Zuzana Kúkelová presents Fast algebraic solvers for computer vision problems

On 2020-02-11 14:30:00 at G205, Karlovo náměstí 13, Praha 2
Many problems in computer vision, but also other fields such as robotics,
control design, or economics, can be formulated using systems of polynomial
equations. For computer vision problems, general algorithms for solving
polynomial systems cannot be efficiently applied. The reasons are twofold
-computer vision and robotic applications usually require real-time solutions,
or they often solve systems of polynomial equations for millions of different
instances. Several approaches based on algebraic geometry have been recently
proposed for the design of very efficient algorithms (solvers) that solve
specific classes of systems of polynomial equations. In this talk, I will
briefly discuss such methods for creating efficient solvers for systems of
polynomial equations. The discussed methods are based on Gröbner bases and
resultants, and they use the structure of the system representing a particular
problem to design an efficient specific solver for the problem. I will discuss
several approaches for improving the efficiency of the final solvers. I will
also introduce an automatic generator of Gröbner basis solvers, which can be
used even by non-experts to efficiently solve problems described by systems of
polynomial equations. Finally, I will demonstrate the usefulness of the
by presenting efficient and numerical stable solutions to several important
computer vision problems.
Responsible person: Petr Pošík