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Separate HSV mask

The following is the original image :

image description

Then, I used the HSV inrange to filter the guidepath. And then the result like this: image description

Is there has any method so that I can separte the guidepath into 3 direction? Just similar the following: image description

Separate HSV mask

The following is the original image :

image description

Then, I used the HSV inrange to filter the guidepath. And then the result like this: image description

Is there has any method so that I can separte the guidepath into 3 direction? Just similar the following: image description

Updated

The following image has already completed the first 2 (@StevenPuttemans suggestion) step image description

I also use 100*100 sliding window to scan thought the whole image. And then calculating the mean point inside the sliding window. The result like following: image description Then, I use the minmum spanning tree with euclidean distance to create the relationship between these point. Now, I have no idea how to remove noise edge in tree and confirm different direction. Anyone have a good suggestion?