What recent 2nd amendment case law can be used to support the scenario below?

Todd Patterson, is a proud gun owner who has multiple handguns, shotguns, and two automatic weapons. Todd Patterson's state of residence passed legislation requiring the registration of all automatic weapons. As part of the registration process, those seeking to register their automatic weapons are required to submit to a mental health background check. Todd's application to register his automatic weapons is denied due to mental breakdown resulting in a six-month institutionalization when he was 17. The state sends Todd a letter demanding that he forfeit his automatic weapons or risk criminal and civil penalties. Because Todd refuses to hand over his automatic weapons, the state police arrest him and charge him with possession of an unregistered automatic weapon (a felony crime).

At his criminal trial, Todd argues that the registration requirements and his subsequent arrest are violations of his Second Amendment rights.