hamming distance of bloom filters

Question

In the introduction of Distance-Sensitive Bloom Filters the authors state:

The relative Hamming distance between two Bloom filters (of the same size, and created with the same hash functions) can be used as a measure of the similarity of the underlying sets.

This statement is followed by a reference to another paper, which could not clarify this statement for me.

Question: What is the precise relation between the hamming distance of two bloom filters and the similarity of the corresponding sets?