Edge Detection using Hough Transform

Edge detection using
Hough Transform
Presented by:
Mrunal K. Selokar [2013BCS065]
Suraj A. Bobade [2013BCS072]

• O/p of edge detection: valid edge points.
• Previous techniques for edge linking:
 Local processing: we should know position of straight lines.
 Region processing: We should have knowledge about region
of interest to find out boundaries.
• Limitation: we should have knowledge about patterns
prior to apply edge linking which is not possible in every
situations.
• Solution??  Hough transform.
Edge Detection and boundary linking Hough Transform

• Hough transform: a way of finding
edge points in an image that lie
along a straight line or curve.

Haugh Transform
• Steps:
• Consider one valid edge point (xi,yi) in xy-plane & the
equation of line passing through it can be,
• As it is a point, infinite lines will be passing through it
given by above equation & different values of a & b.
• We can write this equation as,
which gives us a line in ab-plane(parameter plane)
passing through fixed pair (xi,yi).
baxy ii 
ii yaxb 

Haugh Transform
• Next, we will consider 2nd valid edge point (xj,yj) and
find out equation in parameter plane. It will be,
• If these 2 points lies on a st line in xy-plane, then the
two lines in parameter plane will intersect at point(a’,b’)
where, a’ is slope and b’ is intercept of line passing
through 2 points (xi,yi) and (xj,yj) in xy-plane.
jj yaxb 

• What is the drawback???
• Slope (a) will be infinite in case of vertical lines.
• Example:
If 2 valid points are (3,1) and (3,2)
Line eq in ab-plane will be,
(3,1)b=-3a+1 & (3,2) b=-3a+2
Here, slope of 2 lines is equal, hence they are parallel in ab-
plane.
We can not find point of intersection which gives us slope
and intercept i.e a’ and b’ of line passing through (3,1) and
(3,2) in xy-plane.
• Solution???
Haugh Transform

Haugh Transform
• Solution: use equation,
e.g.
• For horizontal line
theta0
rho+ve x-intercept.
• for vertical line,
theta90 degree
rho+ve y-intercept
  sincos yx

• & gives two sine
waves on  -plane.
• intersection pt (’, ’) corresponds to line passing
through both the pts in xy-plane.
  sincos ii yx   sincos jj yx

The intersection of the
curves corresponding to
points 1,3,5
(’, ’)=(0,-45)
2,3,4
(’,
’)=(D/2,45)
(’, ’)=((71,45)
1,4
1,2
resolution of image101 X 101
D= 142.
range of   -90 to +90
range of   -D to +D , D max dist between 2
opposite corner of image

3.5 Line Detection by Hough
Transform
EE6358-ComputerVision
16

Parameters for analytic curves
Analytic Form Parameters Equation
Line ,  xcos+ysin=
Circle x0, y0,  (x-xo)2+(y-y0)2=r2
Parabola x0, y0, ,  (y-y0)2=4(x-xo)
Ellipse x0, y0, a, b,  (x-xo)2/a2+(y-y0)2/b2=1
EE6358 - Computer Vision 17

Edge Detection using Hough Transform

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