1. Detecting Shape Using Hough Transform Session 8
Course : T Computer Vision
Year : 2013
Detecting Shape Using Hough Transform Session 8

2. Learning Outcomes
After carefully listening this lecture, students will be able to do the following:
Explain how Hough Transforms are used to detect primitive shapes such as line and circle (LO2)
Demonstrate HT-based line and circle detection using MATLAB/OpenCV (LO3)
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3. Line Detection Using Mask
The mask shown below can be used to detect lines at various orientation
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4. Hough Transform
An algorithm to group edge points from edge detectors or from any other process.
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5. Straight Line Case Consider the slope-intercept equation of line:
y = ax + b
a, b are constant, x is a variable, and y is a function of x
Rewrite the equation as follows:
b = -xa + y
Now x, y are constant, a is a variable, b is a function of a
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6. Algorithm The following properties are true
Points lying on the same line in the x-y space, define lines in the parameter space which all intersect at the same point
The coordinates of the point of intersection define the parameters of the line in the x-y space
Algorithm
For each edge point (x,y)
for (a = amin; a ≤ amax; a++)
b = -xa +y;
P[a][b] ++;/*accumulator array*/
Find local maxima in P[a][b]
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7. T Computer Vision

8. Polar Representation of Lines
HT uses the parametric representation of a line:
 = x cos  + y sin  (*)
 is the distance from the origin to the line along a vector
perpendicular to the line.
 is the angle between the x-axis and this vector.
Hough function generates a parameter space matrix
whose rows and columns correspond to  and  values
respectively.
Peak values in this space represent potential lines in the
input image.
T Computer Vision

9. Algorithm Construct accumulator array in 2D (,)
Initial values 0
Select granularity of angle 
For instance 10 increments
For every edge point
Compute  using (*)
Increment accumulator array by one for each computed (,) pair.
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10. T Computer Vision

11. Hough Lines
HoughLines(dst, lines, 1, CV_PI/180, 100, 0, 0 ); for( size_t i = 0; i < lines.size(); i++ ) { float rho = lines[i][0], theta = lines[i][1]; Point pt1, pt2; double a = cos(theta), b = sin(theta); double x0 = a*rho, y0 = b*rho; pt1.x = cvRound(x *(-b)); pt1.y = cvRound(y *(a)); pt2.x = cvRound(x *(-b)); pt2.y = cvRound(y *(a)); line( cdst, pt1, pt2, Scalar(0,0,255), 3, CV_AA); }
T Computer Vision

12. Hough Circle Transform
The Hough Circle Transform works in a roughly analogous way to the Hough Line Transform. In the line detection case, a line was defined by two parameters . In the circle case, we need three parameters to define a circle:
/// Apply the Hough Transform to find the circles HoughCircles( src_gray, circles, CV_HOUGH_GRADIENT, 1, src_gray.rows/8, 200, 100, 0, 0 );
T Computer Vision

13. Latihan (Group, 50 menit) Jelaskan konsep dasar Hough Trasfrom
Buat program untuk mencari titik tengah untuk navigasi robot
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14. References
Textbook
Forsyth, D., Ponce, J. (2012). Computer Vision: A Modern Approach. 2nd ed. Prentice Hall. ISBN:
Web
Hough Transform
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16. THANK YOU
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