How to travel edge / contour points consecutively?

Dear all,

I have a binary image containing several lines. Now I want to get the coordinates of the pixels on each line from one end to the other end consecutively, says, current point and next point are 8-connected. How do I get this order?

I have tried bwconncomp, but it orders points by x coordinate, that's not what I want.

Can anyone help? Thanks very much!

Here's an example: https://lh3.googleusercontent.com/-vQkXvCFkPtc/UdWwocG0gVI/AAAAAAAAAII/1OLgtKYDYAg/s399/example.jpg