How do I do auto localize my robot with just a camera?

Hello everybody. I have some questions, and the issue is that I have a robot placed in a white room. Then, all over the walls there are some marks, specifically, black crosses; also over every corner, there are marks , the only difference is that these ones are white with a black background. What I want to do is, once detecting the marks and then with the information of the position of themselves, calculate the position of my robot in the space. Suppose I already detect the marks, and then I have the centroid of every cross. What is next? My teacher told me I can use a Kalman filter, but I'm not that wise. I had read something about Slam, but sincerely, I don't understand too much.

I hope you can help me. Thank you all.