If you want to do this without a camera calibration your error size will really depend on your camera position in the world, lens, sensor resolution etc…
e.g. With a camera plane quite parallel to the melting pool and with a quite high pixel/cm ratio probably your error It could be low enought (this really depends on your required accurancy).
If you have the camera correctly calibrated (intrinsics + extrinsics) and you know that all the 2d point are almost co-planar in the world you can easly backproject these points in the world coordinates (e.g. 0 on Z) and then measure the real distance between these points on the plane.