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Histograms

Histograms. Outline. Histogram – Definition Histogram of Image Histogram Equalization Histogram Matching. What is a Histogram. What is a Histogram?. {3, 11, 12, 19, 22, 23, 24, 25, 27, 29, 35, 36, 37, 45, 49}. What is a Histogram?.

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Histograms

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  1. LNMIIT DIP Winter Workshop 2011. Manohar Kuse Histograms

  2. Outline • Histogram – Definition • Histogram of Image • Histogram Equalization • Histogram Matching LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  3. LNMIIT DIP Winter Workshop 2011. Manohar Kuse What is a Histogram

  4. What is a Histogram? • {3, 11, 12, 19, 22, 23, 24, 25, 27, 29, 35, 36, 37, 45, 49} LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  5. What is a Histogram? • {3, 11, 12, 19, 22, 23, 24, 25, 27, 29, 35, 36, 37, 45, 49} LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  6. What is a Histogram? LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  7. Computing CDF • Cumulative Distribution Function LNMIIT DIP Winter Workshop 2011. Manohar Kuse Normalized CDF : Divide by total data points. In this case 15.

  8. LNMIIT DIP Winter Workshop 2011. Manohar Kuse Image Histograms

  9. Image Histograms • Assume “I” to be a mxn image matrix • Create an empty array “A” of size 255 • Iterate through rows,cols • A[ I(r,c) ] ← A[ I(r,c) ] + 1 • “A” is the Histogram • Plot it LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  10. Image Histograms LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  11. LNMIIT DIP Winter Workshop 2011. Manohar Kuse Histogram Equalization

  12. Histogram Equalization • Intensity Transform Function • Stretching of Histogram • Enhances Contrast LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  13. Algorithm for Histogram Equalization • Assume “I” to be a MxNimage matrix • Compute Histogram Matrix • Compute CDF • Apply the Intensity transformation at every pixel intensity : LNMIIT DIP Winter Workshop 2011. Manohar Kuse Proof of why is formula works can be found at : http://homepages.inf.ed.ac.uk/rbf/HIPR2/histeq.htm

  14. Example - Image LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  15. Example – Histogram & CDF LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  16. Example – Intensity Mapping * V is Intensity LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  17. Results – Histogram Equalization LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  18. Results – Histogram Equalization LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  19. Enhancement of X-Ray Imagery LNMIIT DIP Winter Workshop 2011. Manohar Kuse One drawback of the technique is that it also enhances noise 

  20. LNMIIT DIP Winter Workshop 2011. Manohar Kuse Histogram Matching

  21. Histogram Matching – Definition Histogram Matching Input Image LNMIIT DIP Winter Workshop 2011. Manohar Kuse Reference Image

  22. Histogram Matching - Algorithm • Assume “I” as input image. “R” to be the reference image • Compute Histograms: “h” & “g” • Compute Normalized CDF: “H”, “G” • Match a value of “H” to a value of “G”. LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  23. Example LNMIIT DIP Winter Workshop 2011. Manohar Kuse H & h (Input Image) G & g (Reference Image)

  24. Example LNMIIT DIP Winter Workshop 2011. Manohar Kuse H & h G & g

  25. Application – Image Mosaic LNMIIT DIP Winter Workshop 2011. Manohar Kuse

  26. Thanks  LNMIIT DIP Winter Workshop 2011. Manohar Kuse Blue Mosque, Istanbul

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