Need help in understanding freeman chain coding

Hello,I have read about freeman coding which connects pixels in 8 neighbourhood area.

Now I am currently using the subpixel edge detection to detect edges,but the edge points are in extremelyrandom order.

So as per the discussion I had with the author of the subpixel code(code is listed below),he has recommended that I use freeman chain coding to link those points

Now f,the two existing implementations of freeman on matlab are incorrect and end up failing on my images.

So I would appreciate it if someone could either point out why the method is failing on my cases or if there are any articles/tutorials that can help me understand this.

Images that I use

freeman chain code on matlab

https://in.mathworks.com/matlabcentral/fileexchange/29518-freeman-chain-code

https://in.mathworks.com/matlabcentral/fileexchange/29518-freeman-chain-code

Subpixel accuracy edge detection

https://in.mathworks.com/matlabcentral/fileexchange/48908-accurate-subpixel-edge-location