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I would add another answer.

• Compute the gradients in the original (color) image

• Get the mean direction in a sliding window: make a 2x2 matrix containing:

  [ Sum(Gx²)    Sum(GxGy) ]
  [ Sum(GxGy)   Sum(Gy²)  ]
  

• Compute the PCA of this matrix. The first eigenvector will give you the mean gradient direction.

• Use the segmented image as a mask to eliminate unwanted areas.
• Segment the direction image to get the different lines. You can also check the histogram of the gradient directions.