Frequency Domain Image Enhancement Techniques

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Frequency Domain Image Enhancement Techniques

  1. 1. Presented by-:Diwaker PantME ECE Regular
  2. 2.  IntroductIon. Image enhancement. Frequency domaIn enhancement. Low pass FILterIng. hIgh pass FILterIng. concLusIon. Image Enhancement Techniques October 9, 2012 2
  3. 3.  Image enhancement is basically improving the interpretability or perception of information in images for human viewers and providing `better input for other automated image processing techniques. The principal objective of image enhancement is to modify attributes of an image to make it more suitable for a given task and a specific observer. During this process, one or more attributes of the image are modified. Image Enhancement Techniques October 9, 2012 3
  4. 4.  There exist many techniques that can enhance a digital image without spoiling it. The enhancement methods can broadly be divided in to the following two categories: Spatial Domain MethodsFrequency Domain Methods Image Enhancement Techniques October 9, 2012 4
  5. 5.  Unfortunately, there is no general theory for determining what is `good image enhancement when it comes to human perception. If it looks good, it is good. However, when image enhancement techniques are used as pre-processing tools for other image processing techniques, then quantitative measures can determine which techniques are most appropriate. Image Enhancement Techniques October 9, 2012 5
  6. 6. Spatial Domain Methods In spatial domain techniques , we directly deal with the image pixels. The pixel values are manipulated to achieve desired enhancement. The value of a pixel with coordinates (x; y) in the enhanced image ‘ F’ is the result of performing some operation on the pixels in the neighborhood of (x; y) in the input image ‘ f’ . Image Enhancement Techniques October 9, 2012 6
  7. 7.  In frequency domain methods, the image is first transferred into frequency domain. It means that, the Fourier Transform of the image is computed first. All the enhancement operations are performed on the Fourier transform of the image and then the Inverse Fourier transform is performed to get the resultant image. Image Enhancement Techniques October 9, 2012 7
  8. 8.  These enhancement operations are performed in order to modify the image brightness, contrast or the distribution of the grey levels. As a consequence the pixel value (intensities) of the output image will be modified according to the transformation function applied on the input values. Image enhancement is applied in every field for example medical image analysis, analysis of images from satellites etc. Image Enhancement Techniques October 9, 2012 8
  9. 9.  Image enhancement simply means, transforming an image F into image G using T. (Where T is the transformation function. The values of pixels in images F and G are denoted by r and s, respectively. As said, the pixel values r and s are related by the expression s= T(r) Where T is a transformation that maps a pixel value r into a pixel value s. Image Enhancement Techniques October 9, 2012 9
  10. 10. Fourier Inverse Fourier Filter Function Transform Transform H(u,v) F(u,v) G(u,v) H(u,v)F(u,v) Pre- Post-processing ProcessingInput Image Enhanced Image F(x,y) G(x,y) Frequency domain filtering operations Image Enhancement Techniques October 9, 2012 10
  11. 11.  We can therefore directly design a transfer function and implement the enhancement in the frequency domain as follows. Image Enhancement Techniques October 9, 2012 11
  12. 12.  The concept of filtering is easier to visualize in the frequency domain. Therefore, enhancement of image can be done in the frequency domain, based on its DFT. Image Enhancement Techniques October 9, 2012 12
  13. 13.  Filtering can be divided in two categories namely Low pass filtering High Pass filtering Image Enhancement Techniques October 9, 2012 13
  14. 14.  Edges and sharp transitions in gray values in an image contribute significantly to high-frequency content of its Fourier transform. Regions of relatively uniform gray values in an image contribute to low-frequency content of its Fourier transform. Image Enhancement Techniques October 9, 2012 14
  15. 15.  Hence, an image can be smoothed in the Frequency domain by attenuating the high-frequency content of its Fourier transform. This would be a low pass filter. For simplicity, we will consider only those filters that are real and symmetric. Image Enhancement Techniques October 9, 2012 15
  16. 16.  An ideal low pass filter with cutoff frequency ‘ r0’ is given by following relation. Image Enhancement Techniques October 9, 2012 16
  17. 17. Image Enhancement Techniques October 9, 2012 17
  18. 18. Image Enhancement Techniques October 9, 2012 18
  19. 19. Image Enhancement Techniques October 9, 2012 19
  20. 20.  The cutofffrequency of the ideal LPF determines the amount of frequency components passed by the filter. Smaller the value of r0 , more the number of image components eliminated by the filter. In general, the value of r0 is chosen such that most components of interest are passed through, while most components not of interest are eliminated. Image Enhancement Techniques October 9, 2012 20
  21. 21.  A two-dimensional Butterworth low pass filter has transfer function: Image Enhancement Techniques October 9, 2012 21
  22. 22. Image Enhancement Techniques October 9, 2012 22
  23. 23.  Frequency response does not have a sharp transition as in the ideal LPF. This is more appropriate for image smoothing than the ideal LPF, since this not introduce ringing. Image Enhancement Techniques October 9, 2012 23
  24. 24. Image Enhancement Techniques October 9, 2012 24
  25. 25. Image Enhancement Techniques October 9, 2012 25
  26. 26.  The form of a Gaussian low pass filter in two- dimensions is given by Where D is the distance from origin in frequency planeThe parameter σ measures the dispersion of the Gaussiancurve. Larger the value of σ, larger the cutoff frequency andmilder the filtering. Image Enhancement Techniques October 9, 2012 26
  27. 27.  Hence, an image can be smoothed in the Frequency domain by attenuating the low-frequency content of its Fourier transform. This would be a high pass filter. For simplicity, we will consider only those filters that are real and symmetric Image Enhancement Techniques October 9, 2012 27
  28. 28.  An ideal high pass filter with cutoff frequency r0. Image Enhancement Techniques October 9, 2012 28
  29. 29. Ideal HPF with r0=36 Image Enhancement Techniques October 9, 2012 29
  30. 30. Image Enhancement Techniques October 9, 2012 30
  31. 31. Image Enhancement Techniques October 9, 2012 31
  32. 32.  A two-dimensional Butterworth high pass filter has transfer function: Image Enhancement Techniques October 9, 2012 32
  33. 33.  Butterworth HPF with cut off frequency r0=47 Order =2 Image Enhancement Techniques October 9, 2012 33
  34. 34.  Frequency response does not have a sharp transition as in the ideal HPF. This is more appropriate for image sharpening than the ideal HPF, since this not introduce ringing. Example of Butterworth high pass filtering is given on next slide. Image Enhancement Techniques October 9, 2012 34
  35. 35. Image Enhancement Techniques October 9, 2012 35
  36. 36.  Image enhancement algorithms offer a wide variety of approaches for modifying images to achieve visually acceptable images. The choice of such techniques is a function of the specific task, image content, observer characteristics, and viewing conditions. Image Enhancement Techniques October 9, 2012 36
  37. 37.  Raman Maini and Himanshu Aggarwal, “ A Comprehensive Review of Image Enhancement techniques” JOURNAL OF COMPUTING, VOLUME 2, ISSUE 3, MARCH 2010, ISSN 2151-9617 .  Rafael C. Gonzalez and Richard E. Woods, digital Image Processing, 3rd Edition, Pearson Education, Boston, 2005, p200-300.  MARIA ANGELA FRANCESCHINI, “ Frequency-domain techniques enhance optical mammography: Initial clinical results” , Publication Year: November 15, 1996.  en.wikipedia.orgOctober 9, 2012 Image Enhancement Techniques 37
  38. 38. Image Enhancement Techniques October 9, 2012 38

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