I've always set the delimiter as this: If they have to reach out and make physical contact then the need either immediate suspicion, or a warrant. By physical contact I mean coming into my house, patting me down or even shooting little microwaves or whatever the TSA scanners do so that they can see under my clothes.
I've had this discussion several times with people at work and this always seems to be the conclusion I come to. Follow me around, listen with parabolic microphones from a distance, even have bomb sniffing dogs sniff the air as I walk by. These are all what I would call passive forms of surveillance. Anything requiring that a person or machine make physical contact with me falls under the right of being secure in my persons, houses, papers, etc. and should require a warrant.
This does not mean that as long as they are not making physical contact that they don't necessarily need a warrant. Only that if they are going to, then they must have one.