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?