The "king" is Franz Josef (1830-1916) the emperor of the Austro Hungarian Monarchy. Koller is Károly Koller (1838-1889) photographer who had a studio in Budapest where the king was photographed few times, but the photographers on the drawing are not Mr Koller, but probably Mr Forche and Mr Gálffy the assistants and the sucessors of the studio. (Message from Bálint Flesch, 21 September 2017)