Fridge line to standard pipe
The picture shows a copper pipe with a compression-fit valve attached. The copper pipe is presumably just a straight section of pipe going into your wall box, and the silver-colored thing with a shutoff knob is a valve attached to the pipe. Are you trying to replace the valve or use the threaded output on the valve itself?

If the existing valve simply has the wrong size output to attach your icemaker line, then the adapter you need is one that takes this valve's male end and adapts it to 1/4" male. If the existing output is a little too wide, then most likely your existing valve is 3/8" (typical for faucet supplies). So you'd need a 3/8" Female to 1/4" Male fitting like this one.

(Note that the linked fitting includes a compression nut that you would simply unscrew and discard for your application - you'd just screw the adapter to your existing valve, and then screw the line to the adapter.)

Another options would be to replace the valve with a similar one that attaches to your copper pipe but has the desired 1/4" male output. You'd buy a new valve with a similar compression fitting designed for 1/2" OD pipe. This would attach to your existing copper pipe, but you may need to cut it and polish it with emery cloth to ensure it is smooth and circular, so that the compression fitting can attach properly.