Edge Detection using Hough Transform

Edge detection using Hough Transform

Presented by:Mrunal K. Selokar [2013BCS065]Suraj A. Bobade [2013BCS072]

Hough transform

Objective:

• 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+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

Haugh Transform• Solution: use equation,

e.g.• For horizontal line theta0rho+ve x-intercept.• for vertical line, theta90 degreerho+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 image101 X 101D= 142.

range of -90 to +90range of -D to +D , D max dist between 2 opposite corner of image

3.5 Line Detection by Hough Transform

EE63

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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

Thank You !