transformation function that creates an

output image with a uniform histogram.

Q. How do we determine this grey scale transformation function?

Assume our grey levels are continuous and have been normalized to lie between 0 and 1.

We must find a transformation T that maps grey values r in the input image F to grey values s = T(r)

in the transformed image F.

It is assumed that, T is single valued & monotonically increasing, and 0 T(r) 1 for 0 r 1.

The inverse transformation from s to r is given by,

r = T-1

(s).

If one takes the histogram for the input image and normalizes it so that the area under the

histogram is 1, we have a probability distribution for grey levels in the input image Pr(r).

Q. If we transform the input image to get s = T(r) what is the probability distribution Ps(s)?

From probability theory it turns out that

Ps(S) = Pr(r)[dr/ds]

Where, r = T-1(s).

Consider the transformation,

s = T(r) = Pr()d

This is the cumulative distribution function of r. using this definition of T we see that the

derivative of s with respect to r is

ds/dr = Pr(r)

Substituting this back into the expression for Ps, we get

Ps(S) = Pr(r)[1/Pr(r)] = 1

for all s, where 0 s 1. Thus, Ps(s) is now a uniform distribution function, which is what we

want.

Faculty/Date: HOD/Date:

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Page 3 of4

LCE/7.5.1/RC 01

TEACHING NOTES


Unit: III Date:

Topic name: Spatial Filtering - 1 No. of marks allotted by JNTUK:


03. www.google.com

Spatial Filtering:

A spatial filter is an optical device which uses the principles of Fourier optics to alter the

structure of a beam of coherent light or other electromagnetic radiation. Spatial filtering is

commonly used to clean up the output of lasers, removing aberrations in the beam due to imperfect,

dirty, or damaged optics, or due to variations in the laser gain medium itself. This can be used to

produce a laser beam containing only a single transverse mode of the lasers optical resonator.

In spatial filtering, a lens is used to focus the beam. Because of diffraction, a beam that is not

a perfect plane wave will not focus to a single spot, but rather will produce a pattern of light and

dark regions in the focal plane. For example, an imperfect beam might form a bright spot

surrounded by a series of concentric rings. It can be shown as follows:

It can be shown that this 2D pattern is the 2DFT of the initial beams transverse intensity

distribution. In this context, the focal plane is often called the transform plane. Light in the very

center of the transform pattern corresponds to a perfect, wide plane wave. Other light corresponds

to structure in the beam, with light further from the central spot corresponding to structure with

higher spatial frequency. A pattern with very fine details will produce light very far from the

transform planes central spot. In the example above, the large central spot and rings of light

surrounding it are due to the structure resulting when the beam passed through a circular aperture.

The spot is enlarged because the beam is limited by the aperture to a finite size, and the rings relate

to passed through a circular aperture. The spot is enlarged because the beam is limited by the

aperture to a finite size, and the rings relate to the sharp edges of the beam created by the edges of

the aperture. This pattern is called an Airy pattern, after its discoverer George Airy.

In practice, the diameter of the aperture is chosen based on the focal length of the lens, the

diameter and quality of the input beam, and its wavelength. If the hole is too small, the beam quality

is greatly improved but the power is greatly reduced. If the hole is too large, the beam quality maynot be improved as much as desired.

The size of aperture that can be used also depends on the size and quality of the optics. To

use a very small pinhole, one must use a focusing lens with a low f-number, and ideally the lens

should not add significant aberrations to the beam. The design of such a lens becomes increasingly

more difficult as the f-number decreases.


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Page 4 of4

LCE/7.5.1/RC 01

TEACHING NOTES


Unit: III Date:

Topic name: Spatial Filtering - 2 No. of marks allotted by JNTUK:


03. www.google.com

In practice, the most commonly used configuration is to use a microscope objective lens for

focusing the beam, and an aperture made by punching a small, precise, hole in a piece of thick metal

foil. Such assemblies are available commercially.


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Digital Image Processing Unit-3

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