1. Image Segmentation – Edge Detection
Dr. Jiajun Wang
School of Electronics & Information Engineering
Soochow University

2. Image Segmentation - 1
Contents
Edge detection
Gradient operators
Edge linking
Hough transform

3. Revisit - Goals of image processing
Image Segmentation - 1
Revisit - Goals of image processing
Image improvement – low level IP
Improvement of pictorial information for human interpretation (Improving the visual appearance of images to a human viewer )
Image analysis – high level IP
Processing of scene data for autonomous machine perception (Preparing images for measurement of the features and structures present )

4. Image Segmentation - 1
Image analysis – HLIP
Extracting information form an image
Step 1: segment the image ->objects or regions
Step 2 : describe and represent the segmented regions in a form suitable for computer processing
Step 3 : image recognition and interpretation

5. Image Segmentation - 1
Image analysis – HLIP (cont’)

6. Based on two properties of gray-level image values
Image Segmentation - 1
Image segmentation
Definition
Subdivide an image into its constituent regions or objects
Based on two properties of gray-level image values
Discontinuity
point / line / edge / corner detection
Similarity
thresholding
region growing / splitting / merging

7. Image Segmentation - 2
Image Segmentation (cont’)

8. Image Segmentation - 1 What Should Good Image segmentation be?
Region interiors
Simple
Without many small holes
Adjacent regions
Should have significantly different values
Boundaries
Not ragged
Spatially accurate
Achieving all these desired properties is difficult. There is no theory of image segmentation. Image segmentation techniques are basically ad hoc.

9. Image Segmentation - 1
Point detection

10. Image Segmentation - 1
Line detection

11. Image Segmentation - 1
Line detection (cont’)

12. Image Segmentation - 1 Edge detection Definition Edge detection steps
An edge is a set of connected pixels that lie on the boundary between two regions
The difference between edge and boundary, pp.68
Edge detection steps
Compute the local derivative
Magnitude of the 1st derivative can be used to detect the presence of an edge
The sign of the 2nd derivative can be used to determine whether an edge pixel lies on the dark or light side of an image
Zero crossing of the 2nd derivative is at the midpoint of a transition in gray level, which provides a powerful approach for locating the edge.

13. Image Segmentation - 1
Edge detection (cont’)

14. Image Segmentation - 1
Edge detection (cont’)

15. Edge detection (cont’)
Image Segmentation - 1
Edge detection (cont’)
The derivatives are sensitive to noise

16. Use gradient for image differentiation
Image Segmentation - 1
Gradient operators
Use gradient for image differentiation
The gradient of an image f(x,y) at point (x,y) is defined as
Some properties about this gradient vector
It points in the direction of maximum rate of change of image at (x,y)
Magnitude
angle

17. Image Segmentation - 1
Edge operator

18. Image Segmentation - 1
Sobel edge operator
Advantages : providing both differencing and a smooth effect and slightly superior noise reduction characteristics.

19. Image Segmentation - 1
Edge detection example

20. Image Segmentation - 1
Edge detection example (cont’)

21. Image Segmentation - 1
Edge detection example (cont’)

22. Laplacian edge operator
Image Segmentation - 1
Laplacian edge operator
A second order derivative
Problems
Very sensitive to noise
Detect double edges
Can’t detect edge direction
Usage
Find the location of edge using zero-crossing property

23. Marr and hildreth’s approach
Image Segmentation - 1
Marr and hildreth’s approach
Smooth the image to reduce noise
Then calculate the 2nd derivative
Finally, find the zero-crossing
LoG (Laplacian of Gaussian, Mexican hat function)

24. Image Segmentation - 1
LoG function

25. Edge detection by gradient operations tends to work well when
Image Segmentation - 1
discussion
Edge detection by gradient operations tends to work well when
Images have sharp intensity transitions
Relative low noise
Zero-crossing approach work well when
Edges are blurry
High noise content
Provide reliable edge detection

26. Gradient operators – examples
Image Segmentation - 1
Gradient operators – examples
Zero-Crossing:
Advantages:
noise reduction capability;
edges are thinner.
Drawbacks:
edges form numerous closed loops (spaghetti effect);
computation complex.

