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Hough Lines

consider the image like this we need to find the lines on this image 

the basic lines would be horizontal ,vertical and inclined line 

we will try to use hough to detect using equations 

ok before that we need to understand the image co ordinate 

top left is 0,0 assume it is the third quadrant , for 

better understanding i have drawn a to show how a pixel is calculated from top left



pixel arrangement for image 


 

this is level zoom of more than 1000 , in real world u cannot see the pixel (1pixel of size 1,1) 

alright now we can need to see how to find the lines on the first image

the triangle on a zoomed in pixel wil look like this 

ok we will start with the horizontal line calculation 

since the pixel calculation is in the quadrant  i will shift or plot the values in 

the first quadrant for my calculation 

when shifted will look like this ,


for horizontal line calculation the theta of r must be at 90 degrees to the horizontal line u can see the value in diagram

r = x cos𝛳 + y sin 𝛳

calculate for [4,2] [5,2] ,[8,2 ] 

if u put random values for 𝛳 starting from  𝛳 >0 and 𝛳  <2𝞹

u could see for 𝛳 = 90

for calculation convert degrees to radians which is 0.5 *𝞹

r =  4 *cos(0.5 *𝞹) + 2 sin (0.5 *𝞹)

= 0 + 2 =2

r =  5 *cos(0.5 *𝞹) + 2 sin (0.5 *𝞹)

 = 0 + 2 =2

so it says for the  𝛳 = 90 r = 2 for these points so according to hough 

it means they lie on the same line which is in our case is the horizontal line.


moving on to the inclined line from the diagram u can see the 𝛳 = 315

so the calculation for the pixel on the slope 

[4,3] [5,4] [7,6]

 r =  4 *cos(1.75 *𝞹) + 3 sin (1.75 *𝞹)

= 0.7 

r =  7 *cos(1.75 *𝞹) + 6 sin (1.75 *𝞹)= 0.7 

so at an angle of  𝛳 = 315 and r =0.7 which is a small line as u can see in the diagram ,the line which is at right angles to this line r would be the

inclined line where the above point lie .

enjoy


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