The Art of Solving Minimal Problems
Minimal problems play an important role in 3D reconstruction and Visual Odometry computation. The state of the art approach to minimal problem solving is based on solving polynomial equations robustly and efficiently. This is a difficult topic since it is often formulated in a very abstract mathematical language. Our goal is to explain the principles and the practice of minimal problem solving to allow engineering to use the most useful methods that have been developed in last ten years. We will present and practically demonstrate how to formulate and solve minimal problems with tools available on pre-‐configured software that will be distributed to the participants of the tutorial.
Syllabus & program:
We will first introduce the topic and provide examples of important applications, which could not be solved without solving minimal problems. Secondly, we will show how minimal problems lead to solving polynomial equations and we will explain the state of the art polynomial solving. We will take an engineering approach avoiding all unnecessary mathematical abstraction but demonstrating the state of the art computational approach that can really be used in applications. Then, we will focus on the issues that are crucial for building fast and robust solvers that can be really used in RANSAC robust estimation. We will demonstrate the principles by solved examples in free software packages. The final part of the tutorial will present a solved example which attendees will be able to work out in their computers on the spot.
A preliminary version of the program is available on the webpage.