Inside Plato’s door: a tour in Multi-view Geometry

Full-day Tutorial at CVPR 2022

ΑΓΕΩΜΕΤΡΗΤΟΣ ΜΗΔΕΙΣ ΕΙΣΙΤΩ – "Let no one ignorant of geometry enter"

According to the tradition, on the door of Plato’s Academy there was an inscription that interdicted the entrance to the non-experts in geometry. This tutorial wants to open the door of multi-view geometry to the non-experts and provides a tour of this discipline from classical foundations to recent trends.

Nowadays we are experiencing a resurgence of interest in the traditional methods of Computer Vision. While the dazzling success of deep learning has inspired the research throughout the last decade, the geometry of vision has never ceased to be a fertile ground for investigation.
This tutorial offers a self-contained overview of multi-view geometry, an essential tool in Computer Vision that is at the core of several classical and modern algorithms involving a variety of applications, including 3D reconstruction, motion segmentation, visual SLAM and augmented reality.

Aimed primarily at an audience unfamiliar with these topics, this tutorial will guide the attendees on a tour that starts from the geometric foundations of 3D vision to reach up some of the research challenges that are still open in the field.
The course will introduce classical topics such as camera models, camera calibration, the epipolar geometry, and then move to multi-view relations. We will also address the problem of robust estimation and structure from motion. Special emphasis will be put on rigorous mathematical formulations and on the practical aspects that separate theory from efficient and working implementations.


  1. Introduction

  2. Rudiments of projective geometry

  3. Single-view geometry

  • camera model

  • camera calibration

  1. Two-view geometry

  • epipolar geometry

  • robust model fitting

  1. Structure from motion

    • multi-view geometry

    • bundle adjustment

    • taxonomy of approaches

    • theoretical assumptions

  1. Concluding remarks & active research areas



Morning session (Geometric prelude)

  • 9:00 - 10:00

  • 10:00 - 10:30 break

  • 10:30 - 12:30

  • 12:30 - 13:30 lunch

Afternoon session (Structure from motion & conclusion)

  • 13:30 - 15:00

  • 15:00 - 15:30 break

  • 15:30 - 17:00


Politecnico di Milano (Italy)

University of Trento (Italy)

“This year, June 19 and 20 marks Juneteenth, a US holiday commemorating the end of slavery in the US, and a holiday of special significance in the US South. We encourage attendees to learn more about Juneteenth and its historical context, and to join the city of New Orleans in celebrating the Juneteenth holiday. You can find out more information about Juneteenth here: