Topic 4 - Image Mapping - I

# Topic 4 - Image Mapping - I

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## Topic 4 - Image Mapping - I

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

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

3. 16-level (4-bit) image 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 Theimage histogram P(f) is simply the probability distribution of the gray level within the image: P(f) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Gray level f

4. Histograms of a Colour Image

5. The Form of the Image Histogram The form of the image histogram P(f) provides useful information on the content/quality of the image: P(f)  P(f)  P(f)  f  f  f  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.

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

7. Discriminating between Gray Levels - II Typically we are able to discern ~ 32 = 25gray levels in any particular image

8. Discriminating between Gray Levels - III Small squares have different intensity but same apparent brightness. Small squares have same intensity but different 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 fout = T(fin) has been defined, we compute a new image by fin fout on a pixel-by-pixel basis 15 20 12 25 30 16 15 22 …  25 32 … … … … … … …

10. Forms of T(f): A Linear Contrast Stretch Example: Linear Contrast Stretching • The parameters of the process f1 & f2 might be determined: • Interactively • Automatically 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. 255 127 0 0 127 255 Improved Contrast? R+G+B zero point sat. point Author: Richard Alan Peters II

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

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

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. • Notes: • The equations are written in terms of continuous variables • C1 & C2 are the cumulative distributions of P1 & P2. A special case is HISTOGRAM EQUALISATION where: P2(fout) = constant i.e. the goal is a uniform distribution. Then:

16. Histogram Equalisation: Problem 7 6 5 4 3 2 1 0 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 D/A previous 3-bit example Look-up Table Hardwired Standard Setting Specific Transform Image Store Video Out • D/A Display • 0 Black • Dark Grey • .. • 3 .. • .. • .. • 6 Light Grey • 7 White • Look-Up Table • fin fout • 0 0 • 1 • 2 • 3 3 • 4 • 5 • 6 6 • 7 7 • Look-Up Table • fin fout • 0 1 • 3 • 5 • 3 6 • 7 • 7 • 6 7 • 7 7

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

19. Histogram Equalisation in Action Original Image Final Image Original Histogram Equalised 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: Equalization General f f • A practical implementation might involve: • For each fin calculate C1(fin) • Compute a look-up table of fout versus C2(fout) • For each fin find the nearest C2 value to C1(fin) • Determine the fout value = the C2 value • Load the resulting mapping fin fout into the display device look-up table

21. Image Enhancement by Histogram Specification

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

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

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