Histogram equalization

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Histogram equalization is a method in image processing of contrast adjustment using the image's histogram. Histogram equalization can be used to improve the visual appearance of an image. Peaks in the image histogram (indicating commonly used grey levels) are widened, while the valleys are compressed.

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Histogram equalization

  1. 1. BI-HISTOGRAM EQUALIZATION wITH A pLATEAU LIMIT FOR DIGITAL IMAGES. MAHESH MOHAN.M.R GECT S1 ECE ROLL NO: 7 GUIDE : Dr.V.S.SHEEBA OM NAMA SIVAYA
  2. 2. OBJECTIVE . TO FAMILARIZE WITH .HISTOGRAM EQUALIZATION .DIFFERENT EQUALIZATION METHODS .THEIR DRAWBACK AND HOW IT IS RECTIFIED.
  3. 3. FLOw OF SEMINAR. 1.WHAT IS A DIGITAL IMAGE? 2.WHAT IS A HISTOGRAM? 3.WHAT IS HISTOGRAM EQUALIZATION? 4.DIFFERENT EQUALIZATION METHODS AND ITS DRAWBACK. 5.HOW DRAWBACK OF EACH METHOD IS RECTIFED?
  4. 4. • A digital image is a matrix representation of a  two-dimensional image.                                                                                 wHAT IS A DIGITAL IMAGE? Colour imageGray scale image(Black and white)
  5. 5. dGray Image Image wHAT IS A GRAy SCALE IMAGE? 243 121 . 34 21 . . . Gray level matrix 0 255
  6. 6. Image matrix Image wHAT IS A COLOUR IMAGE? 234 212 123 135 231 233 . 121 222 . . 243 121 . . . . 112 167 . . . . Red matrix Green matrix Blue matrix . .
  7. 7. wHAT IS A HISTOGRAM? Consider a 5x5 image with integer intensities in the range between zero and seven: 0 7 3 2 3 0 0 0 6 7 7 7 2 2 0 1 1 0 4 1 0 0 7 4 1 Image matrixImage 0 1 2 3 4 5 6 7 Gray scale Black White
  8. 8. wHAT IS A HISTOGRAM? Consider a 5x5 image with integer intensities in the range between one and eight: 0 7 3 2 3 0 0 0 6 7 7 7 2 2 0 1 1 0 4 1 0 0 7 4 1 Image matrixImage 0 1 2 3 4 5 6 7 Grey scale Black White Number of pixel with intensity value 0 [h(r0)] = 8
  9. 9. wHAT IS A HISTOGRAM? 0 7 3 2 3 0 0 0 6 7 7 7 2 2 0 1 1 0 4 1 0 0 7 4 1 Image matrixImage 0 1 2 3 4 5 6 7 Grey scale Black White Number of pixel with intensity value 0 [h(r0)] = 8 Similarly for 1 h(r1) = 4
  10. 10. wHAT IS A HISTOGRAM? 0 7 3 2 3 0 0 0 6 7 7 7 2 2 0 1 1 0 4 1 0 0 7 4 1 Image matrixImage Similarly INTENSITY r 0 1 2 3 4 5 6 7 NUMBER of pixels of r h(r)   h(r0)=8   h(r1)=4 h(r2)=3  h(r3)=2  h(r4)=2  h(r5)=0  h(r6)=1   h(r7)=5
  11. 11. r wHAT IS A HISTOGRAM? Image matrix 0 1 2 3 4 5 6 7 HISTOGRAM Intensity values Number of pixels of intensity r r 0 1 2 3 4 5 6 7 h(r)   8     4    3     2     2     0     1     5 Histogram plots the number of pixels for each intensity value. h(r)
  12. 12. What is a histogram? r 0 1 2 3 4 5 6 7 h(r) 8 4 3 2 2 0 1 5 p(r) h(r)/(5*5) 8/25 4/25 3/25 2/25 2/25 0/25 1/25 5/25 HISTOGRAM - h(r) - Y axis - number of intensities NORMALIZED HISTOGRAM - p(r) - Y axis - probability of intensities
