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Suppose we have a digital image which can be represented by a two dimensional random field A’y ^ . t r

**Image Enhancement: Spatial domain methods:**

Suppose we have a digital image which can be
represented by a two dimensional random field ^{A}’^{y} ^ *.* t *r*

An image processing operator in the spatial domain
may be expressed as a mathematical function L applied to the image *f* to produce a new image -^{v}^
“ ^ ^ '^{X}' -^{v}^ - as follows.

*g{x,y) =
T\{x,y)_*

The operator * ^{T}*
applied on

A single pixel ^{(x,y)} .
In this case * ^{T}* is a grey
level transformation (or mapping) function.

Some neighbourhood of ^{( x ,}^{y)}.

* ^{T}* may
operate to a set of input images instead of a single image.

**Example 1**

The result of the transformation shown in the
figure below is to produce an image of higher contrast than the original, by
darkening the levels below *m* and
brightening the levels above *m* in the
original image. This technique is known as contrast stretching.

**Example 2**

The result of the transformation shown in the
figure below is to produce a binary image. *s
= T(r)*

Frequency domain methods

Let g( x, y) be a desired image formed by the
convolution of an image *f* (x, y) and
a linear, position invariant operator h(x,y), that is:

*g(x,y) =
h(x,y)2f(x,y)*

The following frequency relationship holds:

*G(u, *i’) =* H (a, v)F(u, *i’)* *We can select *H* (u, v)
so that the desired image

*g(x,y) = *3^{_ 1}* i$(ii,v)F(u,v)*

exhibits some highlighted features of *f* (x,y) . For instance, edges in *f* (x,y) can be accentuated by using a
function H(u,v) that emphasises the high frequency components of *F(u,v)*

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