How to separate and detect overlapping curves?

I’m programming hand palm line detector, which detects main palm lines, not wrinkles. So I did pre-processing using HPF and here’s the image

And now, i have to detect main lines. So i used 8 directional contour detect method(8 method). It was fine. But I doesn’t consider a slope. For example, there’s an image A
A
If I apply 8 method to image A, those two overlapping lines would be detected as a one line because 8 method only care about distance between points.

I want to solve this problem. So i have used cv2.HoughLinesP, adjust variable, But doesn’t work(a colored line is one line)(Here’s the image)

I’m not good at computer vision, questioning, googling and math. please let me know how to detect this overlapping curves? Also, please ask me what you want to know about my problem If you can’t understand what i’m asking, instead of just going back to homepage of OpenCV Forum.