08Image Enhancement Using Spatial Filtering Technique - Sharpening Filter

7/31/2019 08Image Enhancement Using Spatial Filtering Technique - Sharpening Filter

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Image Enhancement using

Spatial Filtering Technique Sharpening Filters

Presentation by:

C. Vinoth Kumar, AP/ECE

SSN College of Engineering


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Objectives:

To study about the image enhancement spatial

- sharpening filters.

The first order and second order sharpeningfilters are to be discussed.


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Sharpening Spatial Filters:

The principal objective of sharpening is to

highlight fine detail in an image or to enhance

detail that has been blurred, either in error or as a

natural effect of a particular method of imageacquisition.

Averaging (Low pass) is analogous to

integration and hence sharpening is implemented

by digital differentiation.


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The strength of the response of a derivative

operator is proportional to the degree of

discontinuity of the image at the point at which

the operator is applied. Thus image differentiation

enhances edges and other discontinuities (such

as noise) and de- emphasizes the areas with

slowly varying gray level values.

The sharpening filters are based on first and

second order derivatives.

The derivatives of a digital function are defined

in terms of differences.


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The properties of first derivative are:

(i) must be zero in flat segments

(ii) must be nonzero at the onset of a gray level

step or ramp

(iii) must be nonzero along ramps

The properties of second derivative are:

(i) must be zero in flat areas

(ii) must be nonzero at the onset and end of a gray level step or ramp

(iii) must be nonzero along ramps of constant

slope


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The maximum possible gray level change is

finite and the shortest distance over which that

change occur is between adjacent pixels.

The basic definition of the first order derivative

of a one dimensional function f(x) is the

difference,

Similarly for the second order derivative of a

one dimensional function f(x,y) is,

)()1( xfxfx

f+=

)(2)1()1(2

2

xfxfxfx

f++=


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The first order derivatives generally produce

thicker edges in an image and have a stronger

response to a gray level step.

The second order derivatives have a strongerresponse to fine detail, such as thin lines and isolated

points and produce a double response at step changes

in gray level.


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Second order derivatives for Enhancement The

Laplacian:

We consider 2D second order derivatives for

image enhancement.

The approach consists of defining a discreteformulation of the second order derivative and then

constructing a filter mask based on that

formulation.

Isotropic filters which are rotation invariant, are

implemented.


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The simplest isotropic derivative operator is the

Laplacian, which is defined for an image f(x,y) is,

The Laplacian is a linear operator. The digital Laplacian using neighborhoods is

defined as,

2

2

2

2

2

yf

xff

+

=

),(4)]1,()1,(),1(),1([

),(2)1,()1,(

),(2),1(),1(

2

2

2

2

2

yxfyxfyxfyxfyxff

yxfyxfyxfyf

yxfyxfyxfx

f

+++++=

++=

++=


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The background features can be recovered while

still preserving the sharpening effect of the

Laplacian operation simply adding the original and

Laplacian images.

+

=

positiveismaskLaplacian

theoftcoefficiencentertheifyxfyxf

negativeismaskLaplacian

theoftcoefficiencentertheifyxfyxf

yxg),(),(

),(),(

),(2

2


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Simplification:

)]1,()1,(),1(),1([),(5

),(4)]1,()1,(),1(),1([),(),(

+++++=

++++++=

yxfyxfyxfyxfyxf

yxfyxfyxfyxfyxfyxfyxg


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Unsharp masking and high boost filtering:

The process to sharpen image by subtracting ablurred version of an image from the image

itself, is called as Unsharp masking, which is expressed

as,

The high boost filtered image, fhb, is defined at

any point (x,y) is,

where A 1

),(),(),( yxfyxfyxfs =

),(),(),( yxfyxAfyxfhb =


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),(),()1(),(

),(),(),()1(),(

yxfyxfAyxf

yxfyxfyxfAyxf

shb

hb

+=

+=

The equation may be written as,

Using Laplacian,

+

=

positiveismaskLaplacian

theoftcoefficiencentertheifyxfyxAf

negativeismaskLaplacian

theoftcoefficiencentertheifyxfyxAf

yxfhb),(),(

),(),(

),(2

2


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Summary:

The image enhancement spatial technique

sharpening filters is discussed.

The first order and second order sharpeningfilters are explained.


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Questions:

1. What is Laplacian operator?

2. What are the properties of first order derivative?

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08Image Enhancement Using Spatial Filtering Technique - Sharpening Filter