From experience (and my time in academic world). There is going to be a list of topics declared by your university. Each of the topic will have a supervisor listed, examples might be something like:
Thesis proposed by Prof. Donald Duck, computer graphics professor on Quack university:
Design and implement KD-tree builder for triangular scenes. The KD-tree builder should be able to build tree using multiple heuristics (Surface Area Heuristics, Split in the middle of longest axis, Median split), and should be implemented optimally. The implementation will be done in our provided library, and has to be done in C++ (as reference CPU KD-tree builder) and also CUDA for implementation of GPU KD-tree builder. Results will be tested against other implementations in provided library and other third party software. The resulting implementation will be credited to the actual student, and has to be publicly available together with resulting thesis.
- This is a proposed project by supervisor from the university, such will always be either PhD student or professor (as they have to supervise at least few theses each year). There will always be a name attached.
- If you are interested in such topic, or from the same area - you can always contact & visit him during consulting hours. You should be prepared and ask him about whether he is interested in supervising you thesis with your own topic. It is likely that he will accept, as active students are kind of rarity (and always welcome one).
- In case of need, student can get any additional consultant to help him with research and design of the algorithm
Thesis proposed by The Corporate company, supervised by Greedy George, CTO at The Corporate and MSc. Supervising Sam, PhD. student at Quack university:
The Corporate company wants to propose and develop a solution for counting people entering building and its rooms. Any required hardware will be provided. Associate at the Quack university will provide any theoretical expertise required for implementation. The participating student will be awarded financially and offered permanent position at The Corporate company if he successfully proposes and implements the solution. The Corporate will be the owner of everything created (i.e. source code, binaries, etc.), only thesis will be stored publicly at university.
- This is a typical proposed project by company, although you can't propose thesis without being related to university - Supervising Sam is often mainly offering theses for the company (for which he often also works).
- For the company this is huge opportunity to get a project (which would cost then often 10 or 20 times more to hire an employee) in a very cheap way (reward is often something like $1k or less - for literally at least 6 months of almost full time work). There is a risk though - there is slight chance that the project might fail (which is why Supervising Sam is often associate of the company, to make sure it doesn't)
- Additionally, company can get an entry level employee that already will have some knowledge of their system (as he will most likely work with it)
- And also, they keep all the rights, student is only credit for the thesis, not the actual work. Which may be bad for the student, assuming he doesn't want to work at that company right after.
- The company on the other hand has to reveal their trade secrets, source code, etc. to the supervisor at the university (otherwise he won't be able to consult). Which does have some risk.
Now, as for me in the past, I have went the first way (with completely different topic) - I've contacted a person whom I knew through subjects that works with topic I would like to write thesis about. We had a talk about it, and I have asked him if he is willing to be my supervisor (for BSc. thesis), and explained in detail why I want to make such thesis. He agreed. I technically did the same for MSc. thesis (with the same supervisor).
The other case is mostly quite a painful one, as such cases are not that welcome in academic world (although sometimes accepted due to sponsoring or political support for example).
In conclusion: I don't think you should do what you're doing, and I don't think it is likely you will find any supervisor agreeing to this. Why? I'm sure you can find supervisor with knowledge in topic of your choice, and I'm sure he will propose to do the same, without the company. The problem is simply, unless the company can provide him with complete copy of game engine (with all tools and also source code), he won't be able to supervise the thesis and provide valuable advice during it. Failure of supervising thesis does have a negative impact for him, and therefore it is unlikely he will support it.
If you still want to pursue this, I'd recommend going through all proposed thesis topics on your university as soon as possible - and find a supervisor who is an expert in area you are targeting. If he is going to agree with this, then as stated before, you will have to run between him and the company (as he will definitely require full source code of the project).
And now, as for interesting topics (that never gets old):
- Global Illumination
- Physically plausible soft shadows
- Fluid rendering/simulation
- Skin rendering
- Hair rendering
- DXR (I'd throw this in, as there are not that many resources for it yet)
- D3D12/Vulkan (and performance difference against D3D11/OpenGL ... I can see this one actually being allowed on existing engine)
EDIT: Note. The academic environment in your country may differ, what is unacceptable in my country, might be acceptable in yours! (And I should have noted this earlier)