This thesis analyzes the problem of reconstructing the position of a static, rectangular object in three-dimensional space based on a series of its photographs. The rectangle is described by its vertices in 3D space and the position of its vertices in the photograph (in 2D space) is estimated using a deep learning model. The algorithm takes in a set of estimates along with parameters defining the camera that produced the corresponding images and produces an estimate of the 3D position of the object of interest. An overview of the theoretical background is presented and two standard methods for solving the given problem, the inhomogeneous method and the Loewenberg-Marquardt method, are introduced. Additionally, a new method, based on gradient descent, is proposed. The method ensures that the reconstructed object is indeed rectangular in shape by searching the parameter space of one of the four selected rectangle parameterizations in three-dimensional space. The result of the inhomogeneous method was taken as the initial estimate for the remaining two methods, with which a further optimization was performed. Two metrics were monitored, the reprojection error (m1) and a business metric (m2). Since, to calculate the results of the business metrics, one has to know the true position of the desired object in three-dimensional space, the algorithm monitors m1. However, it was shown that the results of these two metrics do not necessarily follow the same trend. Regardless of that, as expected, it has been shown that the proposed method, in this domain, improves the previous ones. The entire system was implemented in the Tensorflow library.