# Sharpening in spatial domain

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Information about Sharpening in spatial domain

Published on October 25, 2016

Author: SathyaGanesh7

Source: slideshare.net

1. by T Sathiyabama K Shunmuga Priya M Sahaya Preetha R Rajalakshmi Dept of Computer Science and Engineering, MS University, Tirunelveli

2. Definition The principal objective of Sharpening is to highlight transitions in intensity  To fine detail in an image or to enhance detail that has been blurred, either in error or as an natural effect of a particular method of image acquisition Image Sharpening is vary and include applications ranging from electronic printing and medical imaging to industrial inspection and autonomous guidance in military systems 10/25/2016 5:31 AM 2

3. The image blurring is accomplished in the spatial domain by pixel averaging in a neighborhood. Since averaging is analogous to integration. Sharpening could be accomplished by spatial differentiation. 10/25/2016 5:31 AM 3

4. Foundation 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. 10/25/2016 5:31 AM 4

5. Definition for a first derivative Must be zero in flat segments Must be nonzero at the onset of a gray-level step or ramp Must be nonzero along ramps A basic definition of the first-order derivative of a one- dimensional function f(x) is 10/25/2016 5:31 AM 5 )()1( f xfxf x   

6. Definition for a second derivative Must be zero in flat areas Must be nonzero at the onset and end of a gray-level step or ramp Must be zero along ramps of constant slope We define a second-order derivative as the difference 10/25/2016 5:31 AM 6 )(2)1()1(2 2 xfxfxf x f   

7. First and second-order derivatives in digital form => difference 10/25/2016 5:31 AM 7 )()1( xfxf x f    )(2)1()1( )]1()([)]()1([2 2 xfxfxf xfxfxfxf x f    

8. Gray-level profile 10/25/2016 5:31 AM 8 660 1 2 30 0 2 2 2 2 23 3 3 3 30 0 0 0 0 0 0 0 7 7 5 5 7 6 5 4 3 2 1 0

9. Derivative of image profile 10/25/2016 5:31 AM 9 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

10. Analyze 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 10/25/2016 5:31 AM 10

11. 2nd derivatives for image Sharpening  2-D 2nd derivatives => Laplacian 10/25/2016 5:31 AM 11 2 2 2 2 2 y f x f f       ),(4)]1,()1,(),1(),1([ )],(2)1,()1,([ )],(2),1(),1([2 yxfyxfyxfyxfyxf yxfyxfyxf yxfyxfyxff    =>discrete formulation

12. Definition of 2nd derivatives in filter mask 900 rotation invariant 450 rotation invariant (include Diagonals) 4 - - - - - - - - - --- 8 10/25/2016 5:31 AM 12

13. Implementation       ),(),( ),(),( ),( 2 2 yxfyxf yxfyxf yxg ),(2 yxf 10/25/2016 5:31 AM 13 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

14. Laplacian filtering: example 10/25/2016 5:31 AM 14 Original image Laplacian filtered image

15. Implementation 10/25/2016 5:31 AM 15

16. Implementation 10/25/2016 5:31 AM 16 Filtered = Conv(image,mask)

17. Implementation 10/25/2016 5:31 AM 17 filtered = filtered - Min(filtered) filtered = filtered * (255.0/Max(filtered))

18. Implementation 10/25/2016 5:31 AM 18 sharpened = image + filtered sharpened = sharpened - Min(sharpened ) sharpened = sharpened * (255.0/Max(sharpened ))

19. Algorithm Using Laplacian filter to original image And then add the image result from step 1 and the original image We will apply two step to be one mask 10/25/2016 5:31 AM 19 ),(4)1,()1,(),1(),1(),(),( yxfyxfyxfyxfyxfyxfyxg  )1,()1,(),1(),1(),(5),(  yxfyxfyxfyxfyxfyxg

20. 10/25/2016 5:31 AM 20 -1 -1 5 -1 -1 0 0 0 0 -1 -1 9 -1 -1 -1 -1 -1 -1

21. 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 ),(),(),( yxfyxfyxfs  ),( yxfs 10/25/2016 5:31 AM 21 ),( yxf),( yxf Where denotes the sharpened image obtained by unsharp masking, an is a blurred version of

22. High-boost filtering  A high-boost filtered image, fhb is defined at any point (x,y) as 1),(),(),(  AwhereyxfyxAfyxfhb ),(),(),()1(),( yxfyxfyxfAyxfhb  10/25/2016 5:31 AM 22 ),(),()1(),( yxfyxfAyxf shb  This equation is applicable general and does not state explicity how the sharp image is obtained

23. High-boost filtering and Laplacian  If we choose to use the Laplacian, then we know fs(x,y)       ),(),( ),(),( 2 2 yxfyxAf yxfyxAf fhb 10/25/2016 5:31 AM 23 If 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

24. 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                        y f x f G G f y x 10/25/2016 5:31 AM 24

25. Gradient  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. 10/25/2016 5:31 AM 25

26. Robert’s Method  The simplest approximations to a first-order derivative that satisfy the conditions stated in that section are 2 68 2 59 )()( zzzzf  6859 zzzzf  z1 z2 z3 z4 z5 z6 z7 z8 z9 Gx = (z9-z5) and Gy = (z8-z6) 10/25/2016 5:31 AM 26

27. Robert’s Method  These mask are referred to as the Roberts cross- gradient operators. -1 0 0 1 -10 01 10/25/2016 5:31 AM 27

28. 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 10/25/2016 5:31 AM 28

29. Gradient: example defectsoriginal(contact lens) Sobel gradient  Enhance defects and eliminate slowly changing background 10/25/2016 5:31 AM 29

30. 10/25/2016 5:31 AM 30