1. IMAGE PROCESSING INTENSITY TRANSFORMATION AND SPATIAL FILTERING
Editor by
DR. FERDA ERNAWAN
Faculty of Computer Systems & Software Engineering

2. Today’s Lesson Image Enhancement in the Spatial Domain
Introduction to Spatial domain
Intensity transformations
Photographic Negative, Gamma transformation, Logarithmic Transformation, Contrast-stretching transformation
Histogram transformation
Spatial filtering
Smoothing, Sharpening
Learning Outcomes:
To understand the basic operation of image enhancement in Spatial Domain.

3. Introduction to Spatial
Spatial domain is a signal having space as the independent variable (Jayaraman, Veerakumar, Esakkirajan, 2017 ), image is an example of a signal that can be processed in the spatial domain.
There are two principal categories for processing in spatial domain:
Spatial filtering : sharpening and blurring.
Intensity transformation : contras manipulation and thresholding.

4. General Framework in Spatial Domain
The most basic transformation is
h(x, y) = T(f(x, y))
where
f(x, y) denotes input image, h(x, y) represents the output and T(f) is a function of a single (real) variable.

5. Conventions: Digital Images
Left: Digital image where the point of (x,y) is reffered.
Below: Examples of gray-value transformations to enhance the image by controlling the contrast stretching function (i) and thresholding function (ii).

6. Intensity Transformations

7. Basic Gray Level (Intensity) Transformations Function
The simplest image processing technique.
s = T( r )  transformation pixel r into s.
Gray level is used to enhance an image :
Negative
Gamma Transformation
Logarithmic Transformation
Contrast-stretching / Piecewise linear
Bit slicing

8. Negative Transformation
Gray-level transformation function used for image enhancement

9. Negative Transformation Example
This technique is suitable when the image has dominant black areas.
S = L – 1 – r  reversing the intensity (grey) level.
Images taken from Gonzalez and Woods, 2016

10. Negative Transformation Example
Images taken from Gonzalez and Woods, 2016

11. Logarithmic Transformation Example
Enhance details in the darker regions of an image by expensing detail in brighter regions.
Images taken from Gonzalez and Woods, 2016

12. Gamma Transformation
Gamma transformation is an important technique for image display on a computer monitor.
Images taken from Gonzalez and Woods, 2016

13. Piecewise-Linear Transformation Example
Contrast Stretching:
Stretch gray-level ranges where we desire more information
Images taken from Gonzalez and Woods, 2016

14. Piecewise-Linear Example 2
Images taken from Gonzalez and Woods, 2016

15. Intensity Level Slicing
Highlight specific ranges of gray-levels only.
Images taken from Gonzalez and Woods, 2016

16. Histogram Transformation

17. Histogram Processing
A fully automated gray-level stretching technique  one of the image enhancement technique.
What is Histogram?
Images taken from Gonzalez and Woods, 2016

18. Image Histograms “Level of gray is represented by a unique number”
An image histogram is a plot of the gray-level frequencies.
“Level of gray is represented by a unique number”

19. Image Histograms (cont..)
Divide frequencies by total number of pixels to represent as probabilities. 6 18 2 10

20. Properties of Image Histograms
Histograms with small spread correspond to low contrast images (i.e., mostly dark, mostly bright, or mostly gray).
Histograms with wide spread correspond to high contrast images  better image.
Images taken from Gonzalez and Woods, 2016

21. Properties of Image Histograms (cont..)
Histograms clustered at the low end correspond to dark images.
Histograms clustered at the high end correspond to bright images.
Images taken from Gonzalez and Woods, 2016

22. Histogram Equalization
The main idea is to redistribute the gray-level values uniformly.
Images taken from Gonzalez and Woods, 2016

23. Histogram Equalization
In practice, the equalized histogram might not be completely flat.

24. Histogram Equalization
Images taken from Gonzalez and Woods, 2016

25. Histogram Equalization – in Graph
Images taken from Gonzalez and Woods, 2016

26. Advantages of Histogram Equalization
Optimal contrast.
Fully automated (adaptive, no human intervention).
Image normalization: easy to compare two images taken under different lighting conditions.

