DIGITAL IMAGE PROCESSING

SHARPENING PROCESS IN SPATIAL DOMAINPrepared by

T. Sathiyabama M. Sahaya Pretha

K. Shunmuga PriyaR. Rajalakshmi

Department of Computer Science and Engineering,MS University, Tirunelveli

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DefinitionDirect Manipulation of image Pixels.The objective of Sharpening is to highlight

transitions in intensityThe image blurring is accomplished by pixel

averaging in a neighborhood.Since averaging is analogous to integration.

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Some ApplicationsPhoto EnhancementMedical image visualizationIndustrial defect detectionElectronic printing Autonomous guidance in military

systems

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FoundationSharpening Filters to find details about

Remove blurring from images.Highlight edges

We are interested in the behavior of these derivatives in areas of constant gray level(flat segments), at the onset and end of discontinuities(step and ramp discontinuities), and along gray-level ramps.

These types of discontinuities can be noise points, lines, and edges.

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Definition for a first derivativeMust be zero in flat segments

Must be nonzero at the onset of a gray-level step or ramp

Must be nonzero along rampsA basic definition of the first-order derivative of a one-

dimensional function f(x) is

(Diff b/w subsequent values & measures the rate of change of the function)

)()1(f xfxfx

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Definition for a second derivativeMust be zero in flat areas

Must be non zero at the onset and end of a gray-level step or ramp

Must be zero along ramps of constant slopeWe define a second-order derivative as the difference

(the values both before& after the

current value)

)(2)1()1(2

2

xfxfxfxf

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First and second-order derivatives in digital form => difference

The 1st-order derivative is nonzero along the entire ramp, while the 2nd-order derivative is nonzero only at the onset and end of the ramp.

The response at and around the point is much stronger for the 2nd- than for the 1st-order derivative.

)()1( xfxfxf

)(2)1()1(

)]1()([)]()1([2

2

xfxfxf

xfxfxfxfxf

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Gray-level profile

660 12300 2 22 2233 33 300 00000077 5576543210

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Derivative of image profile

0 0 0 1 2 3 2 0 0 2 2 6 3 3 2 2 3 3 0 0 0 0 0 0 7 7 6 5 5 3

0 0 1 1 1-1-2 0 2 0 4-3 0-1 0 1 0-3 0 0 0 0 0-7 0-1-1 0-2

0-1 0 0-2-1 2 2-2 4-7 3-1 1 1-1-3 3 0 0 0 0-7 7-1 0 1-2

first

second

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2nd derivatives for image Sharpening 2-D 2nd derivatives => Laplacian

2

2

2

22

yf

xff

),(4)]1,()1,(),1(),1([)],(2)1,()1,([ )],(2),1(),1([2

yxfyxfyxfyxfyxfyxfyxfyxfyxfyxfyxff

=>discrete formulation

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Implementation

),(),(),(),(

),(2

2

yxfyxfyxfyxf

yxg

),(2 yxf

If the center coefficient is negative

If the center coefficient is positive

Where f(x,y) is the original image

is Laplacian filtered image

g(x,y) is the sharpen image

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Definition of 2nd derivatives in filter mask

900 rotationinvariant

450 rotationinvariant(include Diagonals)

4 -

-

-

- -

- - -

-

---

8

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Implementation

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ImplementationFiltered = Conv(image,mask)

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Implementationfiltered = filtered - Min(filtered) filtered = filtered * (255.0/Max(filtered))

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Implementationsharpened = image + filtered sharpened = sharpened - Min(sharpened ) sharpened = sharpened * (255.0/Max(sharpened ))

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Algorithm1. Using Laplacian filter to original image

2. And then add the image result from step 1 and the original image

3. We will apply two step to be one mask),(4)1,()1,(),1(),1(),(),( yxfyxfyxfyxfyxfyxfyxg

)1,()1,(),1(),1(),(5),( yxfyxfyxfyxfyxfyxg

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Result of Algorithm

-1

-1

5 -1

-1

0 0

0 0

-1

-1

9 -1

-1

-1 -1

-1 -1

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Laplacian filtering: example

Original image

Laplacian filtered image

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Unsharp masking A process to sharpen images consists of

subtracting a blurred version of an image from the image itself. This process, called unsharp masking, is expressed as ),(),(),( yxfyxfyxf s

),( yxf s),( yxf),( yxf

Where denotes the sharpened image obtained by unsharp masking, an is a blurred version of

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High-boost filtering A high-boost filtered image, fhb is defined

at any point (x,y) as

1),(),(),( AwhereyxfyxAfyxfhb

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

),(),()1(),( yxfyxfAyxf shb

This equation is applicable general and does not state explicity how the sharp image is obtained

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High-boost filtering and Laplacian If we choose to use the Laplacian, then

we know fs(x,y)

),(),(),(),(

2

2

yxfyxAfyxfyxAf

fhbIf the center coefficient is negative

If the center coefficient is positive

-1

-1

A+4 -1

-1

0 0

0 0

-1

-1

A+8 -1

-1

-1 -1

-1 -1

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The Gradient (1st order derivative) First Derivatives in image processing are

implemented using the magnitude of the gradient.

The gradient of function f(x,y) is

yfxf

GG

fy

x

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The magnitude of this vector is given by

yxyx GGGGfmag 22)(

-1 1

1

-1

Gx

Gy

This mask is simple, and no isotropic. Its result only horizontal and vertical.

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Robert’s Method The simplest approximations to a first-

order derivative that satisfy the conditions stated in that section are

268

259 )()( zzzzf

6859 zzzzf

z1 z2 z3

z4 z5 z6

z7 z8 z9

Gx = (z9-z5) and Gy = (z8-z6)

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These mask are referred to as the Roberts cross-gradient operators.

-1 0

0 1

-10

01

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Sobel’s Method Using this

equation)2()2()2()2( 741963321987 zzzzzzzzzzzzf

-1 -2 -1

0 0 0

1 2 1 1

-2

10

0

0-1

2

-1

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Gradient: example

defectsoriginal(contact lens) Sobel gradient

Enhance defects and eliminate slowly changing background

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Thank You to all my viewers