Instructor: Rohit
Date: June 2, 2025 (🌅 Morning Session)
In this session, we laid the mathematical and geometric foundations of how cameras capture the world — the first step in many vision and robotics pipelines.
We began with the geometry of image formation, focusing on the pinhole camera model as the ideal abstraction for understanding how 3D points are projected onto 2D images. This led us to the perspective projection equation, which formalizes this mapping using homogeneous coordinates.
From there, we broke down the projection matrix — what it encodes, how it's constructed, and how it intertwines the intrinsic and extrinsic properties of a camera. We explored the anatomy of the projection matrix and how it can be decomposed to recover meaningful camera parameters.
With this structure in place, we moved into camera calibration: the process of estimating camera parameters from known data. We covered Tsai’s method, one of the classical approaches, and then focused on the Direct Linear Transform (DLT) algorithm — a fundamental technique that frames calibration as a linear system solvable via SVD.
Each topic built on the last, tying together geometry, algebra, and practical calibration to help you understand how a robot (or algorithm) begins to make sense of visual input.
- 📘 Exercise Notebook: direct-linear-transform.ipynb
Implement the Direct Linear Transform (DLT) algorithm on images of a Rubik’s Cube to estimate camera projection.
💬 Please post any questions or discussion points in the #module-4-multiview-geometry Slack channel.
| Topic | Link |
|---|---|
| Lecture Slides - Camera Modeling, Camera Calibration | lec-12-mvg-camera-calibration.pdf |
| Mobile Sensing & Robotics II – Cyrill Stachniss (2021) (Lectures 23–27: Camera Parameters & DLT) |  |
| First Principles of Computer Vision – Shree K. Nayar (Channel) |  |
| Image Formation (Playlist) |  |
| Camera Calibration (Playlist) |  |
| Computer Vision – Andreas Geiger (Uni Tübingen) (Course + Playlist) |   |
| Lecture 02: Image Formation (Slides) |  |
| 📷 Cameras and Lenses – Interactive Visual Explainer by Bartosz Ciechanowski |  |