Multi Camera Calibration Theory
In the Multi-Camera Calibration article, we focused on the practicalities of Multi-Camera Calibration. In this article, we will explain some of the theory behind.
Calibration object
The calibration object for multi-camera calibration must be such that it is possible to accurately determine its pose (position and orientation) relative to a camera.
Transformation matrix
Combines both rotation and translation required to transform a position vector in one coordinate frame to another coordinate frame via matrix multiplication.
The transformation between two cameras
Consider the scenario with two cameras.
![Two cameras pointing at same object](../../../_images/multi-camera-calibration-theory.png)
We want to find the transformation matrix \(H^{Right}_{Left}\) which describes the transformation from the camera on the right to the camera on the left.
![Left camera in right camera frame](../../../_images/multi-camera-calibration-theory-left-in-right.png)
What we have though, from either camera, is the pose of the calibration object in the camera reference frame \(H^{Obj}_{Left}\) and \(H^{Obj}_{Right}\). The inverse of these poses, (eq. 1) and (eq. 2), allows the transformation of the points in the point clouds to the calibration objects’ coordinate frame.
![Object in left and right camera frame](../../../_images/multi-camera-calibration-theory-object-in-left-and-right.png)
We could have stopped there, and provided transformation matrices to the calibration object, as a final result. We do not want to have a dependency on the pose of the calibration object, as that is often arbitrary. Thus we want either \(H_{Left}^{Right}\) (eq. 3) or \(H^{Left}_{Right}\).
![Two cameras pointing at same object](../../../_images/multi-camera-calibration-theory-transformations.png)