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Digital Image Procesing Introduction to Image Enhancement Histogram Processing

Digital Image Procesing Introduction to Image Enhancement Histogram Processing. DR TANIA STATHAKI READER (ASSOCIATE PROFFESOR) IN SIGNAL PROCESSING IMPERIAL COLLEGE LONDON. Image Enhancement. The goal is to process an image so that the resulting image is:

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Digital Image Procesing Introduction to Image Enhancement Histogram Processing

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  1. Digital Image ProcesingIntroduction to Image EnhancementHistogram Processing DR TANIA STATHAKI READER (ASSOCIATE PROFFESOR) IN SIGNAL PROCESSINGIMPERIAL COLLEGE LONDON

  2. Image Enhancement • The goal is to process an image so that the resulting image is: • more suitable than the original image for a specific application • of better quality in terms of some quantitative metric • visually better • Spatial domain methods • Frequency domain methods.

  3. Spatial Domain Methods: Local neighborhood processing

  4. Spatial Domain Methods: Point processing

  5. Point Processing: contrast enhancement • In the figures below you can see examples of two different intensity transformations. • The figure on the right shows the process of binarization of the image.

  6. bright image dark image Histogram Processing: definition of image histogram low contrast image high contrast image

  7. Generic figures of histograms

  8. Two different images with the same histogram.

  9. Histogram Processing: definition of intensity transformation

  10. Histogram Processing: definition of intensity transformation • The condition for T(r) to be monotonically increasing guarantees that ordering of the output intensity values will follow the ordering of the input intensity values (avoids reversal of intensities). • If T(r)is strictly monotonically increasing then the mapping from s back to r will be 1-1. • The second condition (T(r)in [0,1]) guarantees that the range of the output will be the same as the range of the input.

  11. Monotonicity versus strict monotonicity • We cannot perform inverse mapping (from s to r). • Inverse mapping is possible.

  12. Modelling intensities as continuous variables

  13. Histogram Equalization: continuous form

  14. Histogram Equalization: continuous form

  15. Histogram Equalization: discrete form

  16. A histogram equalization example in discrete form

  17. A histogram equalization example in discrete form

  18. A histogram equalization example in discrete form • Notice that due to discretization, the resulting histogram will rarely be perfectly flat. However, it will more “extended” compared to the original histogram.

  19. bright image dark image A set of images with same content but different histograms low contrast image • 1 • 3 high contrast image • 4 • 2

  20. Histogram equalization applied to the dark image • 1

  21. Histogram equalization applied to the bright image • 2

  22. Histogram equalization applied to the low and high contrast images • 3 • 4

  23. Transformation functions for histogram equalization for the previous example

  24. An example of an unfortunate histogram equalization • Example of image of Phobos (Mars moon) and its histogram. • Histogram equalization (bottom of right image) does not always provide the desirable results.

  25. Histogram Specification

  26. Histogram Specification

  27. Histogram Specification

  28. Histogram Specification: Example

  29. Histogram Specification: Example

  30. Histogram Specification: Example

  31. Histogram Specification: Example • Notice that due to discretization, the resulting histogram will rarely be exactly the same as the desired histogram. • Top left: original pdf • Top right: desired pdf • Bottom left: desired CDF • Bottom right: resulting pdf

  32. Histogram Specification: Example • Specified histogram. • Transformation function • and its inverse. • Resulting histogram.

  33. Histogram Equalization: Examples

  34. Histogram Equalization: Examples

  35. Histogram Equalization: Examples

  36. Histogram Equalization: Examples

  37. Histogram Equalization: Examples

  38. Histogram Equalization: Examples

  39. Histogram Specification: Examples

  40. Local Histogram Specification • The histogram processing methods discussed previously are global (transformation is based on the intensity distribution of the entire image). • This global approach is suitable for overall enhancement. • There are cases in which it is necessary to enhance details over small areas in an image. • The number of pixels in these areas may have negligible influence on the computation of a global transformation. • The solution is to devise transformation functions based on the intensity distribution in a neighbourhood around every pixel.

  41. Local Histogram Specification: Examples

  42. Local Histogram Specification: Examples

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