Given a set of successive images which contain the positions of people in a certain space and at a certain time, we propose a method to reconstruct their trajectories. A surveillance 3D-camera takes a photo of the place every a certain fraction of the second and provides us with the data, after processing each picture and retrieving the position of the people in its view. We connect points from successive images by considering that people's position evolves with optimal transport. Our approach is mainly implemented by using a linear programming function, already available in Python. As the camera produces imperfect measurements, we define a framework to classify data and filter out noise. After presenting the problem of optimal transport of finite points as a linear programming problem, we provide some details of our modeling procedure. Finally, we show some of the results obtained with our method while we also suggest ideas to further improve our work.