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**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,

y=mx+c

Where, m is the slope and c is the constant.

Let, y=ax+b

Then b=y-ax

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=∞

m= =∞