1. HOUGH TRANSFORM

2. BOUNDARY DETECTION BASED ON HOUGH TRANSFORM

3. Edges vs Boundaries Edges Boundaries
Local Intensity discontinuities
Points
Not Dependent on models
Boundaries
Extensive
Composed of many points
Maybe dependent on models
Typically our goal is to reconstruct
the boundary from local edge
elements

4. Boundaries of Objects from Edges
Brightness Gradient (Edge detection)
Missing edge continuity, many spurious (bogus, fake) edges

5. Boundaries of Objects from Edges
Multi-scale Brightness Gradient
But, low strength edges may be very important

6. Boundaries of Objects from Edges
Machine Edge Detection
Image
Human Boundary Marking

7. Boundaries in Medical Imaging
Detection of cancerous regions.
[Foran, Comaniciu, Meer, Goodell, 00]

8. Boundaries in Ultrasound Images
Hard to detect in the presence of large amount of speckle noise

9. Boundaries of Objects
Sometimes hard even for humans!

10. Knowledge about Boundary

11. Finding lines via Hough Transform
Useful for detecting any parametric curves (eg. Lines, conics)
Relatively unaffected by gaps in curves, and noise
Given a set of edge points, find line(s) which best explain the data

12. Hough Transform

13. Hough Transform

14. Contoh
y=x+1

15. 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

16. Better Parameterization
NOTE:
Large Accumulator
More memory and computations
Improvement:
Line equation:
Here
Given points find
(Finite Accumulator Array Size)
Image Space ?
Hough Space Sinusoid
Hough Space

17. 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.

18. This is 15.1 lower half
Image space
votes

19. 15.2; main point is that lots of noise can lead to large peaks in the array

20. Polar Coordinate Representation of Line

21. Hough Transform

22. Example

23. Example

24. Contoh Perhitungan x y -90 -45 45 90 0.00 100 70.71 100.00 (100.00)45 90
0.00
100
70.71
100.00
(100.00)
(70.71)
141.42

25. Pseudocode

26. Finding Circles by Hough Transform
Equation of Circle:
If radius is known:
(2D Hough Space)
Accumulator Array