If you are sitting behind a router or similar it is not possible for Yawcam to detect the public ip-address. There might be some unreliable methods to do this, but I don't think it's worth implementing.
Yawcam can only detect the ip of the local machine. If this happens to be the public ip, then thats nice. Otherewise the user has to make an effort to get hold of the public address.
You can read more about this in the FAQ, but you can also follow jolivo's examples above.