Minimal Perspective Autocalibration
Authors: Andrea Porfiri Dal Cin, Timothy Duff, Luca Magri, Tomas Pajdla

We introduce a new family of minimal problems for reconstruction from multiple views. Our primary focus is a novel approach to autocalibration a long-standing problem in computer vision. Traditional approaches to this problem such as those based on Kruppa's equations or the modulus constraint rely explicitly on the knowledge of multiple fundamental matrices or a projective reconstruction. In contrast we consider a novel formulation involving constraints on image points the unknown depths of 3D points and a partially specified calibration matrix K. For 2 and 3 views we present a comprehensive taxonomy of minimal autocalibration problems obtained by relaxing some of these constraints. These problems are organized into classes according to the number of views and any assumed prior knowledge of K. Within each class we determine problems with the fewest---or a relatively small number of---solutions. From this zoo of problems we devise three practical solvers. Experiments with synthetic and real data and interfacing our solvers with COLMAP demonstrate that we achieve superior accuracy compared to state-of-the-art calibration methods. The code is available at https://github.com/andreadalcin/MinimalPerspectiveAutocalibration.