Geometric Calibration

Multiple Camera Models

Current Documentation
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Deprecated in Current Release


Requirements Software operation Defining Calibration Tasks Definitions and Theory

Supported Systems

Supported Targets

Required Evidence

Test Setup

Calibration Procedure

Use in Imatest Master

Use in Imatest IT

Module settings

Module outputs

Defining a Device

Defining Distortion

Defining the System of Devices

Defining the Target

Defining a Test Capture

Defining a Test Image

Homogenous Coordinates

Projective Camera Model

Multi-Camera Systems

Distortion Models

Coordinate Systems

Rotations and Translations


 

Multiple camera system models are defined as a set of projective camera models. One camera is chosen to be the reference camera. The extrinsics of each camera can be factored into two parts: the transform from the camera’s coordinate system to the reference camera’s coordinate system and the reference camera’s coordinate system to the world coordinate system. Using this notation, a rigid \(n\)-camera system may be described by a single world to system set of extrinsic parameters and \(n-1\) fixed sets of extrinsics parameters describing the relative position of the cameras.

Imatest Calibration Assumptions

When performing a calibration in imatest, the system of cameras is assumed to be rigid. In a rigid camera system, the position and orientation of the cameras are fixed relative to each other, while the system as a whole is allowed to move.

Example

Let \(\mathbf{P}_1\) be the reference camera model and let \(\mathbf{P}_2\) and \(\mathbf{P}_3\) be other cameras in the camera system. The projective camera matrices for these

\(\mathbf{P}_1=\left[\begin{array}{ccc}&&\\&\mathbf{K}_1&\\&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{W\rightarrow1}&&\mathbf{t}_{W\rightarrow1}\\&&&\end{array}\right]=\left[\begin{array}{ccc}&&\\&\mathbf{K}_1&\\&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{I}&&\mathbf{0}\\&&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{W\rightarrow1}&&\mathbf{t}_{W\rightarrow1}\\&&&\end{array}\right]\)

\(\mathbf{P}_2=\left[\begin{array}{ccc}&&\\&\mathbf{K}_2&\\&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{W\rightarrow2}&&\mathbf{t}_{W\rightarrow2}\\&&&\end{array}\right]=\left[\begin{array}{ccc}&&\\&\mathbf{K}_2&\\&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{1\rightarrow2}&&\mathbf{t}_{1\rightarrow2}\\&&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{W\rightarrow1}&&\mathbf{t}_{W\rightarrow1}\\&&&\end{array}\right]\)

\(\mathbf{P}_3=\left[\begin{array}{ccc}&&\\&\mathbf{K}_3&\\&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{W\rightarrow3}&&\mathbf{t}_{W\rightarrow3}\\&&&\end{array}\right]=\left[\begin{array}{ccc}&&\\&\mathbf{K}_2&\\&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{1\rightarrow3}&&\mathbf{t}_{1\rightarrow3}\\&&&\end{array}\right]\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{W\rightarrow1}&&\mathbf{t}_{W\rightarrow1}\\&&&\end{array}\right]\)

In this case, 

\(\left[\begin{array}{ccc|c}&&&\\&\mathbf{R}_{a\rightarrow b}&&\mathbf{t}_{a\rightarrow b}\\&&&\end{array}\right]\)

is the transformation of points in coordinate system \(a\) to points coordinate system \(b\), and \(W\) represents a world coordinate system.