# Efficient Homotopy Continuation

for Solving Polynomial Systems in Computer Vision Applications

## Organizers

**Ben Kimia**
**Tim Duff**
**Ricardo Fabbri**
**Hongyi Fan**

## Overview

Minimal problems and their solvers play an important role in
RANSAC-based approaches to several estimation problems in vision. Minimal solvers solve
systems of equations, depending on data, which obey a “conservation of number
principle”: for sufficiently generic data, the number of solutions over the complex numbers
is constant. Homotopy continuation (HC) methods exploit not just this conservation
principle, but also the smooth dependence of solutions on problem data.
The classical solution of polynomial systems using Grobner basis, resultants, elimination
templates, etc. has been largely successful in smaller problems, but these methods are
not able to tackle larger polynomials systems with a larger number of solutions. While HC
methods can solve these problems, they have been notoriously slow. Recent research by
the presenters and other researchers has enabled efficient HC solvers with the ability for
real-time solutions.

The main objective of this tutorial is to make this technology more
accessible to the computer vision community. Specifically, after an overview of how such
methods can be useful for solving problems in vision (e.g., absolute/relative pose,
triangulation), we will describe some of the basic theoretical apparatus underlying HC
solvers, including both local and global “probability-1” aspects. On the practical side, we
will describe recent advances enabled by GPUs, learning-based approaches, and how to
build your own HC-based minimal solvers

## Program

TBA

## References

TBA