pronouns - How to tell if "which" refers to subject or object of main clause?

I have not been able to find a satisfactory answer regarding rules about this issue. What I have heard are lots of opinions:

Here is a picture of my house, which I like very much.

Here is a picture of my house that I like very much.

In the second example, that clearly refers to the subject of the main clause, since we could omit it and it would still mean the same thing:

Here is a picture of my house I like very much.

In the first example, is there any rule about what which refers to? There is some ambiguity otherwise.

Answer

There's ambiguity when you try to analyze a sentence devoid of any communicative context. But since language is "quite often" used for communication, other things serve to help disambiguate; such as perceived speaker's intention, the topic of the discourse, the intended function of the sentence. If they don't, you can always ask your interlocutor whether he is referring to the picture or to the house.