27. Spatial filtering (Smoothing and Sharpening)

28. Spatial Filtering
Filter (Mask) refers to “accepting” or “rejecting” a certain frequency components (smooth or sharp).
Mask operation: output pixel value = some algorithm performed on all the pixels in the neighborhood of the corresponding input pixel
Size of neighborhood = size of mask.
Mask slides from left-side to right-side, then from top to bottom
Same operation is performed on every pixel
Neighborhood exceeds image boundary: zero padding or replication of border pixels

29. Spatial Example
“Consider neighborhood pixel in order to do operation in smoothing or sharpening”.

30. Neighbourhood Operations
Origin x y
Image f (x, y)
(x, y)
Neighbourhood
Neighbourhood operations
simply operate on a larger
neighbourhood of pixels than
point operations
Neighbourhoods are mostly a rectangle around a central pixel
Any size rectangle and any shape filter are possible

31. Neighbourhood Operations
Origin
Target x y
Image f (x, y)
(x, y)
Neighbourhood

32. The Spatial Filtering Process
Origin x *
Original Image Pixels
Filter (w)
Simple 3*3 Neighbourhood e
3*3 Filter
eprocessed = o*e + k*a + l*b + m*c + n*d + p*f + q*g + r*h + s*i y
Image f (x, y)
For each pixel is computed based on neighbourhood operation to generate the smoothed image

33. Smoothing Spatial Filtering
Origin x
104
100
108 99
106 98 95 90 85
1/9 *
Original Image Pixels
Filter
1/9
104 99 95
100
108 98 90 85
Simple 3*3 Neighbourhood
3*3 Smoothing Filter
106
e = 1/9* /9* /9* /9* /9*99 + 1/9* /9*95 + 1/9*90 + 1/9*85 = y
Image f (x, y)
For each pixel is computed based on neighbourhood operation to generate the smoothed image

34. Weighted Smoothing Filters
An effective smoothing filter uses different weights in the averaging function.

35. Linear Filter Example
g(x,y) = w(-1,-1)f(x-1,y-1) +w(-1,0)f(-1,0) +…… + w(1,1)f(x+1, y+1)

36. Spatial Filtering - Smoothing
Spatial filter is suitable for blurring and noise reduction
The aims are to remove the detail information and bridging of small gaps in lines or curves

37. Smoothing Masks
Smoothing masks are normally adjusted to preserve average value (∑wi = 1)

38. Spatial Filtering - Sharpening
Highlight/enhance fine detail that has been blurred
Application ranging from electronic printing and medical imaging to industrial inspection

39. Laplacian Filter The Laplacian filter is given as: Where:
The filter mask of Laplacian filter is shown as follows:

40. Laplacian Filter
The result obtained from Laplacian filer produces highlights edges.
Images taken from Gonzalez and Woods, 2016

41. Result of Laplacian Filter
In order to produce the final sharpened image, the original image is subtracted by the Laplacian result
Laplacian Filtered
Images taken from Gonzalez and Woods, 2016

42. Laplacian Filter
Images taken from Gonzalez and Woods, 2016

43. Laplacian Filter
Images taken from Gonzalez and Woods, 2016

44. Variants Laplacian Filter
Some variants Laplacian filters are given as follows:
Simple Laplacian
Variant of Laplacian
Images taken from Gonzalez and Woods, 2016

45. Cont..

46. References
R.C. Gonzalez and R.E. Woods, Digital Image Processing, Pearson Education India; Third edition.
A.K. Jain, Fundamentals of Digital Image Processing, Pearson Education India; First edition.
R.C. Gonzalez, R.E. Woods and S.L. Eddins, Digital Image Processing Using MATLAB. McGraw Hill Education; 2 edition.
S. Jayaraman, T. Veerakumar, S. Esakkirajan, 2017.Digital Image Processing, McGraw Hill Education; 1 edition.