Abstract
The minimal problems for pose and relative pose have provided many challenging problems for the computer vision community. The solution of many of these problems is much easier when using the right tools from Algebraic Geometry. We will give a very brief introduction to algebraic geometry and direct our the course towards the construction of Gröbner bases and we demonstrate how they can be used for solving geometric problems in computer vision. We will do our best to make the course mathematically self-contained and will present the theory in an intuitive manner in order to quickly get to where it is interesting from a computer vision standpoint.As examples to illustrate the method we will demonstrate a few trivial examples, an easy way to solve the 5 point calibrated relative pose problem as this problem is well known and the previous solvers are rather complicated, finally we will demonstrate our solver for the relative pose for the semi-calibrated case of unknown focal length.
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