how a Roman emperor crowned?

[Lord Hobbers]

Purple cloaks weren't exclusive to Emperors, Magistri Militum also wore Cloaks of Tyrian purple with roundels. I don't remember what the roundels were supposed to depict, possibly the imperial family? It's outlined in the Justinianic Code or some other text IIRC.

True, but the Justinianic Code covers a much later period. The original poster wanted to know about the era of the Five Good Emperors, which was a few hundred years earlier, when there were no Magistri Militum, and I believe, no roundels on clothing. As a result, I'd argue that the Code has limited validity, and certainly the sources that cover the Second Century make note of the use of purple for an emperor. In the Year of the Five Emperors, if I recall, Herodian mentions that Albinus discarded his purple cloak after losing the war against Severus (as just one example that I can think of off the top of my head now), and certainly there are references to Commodus being "born to the Purple", meaning he was born as the son of an emperor. Surely this reference to purple as an imperial symbol is notable. I'm not saying that the emperors exclusively wore purple, but I'd argue that a purple garment was certainly something that was closely associated with the emperors of the Principate.