Using data as an input to parameterized polynomial systems

Abstract

Parameterized systems of polynomial equations arise in many applications including computer vision, chemistry, and kinematics. Numerical homotopy continuation methods are a fundamental technique within numerical algebraic geometry for both solving these polynomial systems and determining more refined information about their structure. Imperative to these solving methods is the use of data either synthetic or from the application itself, such as image pixel data for computer vision and leg length parameters for kinematics. This paper will describe projects that incorporate the use of data to find real solutions and/or the structure of real solutions for problems in applications. Illustrative examples are given to highlight various uses of data within computer vision, machine learning, and kinematics applications.