  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
