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The threshold image segment has resulted into following edge point. Find eq. of the line that passes through max number of points using Hough Transform.

The threshold image segment has resulted into following edge point. Find eq. of the line that passes through max number of points using Hough Transform. (3,4), (0,-4), (1,4), (6,12),(4,1),(1.5,0),(-2,2), (-1,-3), (3,-2)

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The equation of straight line is y = ax + b

Changing co-ordinates, we get

b = -ax + y

Line x y
1 3 4 b = -3a+4
2 0 -4 b = -4
3 1 4 b = -a + 4
4 6 12 b = -6a + 12
5 4 1 b = -4a+1
6 1.5 0 b = -1.5a
7 -1 2 b = 2a + 2
8 -2 -3 b = a-3
9 3 -2 b = -3a - 2

Plot the above obtained eq. of line on the graph paper and then find a point through which maximum number of lines pass

From the graph, we observe that 4 lines intersect a common point i.e. a = 2.7 & b = -4.

By using these values of a and b we can write another eq. of line in xy-plane i.e. y = 2.7x – 4

enter image description here

Hence, four lines intersecting at one point in ab-plane means there are three points on one line in xy-plane

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