 # The Art of Solving Minimal Problems

CVPR 2019 Tutorial
Long Beach, California, 16th June 2019

## About the Tutorial

### The Art of Solving Minimal Problems

One of the success stories of computer vision is using robust estimation schemes such as RANSAC in multiple view geometry estimation. With a hypothesis and test framework, one can efficiently handle large amounts of outliers in the measured data. Outliers are always present to some (and often to a large) extent due to the ambiguous feature matching process. A key element in such a framework is the ability to estimate the model from a small or minimal subset of data points - a so-called minimal problem. A classic example is the 5-point algorithm for estimating the relative pose between two cameras, given only image point measurements. Minimal solvers play an important role in many computer vision problems such as 3D Reconstruction, Visual Localization, Augmented/Mixed Reality, Visual Odometry or Robotics. 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. The goal of this tutorial is to explain the principles behind solving minimal problems and give practical means for engineers and researchers (whose main competences may lie elsewhere), to apply the most powerful methods that have been developed in the last ten years. We will present and practically demonstrate how to formulate and solve minimal problems with freely available software that will be distributed to the participants of the tutorial.

## Preliminary program available

We will first introduce the topic and provide examples of important applications, that could not be handled efficiently without solving minimal problems. Secondly, we will show how minimal problems lead to solving polynomial equations and we will explain the methods used in computer vision. We will take an engineering approach, avoiding unnecessary mathematical abstraction, and demonstrating the state-of-the-art computational approach that can be used in real applications. Then, we will focus on the issues that are crucial for building fast and robust solvers. We will demonstrate the principles by using free software packages on real examples. In the final part of the tutorial we will show worked examples for minimal problems which attendees will be able to work out on their computers on the spot.

A preliminary program is available at: Program.

### Important dates

• #### Tutorial

16th June, 2019