Find 3D coordinates of unknown amount of points with multiple cameras

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So I have a number of cameras laid around a room to track the objects insie the room. The objects uses reflective markers, and from these markers the cameras record their respective x-y image coordinates of the markers they see, the raw pictures are discarded. I have the parameters of these cameras and I want to find the 3D coordinates of these markers.

I was thinking about calculating them through triangulation, but to do that I need to know how many markers I have, and which coordinates recorded in each camera belongs to which marker. I do not have that information. Is there an algorithm to find that out?