  13. 13. SAMPLE IMAGES AND ITS HISTOGRAM Bright image Intensity range 0 - 255
  14. 14. SAMPLE IMAGES AND ITS HISTOGRAM Bright image Intensity range 0 - 255 0 50 100 150 200 255 Intensity No:ofpixels DARK BRIGHT h(r)
  15. 15. SAMPLE IMAGES AND ITS HISTOGRAM Dark image Intensity range 0 - 255
  16. 16. SAMPLE IMAGES AND ITS HISTOGRAM Dark image Intensity range 0 - 255 0 50 100 150 200 255 Intensity No:ofpixels h(r)
  17. 17. SAMPLE IMAGES AND ITS HISTOGRAM Low contrast image Intensity range 0 - 255
  18. 18. SAMPLE IMAGES AND ITS HISTOGRAM Light image Intensity range 0 - 255 0 50 100 150 200 255 Intensity No:ofpixels h(r)
  19. 19. SAMPLE IMAGES AND ITS HISTOGRAM Bright image Dark image Low contrast image
  20. 20. SAMPLE IMAGES AND ITS HISTOGRAM High contrast image Intensity range 0 - 255 0 50 100 150 200 255 Intensity No:ofpixels h(r)
  21. 21. CoNCEPt oF histogram EQUaLiZatioN ORIGINAL IMAGE EQUALIZED IMAGE MAXIMIZES ENTROPY OF AN IMAGE. s1 s2
  22. 22. thEorY BEhiND histogram EQUaLiZatioN TRANSFORMATION FUNCTION THAT MAPS THE INPUT INTENSITY TO ALL AVAILABLE INTENSITIES. I/p intensity O/p intensity
  23. 23. THEORY BEHIND HISTOGRAM EQUALIZATION ORIGINAL IMAGE EQUALIZED IMAGE s1 s2
  24. 24. THEORY BEHIND HISTOGRAM EQUALIZATION CUMULATIVE DISTRIBUTION FUNCTION T(r) 0 50 100 150 200 255 [76 – 213] [0 – 48] [15 – 100] [25 – 125] O/P INTENSITY = X0 + [( Xl-1 –X0 )*C(x)] I/P intensity
  25. 25. DIFFERENT STAGES GLOBAL HISTOGRAM EQUALIZATION BI-HISTOGRAM EQUALIZATION BI-HISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT
  26. 26. GLOBAL HISTOGRAM EQUALIZATION OBTAIN HISTOGRAM OBTAIN PDF OBTAIN CDF OBTAIN TRANSFORMATIO N FUNCTION MAPPING OF NEW INTENSITY VALUES NEW HISTOGRAM Original histogram M*N PDF 1.. CDF 1 x0 XL-1 O/P x0 XL-1 MappingTransformation function t1 t2 t2 New histogram t1t1 t2 t2t1t2t1
  27. 27. GLOBAL HISTOGRAM EQUALIZATION RESULTS GHE O/P MEAN CONSTANTWHY ?
  28. 28. GLOBAL HISTOGRAM EQUALIZATION DRAWBACK DO NOT CONSERVE THE MEAN. WHY MEAN IMPORTANT? Video frames GHE
  29. 29. THEORY OF BIHISTOGRAM EQUALIZATION HISTOGRAM EQUALIZED SEPERATELY AROUND MEAN. THUS CONSERVE THE MEAN. ORIGINAL HISTOGRAM BIHISTOGRAM EQUALIZED
  30. 30. BIHISTOGRAM EQUALIZATION OBTAIN PDF (lower subimage)[X0-Xm] OBTAIN CDF OBTAIN TRANSFORMATIO N FUNCTION MAPPING OF NEW INTENSITY VALUES NEW HISTOGRAM DIVIDE HISTOGRAM WITH RESPECT TO INTENSITY MEAN (X m ). OBTAIN HISTOGRAM OBTAIN PDF (upper subimage)[Xm-Xl-1] OBTAIN CDF OBTAIN TRANSFORMATIO N FUNCTION MAPPING OF NEW INTENSITY VALUES + GHE GHE Partition Merging
  31. 31. BI-HISTOGRAM EQUALIZATION RESULTS BHE
  32. 32. BIHISTOGRAM EQUALIZATION DRAWBACK LEVEL SATURATION DUE TO HIGH PROBABLE INTENSITY VALUES. BHE EXAMPLE WHY IT HAPPENS ?
