HOUGH ALGORITHM USING EDGE INFORMATION

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HOUGH ALGORITHM USING EDGE INFORMATION
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Hough Algorithm So far we have seen..

• Choose an analytic form f(x,y,a1,a2,,an) and
  choose a range of values for parameters a1, a2,
  a3,.,an.
• Create accumulator array A(a1,a2,,an) which
  represents direct match of f(x,y,a1,a2,,an) with
  binary image.
• Local for local maximum which exceeds certain
  threshold.

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Hough Algorithm Consider this simple
modification..
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Hough Algorithm Revisited An Example..
f(x,y,a1,a2,a3)0
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Hough Algorithm Revisited
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Hough Algorithm Revisited
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Modified Hough Algorithm(More Efficient)

• Note that for p-parameters a1,a2,,ap containing
  2 translation parameters that the accumulator
  array is now (p-2) dimensional.
• Also note reduction in the number of pixels that
  are effectively visited
• Instead of examining all pixels as a possible
  center for the shape we now only examine edge
  points as possible boundary points for the shape.

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GENERALIZED HOUGH ALGORITHM

• In general many important shapes do not have an
  analytic form f(x,y,a1,a2,,an).
• How do we incorporate general shape matching into
  this modified scheme for the Hough Algorithm ?
• ANSWER Use an R-Table to represent a general
  shape relating edge orientation, f, at a boundary
  point (Bx,By) to the center (Xc,Yc) using
  vector displacement, r(Xc-Bx,Yc-By).

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GENERALIZED HOUGH ALGORITHM
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Generalized Hough Algorithm