Does the observer or the camera collapse the wave function in the double slit experiment?
If you place a camera you will not see any interference pattern. So, the answer is yes. The camera will cause the wavefunction to "collapse". But I don't like the term "wavefunction collapse", because wavefunction is not really any physical object. What the camera will basically do is cause an abrupt change in the state of the particle.
Here is the defintion of measurement from Landau's book
By measurement, in quantum mechanics, we understand any process of interaction between classical and quantum objects, occurring apart from and independently of any observer. The importance of the concept of measurement in quantum mechanics was elucidated by N. Bohr. We have defined "apparatus" as a physical object which is governed, with sufficient accuracy, by classical mechanics. Such, for instance, is a body of large enough mass. However, it must not be supposed that apparatus is necessarily macroscopic. Under certain conditions, the part of apparatus may also be taken by an object which is microscopic, since the idea of "with sufficient accuracy" depends on the actual problem proposed.
If we setup the camera to record like above but NEVER EVER EVER look at the result of what was recorded. Does the wave function still collapse?
The answer is that we just don't know. We can tell that the wave function has collapsed (in Copenhagen terms) only when we humans look at the system -- in the canonical experiment that means looking at the landing pattern to see if we have fringes or clumps. And even though in your example we are, on purpose, not looking at the "which path" information in the camera, it's not at all clear that what makes that camera information be "which path" information is not conscious observation.
But the problem is actually much deeper than that. It doesn't matter what if any "role" -- in the sense of a mechanism of interaction -- conscious observation plays in inducing collapse in the system. What matters is, saying anything about the system first requires a conscious observation. In science (as opposed to metaphysics, say, or mathematics) that -- our observations -- is the basis of what we say stuff about when we say stuff. So conscious observation is always in there, getting in the way, and leaving us uncertain - in fact in scientific terms, utterly clueless to be precise -- as to what part, if any, it's playing.
Re: @user774025's, Landau quote in which measurement is defined as "...occurring apart from and independently of any observer". That runs straight into one of the most fundamental challenges in science, not just QM[1], namely that science Just Is an activity performed by conscious observers. Landau's definition tries to de-couple science from the observer, but in doing that he is no longer talking about science. Science is the act of observation (plus a bunch of other things, of course[2]).
Consider: there is not a single scientific experiment, ever, that did not culminate in an observation by a consciousness[3]. So in science, the answer to the question:
"What happens if we don't look?"
is at very least
"We don't and can't know"
but in fact is probably better put as
"Why are you asking that? Science Just Is looking. I thought we were doing science!?"_
And of course, once we've looked, we have "contaminated" our experiment with a conscious observation, and we cannot tell what effect that has had.
Which is why we don't know and cannot know if the not-looked-at-directly camera-based which-path detector caused collapse until we look at the electrons' landing pattern to see if collapse occurred at all. And by then, although we have confirmed collapse, we've added a new factor -- the looking.
We can never tell what an unlooked-at system looks like without looking at it, at which point it is no longer unlooked-at.
[1] The reason this kind of thing gets attention in QM is because experiments like double-slit served to highlight the problem by showing us a peculiar form of measurement error that is fundamentally different from the everyday kind, such as turning on a light so we can see to count how many cockroaches there are in a dark room. But the problem pre-dates QM, and in fact is fundamental to what science is -- in fact what observation overall is.
[2] For example, in the professional scientist's case: writing up those observations and their opinions about them, presenting them at conferences, kicking doctoral students into doing the same, and playing multi-user Call of Duty because although their current grant money is about to run out, and their doc-students are whining about it, they just can't face the prospect of another mind-numbing, morale-destroying, rather-poke-myself-in-the-eye-with-a-sharp-stick round of writing the next grant proposal.
[3] Even if we take an eliminative view of what consciousness is.