How to extract the line segment information in a picture accurately in Python

Question

I'm trying to get detailed information on each line segment, such as the coordinates of two endpoints and whether it is straight or curved, in a picture in Python.

For example, an input image below is expected to lead to an output likes: {1: {"start": (92, 162), "end": (92, 5), "type": "straight"}, 2:...}, which contains 14 lines.

I've tried the HoughLinesP, but it didn't recognize correctly and cannot recognize a curve. Here is my code and result.

img = cv2.imread(path)
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
edges = cv2.Canny(gray, 50, 100)
lines = cv2.HoughLinesP(edges, 1, np.pi/180, 100)
counts = 0
for line in lines:
    counts += 1
    for x1, y1, x2, y2 in line:
        print(counts, (x1, y1, x2, y2))
        cv2.line(img, (x1, y1), (x2, y2), (0, 255, 0), 2)
cv2.imencode('lines.jpg', img)[1].tofile('lines.jpg')