27. Image Segmentation - 1
Edge linking
How to deal with gaps in edges?
How to deal with noise in edges?
Linking points by determining whether they lie on a curve of a specific shape

28. Edge linking – Local Processing
Image Segmentation - 1
Edge linking – Local Processing
Analyze the characteristics of the edge pixels in a small neighborhood
Its magnitude
Its direction

29. Edge linking - Hough transform
Image Segmentation - 1
Edge linking - Hough transform
Can tolerate noise and gaps in edge image
Look for solutions in a parameter space
Classical Hough transform
Detect simple shape
Line detection
Circle detection
Generalized Hough Transform
Detect complicated shapes

30. Image Segmentation - 1
Edge linking - Hough transform

31. Image Segmentation - 1
Edge linking - Hough transform

32. Image Segmentation - 1
Edge linking - Hough transform

33. Image Segmentation - 1
Edge linking - Hough transform

34. Image Segmentation - 1
Edge linking - Hough transform

35. School of Electronics & Information Engineering
Image Segmentation - 2
Dr. Jiajun Wang
School of Electronics & Information Engineering
Soochow University

36. Foundation of thresholding
Idea: object and background pixels have gray levels grouped into two dominant modes
Original image
histogram

37. Foundation of thresholding
Input f(x,y), given threshold T

38. Issues of thresholding
Selection of threshold T ?
Complex environment – illumination
Multiple thresholds – more than one object
Global threshold
Local threshold
Thresholding as a multi-variable function:
g(x,y) = T[ f(x,y), x, y, p(x,y) ]
Adaptive: Depend on
position
Local: local property func.

39. 1. Automatic selection of T
1. Select an initial T
Average gray level
Mean of max. and min. gray level G1 G2 m1 m2
2. Segment the image using T T
3. Calculate mean of G1 and G2 T2
4. New threshold: T2 = 0.5(m1 + m2)
5. Repeat steps 2~4 until difference in successive T is small

40. Example: automatically select T
Initial: gray level mean
3 iterations
T = 125.4
fingerprint

41. 2. Effects of illumination
Recall: f(x,y)=i(x,y) r(x,y)
illumination:
reflectance:
Illumination source
scene
reflection

42. Example: illumination
Original image
Illumination
source
histogram
histogram

43. Example: bad histogram
* The gray levels of the object is mixed with background

44. 4. Motivation for adaptive thresholding
A single
Global threshold
histogram

45. Adaptive local thresholding
Subdivide image into blocks
Q: Improperly segmented subimages !

46. Iterative subdivision
histogram
subdivision

47. Region based segmentation
Image Segmentation - 2
Region based segmentation
R: the entire image
Segmentation: partition R into n subregions R1,…Rn
Ri is a connected region
P(Ri) = true
P( ) = false

48. Step 2: Use different labels to identify different objects
Image Segmentation - 2
Region growing
Groups pixels or subregions into larger regions based on predefined criteria (gray tone or texture).
Step 1: Assume we find a good threshold, and use it to partition the regions into pure black and white.
Step 2: Use different labels to identify different objects
Use region growing to connect parts that should have belong to the same region
This is called “Connected component analysis”
The region with the same label generate one segment

49. Image Segmentation - 2
Region growing - example

50. Region Splitting and Merging
Image Segmentation - 2
Region Splitting and Merging
QuadTree Decomposition

51. Motion as a clue to extract object
Image Segmentation - 2
Motion as a clue to extract object
Spatial technique
Thresholded
difference image
1 if |d(x,y)| > T
0 otherwise
Reference image
f(x,y,1)
next image
f(x,y,2)
time index

52. Use more than one images in time: eliminate noise…
Reference image
R(x,y)
Image f(x,y,2)
Image f(x,y,3)
d(x,y)=R(x,y)-f(x,y,t)
counter
counter + 1,
a. if d(x,y) > T
positive ADI
b. if d(x,y) < -T
negative ADI
c. if |d(x,y)| > T
absolute ADI
Accumulative
difference image

53. Example:
Negative ADI
Positive ADI
Absolute ADI
* Object shape
* Location in ref. image