Question: 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.
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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. (3,4), (0,-4), (1,4), (6,12),(4,1),(1.5,0),(-2,2), (-1,-3), (3,-2)

Subject : Digital Image Processing

Topic: Chap 3: Image Segmentation and Representation

Difficulty: Medium

mumbai university dip(47) • 25 views
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modified 29 days ago  • written 29 days ago by gravatar for tanya.tanyabarnwal tanya.tanyabarnwal0
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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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written 29 days ago by gravatar for tanya.tanyabarnwal tanya.tanyabarnwal0
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