Camera Transformations: Intrinsic and Extrinsic Parameters

This Jupyter notebook provides a practical guide to understanding and implementing camera transformations in computer vision, with a focus on the intrinsic and extrinsic parameters of a camera. The notebook includes examples of how to compute and apply transformation matrices to move between world and camera coordinate systems.

Notebook Overview

The notebook covers the following topics:

1. Extrinsic Matrix

• Explains the role of the extrinsic matrix in transforming points from world coordinates to camera coordinates.
• Provides a link to further reading on the topic.
• Discusses the interpretation of translation vectors and rotation matrices for transforming coordinate systems.

2. Coordinate Transformations

• Translation Only: Demonstrates how to transform points between the world and camera coordinate systems with only translation (no rotation).
• Translation and Rotation: Introduces rotation matrices and shows how to apply both translation and rotation to transform points.

3. Ray Direction from Camera to Image Plane

• Explains how to compute the direction of a ray from the optical center of a camera to a specific point on the image plane, using the camera’s intrinsic parameters.
• Demonstrates how to compute the camera coordinates of a point along this ray at a given distance from the optical center.

4. Practical Examples

• The notebook includes practical code examples that compute the translation vectors, rotation matrices, and transformations between different coordinate systems, helping you visualize the process.

Dependencies

The notebook requires the following Python libraries:

• numpy

To install the required libraries, run:

pip install numpy