  33. 33. THOERY OF BIHISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT . BIHISTOGRAM CLIPPING HISTOGRAM ABOVE PLATEAU LIMIT TL PLATEAU LIMITS FOR LOWER HISTOGRAM. TU PLATEAU LIMITS FOR UPPER HISTOGRAM. SELECT PLATEAU LIMIT
  34. 34. BIHISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT OBTAIN PDF (lower subimage)[X0-Xm] OBTAIN CDF OBTAIN TRANSFORMATION FUNCTION MAPPING OF NEW INTENSITY VALUES NEW HISTOGRAM DIVIDE HISTOGRAM WITH RESPECT TO INTENSITY MEAN (X m ). OBTAIN HISTOGRAM OBTAIN PDF (upper subimage)[Xm-Xl-1] OBTAIN CDF OBTAIN TRANSFORMATION FUNCTION MAPPING OF NEW INTENSITY VALUES + GHE GHE Partition Merging CLIP WRT AMPLITUDE MEAN CLIP WRT AMPLITUDE MEAN Clipping
  35. 35. BIHISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT RESULTS BHEPL
  36. 36. SIMULATION RESULTS TEST IMAGES GLOBAL HISTOGRAM EQUALIZATION BI-HISTOGRAM EQUALIZATION BIHISTOGRAM EQUALIZATION WITH PLATEAU LIMIT DARK 86 126 82 91 BRIGHT 143 126 154 153 LOWCONTRAST 77 124 99 103 MEAN VALUES
  37. 37. SIMULATION RESULTS LEVEL SATURATION TEST IMAGES BI-HISTOGRAM EQUALIZATION BIHISTOGRAM EQUALIZATION WITH PLATEAU LIMIT WHITE DOT YES NO
  38. 38. d WHY GRAY SCALE IMAGES INSTEAD OF COLOUR IMAGES? .
  39. 39. CONCLUSIONHistogram? IN AN IMAGE NOTHING WORSE MORE THAN LOW CONTRAST GLOBAL HISTOGRAM EQUALIZATION NOTHING WORSE MORE THAN MEAN CONSERVATION BI-HISTOGRAM EQUALIZATION NOTHING WORSE MORE THAN ………………? NOTHING WORSE MORE THAN LEVEL SATURATION BI-HISTOGRAM EQUALIZATION WITH PLATEAU LIMIT
  40. 40. REFERENCESStogram? Bi-Histogram Equalization with a Plateau Limit for Digital Image Enhancement Chen Hee Ooi, Student Member, IEEE, Nicholas Sia Pik Kong, Student Member, IEEEand Haidi Ibrahim, Member, IEEE IEEE Transactions on Consumer Electronics, Vol. 55, No. 4, NOVEMBER 2009 Contrast Enhancement Using Brightness Preserving Bi-Histogram Equalization YEONG-TAEG KIM, MEMBER, IEEE Color Image Enhancement Using Brightness Preserving Dynamic Histogram Equalization Nicholas Sia Pik Kong, Student Member, IEEE, and Haidi Ibrahim, Member, IEEE. Preserving brightness in histogram equalization based contrast enhancement techniques Soong-Der Chen a, Abd. Rahman Ramli Digital image processing by Gonzalez and Woods
  41. 41. NAMASIVAYA
  42. 42. • Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. • Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. 1
  43. 43. • Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. • Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Vivamus et magna. Fusce sed sem sed magna suscipit egestas. 1

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