word usage - What is the proper way of addressing a professor?

I am a graduate student. Some part of my master thesis requires me to contact a professor from another university. In the first email I addressed him as "Dear Professor Smith". He started his reply with, let's say, "Dear Emily".

Does it mean that he also asked me to call him by his first name? He didn't do it explicitly. How should I address him in my next email?

We are going to meet face to face in the foreseeable future.

Edit: My question isn't about addressing a professor in the US. If it were, I'd have pointed it out. It's about general politeness. Enlish is the first language either for me nor for the professor. I don't have the problem in my mother tongue. So if English were my mother tongue, I'd have so much experience, that it would be obvious for me.

I don't care what is customary in the US or the Great Britain. All I want to know is how to be polite if we communicate in Enlish, so my inquiry refers to the English language, not the (English or American) culture.

Edit2: Let me rephrase the question: dis the professor suggest that I we should be on first name basis by addressing me as "Dear Emily" in his email? That shouldn't be country-depenent.

The email was sent to me and other members of my group. It started with "Dear Emily and all" and ended with "Cheers, John". The professor is on first name basis with the rest of the group.

He doesn't teach me.