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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.

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csse463 image recognition day 25
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?
finding lines in real images
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)
hough transform
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
parametric equation of a line
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

voting
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

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

Q4

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

Q5

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

Q6

limitations
Limitations
  • Finding the right grid size in parameter space may be tricky
    • Trial and error
matlab
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
another demo
Another demo

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

generalizations
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

my circle finder
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
reducing the number of votes
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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