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Understanding Hough Transform for Image Recognition

Explore the Hough transform method for detecting lines in images, using parameters to represent lines and voting for accurate detection. Learn about limitations, Matlab implementation, generalizations, and potential applications. Discover how to detect circles and arbitrary shapes using this technique.

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Understanding Hough Transform for Image Recognition

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  1. CSSE463: Image Recognition Day 25 • This week • Today: Finding lines and circles using the Hough transform (Sonka 6.26) • Please fill out Angel evaluation of Sunset partner if you had one. Use "Term Project Partner Evaluation" • Tomorrow: Applications of PCA • Weds: k-means lab due. • Sunday night: project plans and preliminary work due • Questions?

  2. Finding lines in real images • Input: set of edge points • Output: the equation of a line containing them • Methods: • Least-squares (if you know which points belong to the line…) • Hough transform (today)

  3. Hough transform • Idea (Sonka 6.2.6; Forsyth and Ponce, ch 15): • Represent a line using parameters • Each edge point in the image casts a vote for all lines of which it could be part. • Only the true line receives lots of votes

  4. Parametric Equation of a Line • Represent a line using 2 parameters • y = mx + b? • Problem? • Ax + By + C = 0? • 3 parameters; but A, B, and C are related…we only need 2 • r and q • r is distance from line to origin • Q is the angle the distance segment makes with x-axis • x cosq + y sinq = r Q1

  5. Voting • Each point in image votes for all lines of which it could be part. • Only “true” line receives lots of votes. • Quiz question: show (4,4), (2,2), and (0,0) voting for a line in y = mx+b space (for simplicity) Q2-3

  6. Perfect line • Notice sharp peak in voting space • (next 3 images from Forsyth and Ponce, ch 15) Q4

  7. Approximate line • Notice the broader peak. Can we detect it? • Could smooth or use a coarser quantization? • Accumulator array: bin size? Range? Q5

  8. Random noise • Votes spead all over the place: no line • Too much noise creates “phantom lines” • Smoothing can sometimes help Q6

  9. Limitations • Finding the right grid size in parameter space may be tricky • Trial and error

  10. Matlab • Run an edge detector first to find points that are voting • [H, theta, rho] = hough(edgeImg); • peaks = houghpeaks(H,nPeaks); • This works for lines only

  11. Another demo http://www.rob.cs.tu-bs.de/content/04-teaching/06-interactive/HNF.html

  12. Generalizations • Finding circles with fixed radius… • Finding circles with arbitrary radius… • Finding line segments • Finding arbitrary shapes… • Ballard, Dana. 1981. Generalizing the Hough transform to detect arbitrary shapes. Pattern Recognition, 13(2):111-122. • Dana was a long-time member of Rochester’s computer vision group. Q7-8

  13. My Circle Finder • Demo • Wouldn’t this be a great lab? • Like Matlab’shough and houghpeaks (for lines), but from scratch • Easier would be to find circles of fixed radius

  14. Reducing the number of votes • Use the edge gradient information as well • Only need to cast votes for centers along the gradient • I’ve done this; it works really well • Use partial curves. If you had a way of grouping relating points, you could use curvature. • Haven’t done yet.

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