Is my adviser supposed to be assigning me my research?
This depends very much on:


How much interests and your advisor's interests align
Where your funding comes from


First, interest alignment: Starting a grad program, you find an advisor with interests that overlap with your own, do the foundational things that need to get done, then expand on it with your own ideas.  Later, when you are pitching grants, very much the same thing but with program officers: you have a great idea, and you find a way to dovetail it with their calls for proposals.  Finding the common ground between your research and others' research is a fundamental academic skill.

Second, money: if you are funded through a grant that needs image processing research done, do you think that your advisor or the funding sponsor will give you a big thumbs up when you say, "Actually, I have some great ideas for embedded security devices I would rather work on."  Nope.  If you were in their shoes, shelling out $30-60k on a student for a year, wouldn't you expect them to help get the grant completed successfully?  If you want full control over your research, become independently wealthy first.

Successfully doing your own research in academia, in grad school and beyond, involves a lot of meeting in the middle.  Given the huge disparity of research topics you mentioned (image processing versus security), I genuinely wonder about the overlap of interests.  If there really isn't much overlap, it might be worth looking for a different advisor.  You won't become an expert in one field by being mentored by a guy in another field, even if your advisor lets you run wild with any idea that comes into your head.

Update

Since more info was added about the funding and interest overlap, I can note a bit more here.  It sounds like your funding is relatively portable and not tied to a project.  In that case, you should have pretty strong control over what you want to do.  You should not be using this control to just pitch ideas and run with them.  The benefit of a PhD program (as opposed to learning how to research while living in a shack) is to apprentice with people who are experts in what you want to do.

However, having your own "batteries included" funding means you should be able to match with the best advisor for your interests. It sounds like you need to discuss the issue of overlapping interests with your current advisor.  If you don't want to go in the same direction as the lab, maybe they can suggest another group who does something that is a better fit.  Alternatively, maybe they will hit topics that you find more interesting during other phases of projects. It's not uncommon to switch advisors in the first year: I knew a professor in undergrad who actually recommended avoiding even starting in a given lab, so you could just meet with professors to find the best match.