Well, it's too late/early today for any code (sorry), perhaps tomorrow if it won't look too stupid in the morning, and it appears like roboticus knows much better, but I started with this answer before his, so FWIW:

0. Slightly modify your algorithm to eliminate corner points (see below why).

1. Starting with original image, triple it, i.e. each pixel (point).

2. Apply your algorithm.

Original fragment:

# # # # .
# # # . .
# # . . .
# # # # .
# # . . .

After your algorithm:

# # # # .
o o # . .
o # . . .
o o # # .
# # . . .

Original was tripled, algorithm applied (corners eliminated),

###########.
...........#
.........##.
      ..#
      ..#
     .##.
   ..#
   ..#
   ..#
......#####.
...........#
......#####.
   ..#
   ..#
#####.

So, now every marked pixel is guaranteed to have only 2 neighbours.

4. Then it's trivial to start anywhere and just pick unused neighbour until polyline closed.

5. Scale polyline to original (integer division?).

6. Reduce it to eliminate same points as begin-end.

In reply to Re: Polygon Creation -- Request for Algorithm Suggestions by vr
in thread Polygon Creation -- Request for Algorithm Suggestions by golux

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