1. CIS 601 – 04 Image ENHANCEMENT in the SPATIAL DOMAIN Longin Jan Latecki Based on Slides by Dr. Rolf Lakaemper

2. Most of these slides base on the textbook Digital Image Processing by Gonzales/Woods/Eddins Chapter 3

3. Introduction Image Enhancement ? Enhance otherwise hidden information Filter important image features Discard unimportant image features Spatial Domain ? Refers to the image plane (the ‘natural’ image) Direct image manipulation

4. Remember ? A 2D gray value - image is a 2D -> 1D function, v = f(x,y)

5. Remember ? As we have a function, we can apply operators to this function, e.g. T(f(x,y)) = f(x,y) / 2 Operator Image (= function !)

6. Remember ? T transforms the given image f(x,y) into another image g(x,y) f(x,y) g(x,y) T

7. Spatial Domain The operator T can be defined over The set of pixels (x,y) of the image The set of ‘neighborhoods’ N(x,y) of each pixel A set of images f1,f2,f3,…

9. Operation on the set of image-pixels 6820 122002010 3410 6100105 Spatial Domain (Operator: Div. by 2)

10. Operation on the set of ‘neighbourhoods’ N(x,y) of each pixel 6820 122002010 226 Spatial Domain 68 12200 (Operator: sum)

11. Operation on a set of images f1,f2,… 6820 122002010 Spatial Domain 5510 22034 111330 142202314 (Operator: sum)

12. Operation on the set of image-pixels Remark: these operations can also be seen as operations on the neighborhood of a pixel (x,y), by defining the neighborhood as the pixel itself. The easiest case of operators g(x,y) = T(f(x,y)) depends only on the value of f at (x,y) T is called a gray-level or intensity transformation function Spatial Domain

13. Basic Gray Level Transformations Image Negatives Log Transformations Power Law Transformations Piecewise-Linear Transformation Functions For the following slides L denotes the max. possible gray value of the image, i.e. f(x,y)  [0,L] Transformations

14. Image Negatives: T(f)= L-f Transformations Input gray level Output gray level T(f)=L-f

15. Log Transformations: T(f) = c * log (1+ f) Transformations

16. Log Transformations Transformations InvLogLog

17. Log Transformations Transformations

18. Power Law Transformations T(f) = c*f  Transformations

19. varying gamma (  ) obtains family of possible transformation curves  > 1 Compresses dark values Expands bright values  < 1 Expands dark values Compresses bright values Transformations

20. Used for gamma-correction Transformations

21. Used for general purpose contrast manipulation Transformations

22. Piecewise Linear Transformations Transformations

23. Thresholding Function g(x,y) =L if f(x,y) > t, 0 else t = ‘threshold level’ Piecewise Linear Transformations Input gray level Output gray level

24. Gray Level Slicing Purpose: Highlight a specific range of grayvalues Two approaches: 1. Display high value for range of interest, low value else (‘discard background’) 2. Display high value for range of interest, original value else (‘preserve background’) Piecewise Linear Transformations

25. Gray Level Slicing Piecewise Linear Transformations

26. Image Histogram (3, 8, 5)

27. Image histogram is a vector If f:[1, n]x[1, m]  [0, 255] is a gray value image, then H(f): [0, 255]  [0, n*m] is its histogram, where H(f)(k) is the number of pixels (i, j) such that F(i, j)=k Similar images have similar histograms Warning: Different images can have similar histograms

28. Histograms Histogram Processing gray level Number of Pixels 1450 3151

29. Hg Hr Hb

31. Histogram Equalization Let h=[n 1, n 2, …, n G ] be an image histogram, i.e., h(r k )=n k for r k is kth intensity level in interval [0,G] Normalized histogram is a probability density function (PDF) : p(r k ) = h(r k ) / n = n k / n - probability of occurrence of intensity level r k, where n is the total number of pixels. Equalized histogram is a cumulative distribution function (CDP):

34. Homework 2 Implement in Matlab histogram equalization and " Find an example image for which histogram equalization improves its quality " Find an example image for which histogram equalization degrades its quality