i) Hough Transform:
Consider two points $A(x_1,y_1)$ and $B(x_2,y_2)$ in xy plane. The Equation of line AB is then given by,
Where, m is the slope and c is the constant.
For pt $A(x_1,y_1)$ we get $b=y_1-ax_1$
For pt $B(x_2,y_2)$ we get $b=y_2-ax_2$
Hough transformation is POINT to LINE and LINE to POINT transformation
At Each intersecting point in ab plane we get slope value and y constant value of line that exists in xy plane The equation of line is given by y=a’x+b’
ii) Line detection using Hough transform:
Map all the edge points from xy plane to ab plane using Hough Transform.
Eg: Consider a edge points in $A(x_1,y_1), B(x_2,y_2), C(x_3,y_3) and D(x_4,y_4)$ as shown in below figure.
Count the number of intersecting lines at each point in ab plane
Select the point with maximum value of count. Eg: Max value of count is 3 at point (a’,b’)
Define line with slope value =a’ and y constant value=b’
The equation of line is y’=a’x+b’
Determine co-linear points
Eg:pt A, B, C are co-linear pts
Link Co-linear points
Limitations of the Hough transform:
This algorithm is not suitable for vertical lines where slope=∞