There are a few possibilities that come immediately to mind, but I'll suggest that the signing of the Anglo-Japanese Treaty of Commerce and Navigation in July 1894 is a good point at which to mark the change in perception.

Although it didn't completely return sovereignty to Japan, this was the first treaty under which a European nation agreed to give up the right of extraterritoriality for its citizens. It thus recognized that Japanese laws were "civilized" enough to apply to Europeans.

Other good possibilities would be the formation of the alliance with Britain in 1902 and the defeat of the Russians in 1905.