Edge Detection using Hough Transform
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Transcript of Edge Detection using Hough Transform
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Edge detection using Hough Transform
Presented by:Mrunal K. Selokar [2013BCS065]Suraj A. Bobade [2013BCS072]
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Hough transform
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Objective:
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• 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
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• Hough transform: a way of finding edge points in an image that lie along a straight line or curve.
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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
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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
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• 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+2Here, 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
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Haugh Transform• Solution: use equation,
e.g.• For horizontal line theta0rho+ve x-intercept.• for vertical line, theta90 degreerho+ve y-intercept
sincos yx
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• & 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
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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 image101 X 101D= 142.
range of -90 to +90range of -D to +D , D max dist between 2 opposite corner of image
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3.5 Line Detection by Hough Transform
EE63
58 -
Com
pute
r Visi
on
16
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EE6358 - Computer Vision 17
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
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Thank You !