Download General

Hough Transform
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Given marked edge pixels, find examples of specific
shapes
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Line segments
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Circles
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Generalized shapes (GHT)
Basic idea - Patented 1962
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Every edge pixel is a point that votes for all shapes that
pass through it.
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Votes are collected in “parameter space” - look for peaks
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“Parameter space” is a k-dimensional histogram!
Ellen L. Walker
Hough Transform for Lines
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Parameter space:
(But A,B, C aren’t unique!)
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Ax+By+C = 0
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Divide by sqrt(A*A+B*B); first two terms are sin,cos of the
angle
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Angle, distance from 0
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Angle = arctan(A/B), distance = C/(A*A+B*B)
Given a point (x0,y0), find all theta, distance pairs
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cos(theta)*x0 + sin(theta)*y0 + distance = 0
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If theta is known (e.g. from Sobel detector), only 1
distance needs to be calculated, otherwise calculate a
distance for each theta
Ellen L. Walker
Hough Transform for Lines (cont.)
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Increment all “cells” in p-space through which curve
passes
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Ellen L. Walker
Hough Transform Example: Line Detecton
Image (enlarged)
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Hough P-Space
Ellen L. Walker
Alternative Parametrization for Lines
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Number border pixels of the image
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For each line segment, store the two border pixels
where the (extended) line enters / exits the image
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Why?
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Values are integers in a fixed range
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No trigonometry is needed to find all lines passing through
a point
Ellen L. Walker
Hough Transform for Circles
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Parameter space is (centerx, centery, radius)
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Update:
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6
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For every point, computer center, radius of all circles
passing through the point
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Mark each center, radius pair
Alternative computation: for each cell, compute
distance from that cell to point - increment if close
enough.
Ellen L. Walker
GHT: Generalized Hough Transform
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Parameters are translation, rotation & scale of a fixed
2D shape,represented as a point set
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Given a point and a location in the transform space, if
the point is in (or close enough to a point in) the
transformed point set, then record a vote.
Ellen L. Walker
Hough Transform Issues
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Space usage
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Need large arrays for accurate results!
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More complex objects need more parameters (fast!)
Peak detection
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Large spaces take long to search - threshold unreliable
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“Accidental peaks” are not unusual
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Noise causes “cluster” rather than “peak” - may need to
use cluster detection (remember K-means?)
Easily parallelizable!!
Ellen L. Walker