1. Topic 4 - Image Mapping - I DIGITAL IMAGING Course 3624 Department of Physics and Astronomy Professor Bob Warwick

2. Typical Image Processing Steps ORIGINAL IMAGE PRE-PROCESSING STEPS ENHANCEMENT & RESTORATION IMPROVED IMAGE IMAGE ANALYSIS Mapping Filtering Restoration focus of this course

3. Image Mapping Processes Image Mapping encompasses a range of enhancement methods which adjust the way the image data are displayed (ie how the data are "mapped" onto the display device). 4.1 Image Enhancement by Histogram Modification The image histogram P(f) is simply the probability distribution of the gray level within the image: 16-level (4-bit) image 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Gray level f P(f)

4. Histograms of a Colour Image

5. The form of the image histogram P(f) provides useful information on the content/quality of the image: The Form of the Image Histogram Good contrast Poor contrast Saturated? Image histogram modification techniques aim to improve the gray level distribution in the displayed image so as to make as much use as possible of the rather limited ability of the eye to discern gray shades. f  P(f) 

6. Discriminating between Gray Levels - I I = Intensity of Scene

7. Discriminating between Gray Levels - II Typically we are able to discern ~ 32 = 2 5 gray levels in any particular image

8. Discriminating between Gray Levels - III Small squares have same intensity but different apparent brightness. Small squares have different intensity but same apparent brightness.

9. Image Enhancement by Histogram Modification Original Image “New" image The goal is to find a suitable transformation: Notes: we assume T(f) is strictly monotonically increasing, i.e., T -1 exists (Inefficient) Implementation Method: Once f out = T(f in ) has been defined, we compute a new image by f in  f out on a pixel-by-pixel basis 15 20 12 25 30 16 15 22 …  25 32 … … … …

10. Example: Linear Contrast Stretching The parameters of the process f 1 & f 2 might be determined: Interactively Automatically Forms of T(f): A Linear Contrast Stretch For example: If we calculate the Cumulative Probability Distribution C(f), then we might use:

11. Example of Contrast Stretching ---- Discernable shades of gray

12. Author: Richard Alan Peters II Improved Contrast? 0127255 0 127 255 zero point sat. point R+G+B

13. Author: Richard Alan Peters II Forms of T(f): Increased Gamma 0127255 0 127 255

14. Author: Richard Alan Peters II Forms of T(f): Decreased Gamma 0127255 0 127 255

15. 4.2 Image Enhancement by Histogram Matching The objective is to set up the displayed image so that its histogram has a specified form. A special case is HISTOGRAM EQUALISATION where: P 2 (f out ) = constant i.e. the goal is a uniform distribution. Then: Notes: The equations are written in terms of continuous variables C 1 & C 2 are the cumulative distributions of P 1 & P 2.

16. Histogram Equalisation: Problem 7654321076543210 Note that the result is only a crude approximation to the target uniform distribution – due to the very coarse digitization of the input image data

17. Comments on Implementation Highly Efficient Method: Load the look-up table of the display device with the required transformation Image Store Look-up Table D/A Video Out Look-Up Table fin fout 0 1 1 3 2 5 3 6 4 7 5 7 6 7 7 Specific Transform D/A Display 0 Black 1 Dark Grey 2.. 3.. 4.. 5.. 6 Light Grey 7 White Look-Up Table fin fout 0 1 2 3 4 5 6 7 HardwiredStandard Setting previous 3-bit example

18. Histogram Equalisation in Action Original Image Final ImageEqualised Histogram Original Histogram

19. Histogram Equalisation in Action Original ImageFinal Image Equalised HistogramOriginal Histogram

20. The General Case The general formula above can be applied to give any form for the output image histogram. The procedure to apply this formula is: A practical implementation might involve: (a)For each f in calculate C 1 (f in ) (b)Compute a look-up table of f out versus C 2 (f out ) (c)For each f in find the nearest C 2 value to C 1 (f in ) (d)Determine the f out value = the C 2 value (e)Load the resulting mapping f in  f out into the display device look-up table Equalization General f f

21. Image Enhancement by Histogram Specification

22. Author: Richard Alan Peters II Example: Histogram Specification Image P(f) f Cumulative Distribution Image C(f)

23. Author: Richard Alan Peters II Histogram to be matched taken from a second image Target P(f) f Cumulative Distribution Target C(f)

24. Author: Richard Alan Peters II Image CDF Target CDF Histogram Matching Example Original Remapped Target