xeonqq / multiple_view_geometry

A demonstration of how multple view geometry works

Multi view geometry key concepts in Python

1. Demo on how to calculate epipolar line

Given:

• The two camera positions in world frame,
• The position of the cube in world frame,
• The camera intrinsics

Then:

• Calculate the projection of the keypoints from the cube onto the image frame
• Calculate the epipolar line in each image using its coorespondence and essential matrix

Demo

Command to run the demo:

python ./epipolar_geometry.py

or interact with the notebook

jupyter notebook epipolar_geometry.ipynb

2. Eight points algorithm

Given

• The positions of 8 or more pairs of point correspondence in two frames
• The camera intrinsics

Then:

• Calculate the essential matrix, and derive the translation (with a scale) and rotation of the two camera poses.

3. Structure from motion

Given

• The positions of points correspondence in two frames
• The camera intrinsics
• The poses of the two cameras in world frame

Then:

• Calculate the 3d position of the observed points in world frame, by solving a least square error problem

4. Bundle adjustment

Given

• Initial guess of the two camera poses in world frame
• Noisy observation of points correspondence in image frame
• Estimation of the 3d points in world frame
• The camear intrinsics

Then:

• Optimize the pose of the cameras' poses and 3d points positions using bundle adjustment from g2o library

Command to run the tests above:

pytest