1. CIS 601 – 03 Image ENHANCEMENT SPATIAL DOMAIN Longin Jan Latecki
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
Chapter 3

3. Image Enhancement ? Spatial Domain ?
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. A 2D grayvalue - image is a 2D -> 1D function,
Remember ?
A 2D grayvalue - image is a 2D -> 1D function,
v = f(x,y)

5. As we have a function, we can apply operators to this function, e.g.
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. T transforms the given image f(x,y) into another image g(x,y)
Remember ?
T transforms the given image f(x,y)
into another image g(x,y) T
f(x,y)
g(x,y)

7. The operator T can be defined over
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,…

8. Operation on the set of image-pixels
Spatial Domain
Operation on the set of image-pixels 6 8 2 3 4 1 12
200 20 10 6
100 10 5
(Operator: Div. by 2)

9. Operation on the set of ‘neighborhoods’ N(x,y) of each pixel
Spatial Domain
Operation on the set of ‘neighborhoods’ N(x,y) of each pixel 6 8 12
200
(Operator: sum) 6 8 2
226 12
200 20 10

10. Operation on a set of images f1,f2,…
Spatial Domain
Operation on a set of images f1,f2,… 6 8 2 12
200 20 10 11 13 3
(Operator: sum) 14
220 23 14 5 5 1 2 20 3 4

11. Operation on the set of image-pixels
Spatial Domain
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

12. 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]

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

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

15. Transformations
Log Transformations
InvLog
Log

16. Transformations
Log Transformations

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

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

19. Used for gamma-correction
Transformations
Used for gamma-correction

20. Used for general purpose contrast manipulation
Transformations
Used for general purpose contrast manipulation

21. Piecewise Linear Transformations

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

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

24. Piecewise Linear Transformations
Gray Level Slicing

25. Operation on a set of images f1,f2,…
Operations on a set of images
Operation on a set of images f1,f2,… 6 8 2 12
200 20 10 11 13 3
(Operator: sum) 14
220 23 14 5 5 1 2 20 3 4

26. Logic (Bitwise) Operations
Operations on a set of images
Logic (Bitwise) Operations
AND OR
NOT

27. The operators AND,OR,NOT are functionally complete:
Operations on a set of images
The operators AND,OR,NOT are functionally complete:
Any logic operator can be implemented using only these 3 operators

28. Any logic operator can be implemented using only these 3 operators:
Operations on a set of images
Any logic operator can be implemented using only these 3 operators: A B Op 1
Op=
NOT(A) AND NOT(B) OR
NOT(A) AND B

29. Image 1 AND Image 2 Operations on a set of images 1 2 3 9 7 3 6 4 1 11 1
(Operator: AND) 2 2 2 1 1 1 1 2 2 2 2

30. Used for Bitplane-Slicing and
Operations on a set of images
Image 1 AND Image 2:
Used for Bitplane-Slicing and
Masking

31. Operations on a set of images
Exercise: Define the mask-image, that transforms image1 into image2 using the OR operand 1 2 3 9 7 3 6 4
255 2 7
255
(Operator: OR)
255 3 7
255

32. Arithmetic Operations on a set of images1 2 3 9 7 3 6 4 2 3 4 10
(Operator: +) 9 5 8 6 1 1 1 1 2 2 2 2

33. What could the operators + and – be used for ?
Operations
Exercise:
What could the operators + and – be used for ?

34. Foreground-Extraction
Operations
Example: Operator –
Foreground-Extraction

35. Operations
Example: Operator +
Image Averaging