The problem of self-calibration of two cameras from a given fundamental matrix is one of the basic problems in geometric computer vision. Under the assumption of known principal points and square pixels, the Bougnoux formula offers a means to compute the two unknown focal lengths. However, in many practical situations, the formula yields inaccurate results due to commonly occurring singularities. Moreover, the estimates are sensitive to noise in the com-puted fundamental matrix and to the assumed positions of the principal points. In this paper, we therefore propose an efficient and robust iterative method to estimate the focal lengths along with the principal points of the cameras given a fundamental matrix and priors for the estimated camera intrinsics. In addition, we study a computationally efficient check of models generated within RANSAC that improves the accuracy of the estimated models while reducing the to-tal computational time. Extensive experiments on real and synthetic data show that our iterative method brings signifi-cant improvements in terms of the accuracy of the estimated focal lengths over the Bougnoux formula and other state-of-the-art methods, even when relying on inaccurate priors. The code for the methods and experiments is available at https://github.com/kocurvik/robust.self.calibration

During astronomical observations, images of selected part of the sky are made by the Slovak 70cm telescope specialized on space debris tracking. Every pixel of this frame can be represented by three data: position on the horizontal$X$axis, vertical$Y$axis, respectively and the intensity value that can range from 0 to 65536. The intensity value in the order of thousands or higher indicates presence of an orbital or extraterrestrial object such as a star, planet, space debris, or even electromagnetic field interference, celestial plane background and other artefacts. In this paper, we present the methodology and proof of concept of our design for processing of astronomical images and a novel space debris tracklet building process using a machine learning method by exploiting Long Short Term Memory (LSTM) architectures. Machine learning models need a fair amount of data examples for training. However, there are not enough sequences captured by the telescope, therefore we train a neural network with synthetic artificial training data based on known sky observations. Information about moving objects in the Earth's orbit is visualized as sequences of positions in time.