1. Miguel Tavares Coimbra
VC 17/18 – TP8 Segmentation
Mestrado em Ciência de Computadores
Mestrado Integrado em Engenharia de Redes e Sistemas Informáticos
Miguel Tavares Coimbra

2. Outline Thresholding Geometric structures Hough Transform
VC 17/18 - TP8 - Segmentation

3. Topic: Thresholding Thresholding Geometric structures Hough Transform
VC 17/18 - TP8 - Segmentation

4. Boundaries of Objects Marked by many users
VC 17/18 - TP8 - Segmentation

5. Boundaries of Objects from Edges
Brightness Gradient (Edge detection)
Missing edge continuity, many spurious edges
VC 17/18 - TP8 - Segmentation

6. Boundaries of Objects from Edges
Multi-scale Brightness Gradient
But, low strength edges may be very important
VC 17/18 - TP8 - Segmentation

7. Machine Edge Detection
Image
VC 17/18 - TP8 - Segmentation
Human Boundary Marking

8. Boundaries in Medical Imaging
Detection of cancerous regions.
VC 17/18 - TP8 - Segmentation
[Foran, Comaniciu, Meer, Goodell, 00]

9. Boundaries in Ultrasound Images
Hard to detect in the presence of large amount of speckle noise
VC 17/18 - TP8 - Segmentation

10. Sometimes hard even for humans!
VC 17/18 - TP8 - Segmentation

11. What is ‘Segmentation’?
Separation of the image in different areas.
Objects.
Areas with similar visual or semantic characteristics.
Not trivial! It is the holy grail of most computer vision problems!
VC 17/18 - TP8 - Segmentation

12. What is the correct segmentation?
Subjectivity
A ‘correct’ segmentation result is only valid for a specific context.
Subjectivity!
Hard to implement.
Hard to evaluate.
What is the correct segmentation?
Face
Person
Suitcase
VC 17/18 - TP8 - Segmentation

13. Core Technique: Thresholding
Divide the image into two areas:
1, if f(x,y)>K
0, if f(x,y)<=K
Not easy to find the ideal k magic number.
Core segmentation technique
Simple
Reasonably effective
Adequate threshold
VC 17/18 - TP8 - Segmentation

14. Finding the ‘magic number’
Wrong!
(k = 128)
Correct
(k = 74)
VC 17/18 - TP8 - Segmentation

15. Global thresholds are not always adequate...
VC 17/18 - TP8 - Segmentation

16. Adaptive Thresholding
Adapt the threshold value for each pixel.
Use characteristics of nearby pixels.
How?
Mean
Median
Mean + K
...
Mean of 7x7 neighborhood
VC 17/18 - TP8 - Segmentation

17. 7x7 window; K = 7
75x75 window; K = 10
VC 17/18 - TP8 - Segmentation

18. Topic: Geometric structures
Thresholding
Geometric structures
Hough Transform
VC 17/18 - TP8 - Segmentation

19. Points What is a point? Spatial Mask! Need to define a threshold K.
Pixel with a significant illumination difference to its neighbors.
Group of pixels?
Spatial Mask!
Need to define a threshold K. -1 8
VC 17/18 - TP8 - Segmentation

20. Lines Spatial filter One per line direction Sensitive to line width-1 2 -1 2
Horizontal
Vertical
Diagonal?
VC 17/18 - TP8 - Segmentation

21. Edges Edge: Spatial discontinuity of pixel amplitude.
High spatial gradient
First derivative (peak)
Second derivative (zero crossing)
VC 17/18 - TP8 - Segmentation

22. Popular operators Edge detection A variety of solutions exists.
Great utility for several problems.
Well studied problem.
A variety of solutions exists.
VC 17/18 - TP8 - Segmentation

23. VC 17/18 - TP8 - Segmentation

24. Processing Edge Images
Edge detection
and Thresholding
Noisy edge image
Incomplete boundaries
Image
Edge Tracking
Thinning
VC 17/18 - TP8 - Segmentation

25. Edge Tracking Methods Adjusting a priori Boundaries
Given: Approximate Location of Boundary
Task: Find Accurate Location of Boundary
Search for STRONG EDGES along normals to approximate boundary.
Fit curve (eg., polynomials) to strong edges.
VC 17/18 - TP8 - Segmentation

26. Edge Tracking Methods Divide and Conquer
Given: Boundary lies between points A and B
Task: Find Boundary
Connect A and B with Line
Find strongest edge along line bisector
Use edge point as break point
Repeat
VC 17/18 - TP8 - Segmentation

27. Fitting Lines to Edges (Least Squares)
Given: Many pairs
Find: Parameters
Minimize: Average square distance:
Using:
Note:
VC 17/18 - TP8 - Segmentation

28. Topic: Hough Transform
Thresholding
Geometric structures
Hough Transform
VC 17/18 - TP8 - Segmentation

29. Hough Transform Elegant method for direct object recognition
Edges need not be connected
Complete object need not be visible
Key Idea: Edges VOTE for the possible model
VC 17/18 - TP8 - Segmentation

30. Image and Parameter Spaces
Equation of Line:
Find:
Consider point:
Image Space
Parameter
Space
Parameter space also called Hough Space
VC 17/18 - TP8 - Segmentation

31. Line Detection by Hough Transform
Algorithm:
Quantize Parameter Space
Create Accumulator Array
Set
For each image edge increment:
If lies on the line:
Find local maxima in
Parameter Space 1 2
VC 17/18 - TP8 - Segmentation

32. Better Parameterization
NOTE:
Large Accumulator
More memory and computations
Improvement:
Line equation:
Here
Given points find
Image
Space
(Finite Accumulator Array Size) ?
Hough
Space
Hough Space Sinusoid
VC 17/18 - TP8 - Segmentation

33. Horizontal axis is θ, vertical is rho.
Figure 15.1, top half. Note that most points in the vote array are very dark, because they
get only one vote.
Image space
Votes
Horizontal axis is θ, vertical is rho.
VC 17/18 - TP8 - Segmentation

34. This is 15.1 lower half
VC 17/18 - TP8 - Segmentation

35. 15.2; main point is that lots of noise can lead to large peaks in the array
VC 17/18 - TP8 - Segmentation

36. Mechanics of the Hough Transform
Difficulties
how big should the cells be? (too big, and we merge quite different lines; too small, and noise causes lines to be missed)
How many lines?
Count the peaks in the Hough array
Treat adjacent peaks as a single peak
Which points belong to each line?
Search for points close to the line
Solve again for line and iterate
VC 17/18 - TP8 - Segmentation

37. single bin when noise increases.
Fewer votes land in a
single bin when noise increases.
This is the number of votes that the real line of 20 points gets with increasing noise (figure15.3)
VC 17/18 - TP8 - Segmentation

38. Adding more clutter increases number of bins with false peaks.
Figure 15.4; as the noise increases in a picture without a line, the number of points in the max cell goes
up, too
VC 17/18 - TP8 - Segmentation

39. Real World Example
Original
Edge Detection
Found Lines
Parameter Space

40. Edges when using circle model
Other shapes
Edges when using circle model
Original
VC 17/18 - TP8 - Segmentation

41. Resources Gonzalez & Woods – Chapter 7
N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Sys., Man., Cyber., vol. 9, pp. 62–66, 1979.
VC 17/18 - TP8 - Segmentation