Camera Parameters: Difference between revisions
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* Focal Length \(f\) - this determines the field of view. | * Focal Length \(f\) - this determines the field of view. | ||
* Image Center \(\mathbf{o} = (o_x, o_y)\) (also known as principal point) | * Image Center \(\mathbf{o} = (o_x, o_y)\) (also known as principal point) | ||
* Size of pixels \(\mathbf{s} = (s_x, s_y)\) (based on the resolution | * Size of pixels \(\mathbf{s} = (s_x, s_y)\) (based on the resolution) | ||
* Axis skew \(s\) typically 0 | * Axis skew \(s\) typically 0 | ||
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M_{int} = | M_{int} = | ||
\begin{bmatrix} | \begin{bmatrix} | ||
f | f & s & o_x\\ | ||
0 & f | 0 & f & o_y\\ | ||
0 & 0 & 1 | 0 & 0 & 1 | ||
\end{bmatrix} | \end{bmatrix} |
Revision as of 17:05, 27 June 2022
Camera Parameters
Intrinsics
The is the projection matrix which turns camera coordinates to image coordinates.
It consists of the following:
- Focal Length \(f\) - this determines the field of view.
- Image Center \(\mathbf{o} = (o_x, o_y)\) (also known as principal point)
- Size of pixels \(\mathbf{s} = (s_x, s_y)\) (based on the resolution)
- Axis skew \(s\) typically 0
The formula for this matrix is: \[ \begin{equation} M_{int} = \begin{bmatrix} f & s & o_x\\ 0 & f & o_y\\ 0 & 0 & 1 \end{bmatrix} \end{equation} \]
E.g. if your camera has a 90 deg FOV on each side and outputs a resolution of \(\displaystyle 256 \times 256\), then the intrinsic matrix should project \(\displaystyle (1,0,1)\) to \(\displaystyle (256, 0)\): \[ \begin{equation} M_{int} = \begin{bmatrix} 128/256 & 0 & 128/256\\ 0 & 128/256 & 128/256\\ 0 & 0 & 1 \end{bmatrix} \end{equation} \]
- Note you can also write \(\displaystyle f/s_x\) as \(\displaystyle f_x\), and similar for \(\displaystyle f_y\).
Extrinsics
This is the view matrix which encodes the camera's position and rotation.
Suppose the camera position is \(\mathbf{C}\) and rotation \(\mathbf{R}_c\).
\[ \begin{equation} M_{ext}= [\mathbf{R} | \mathbf{t}] = [\mathbf{R}_c^T | -\mathbf{R}_c^T \mathbf{C}] \end{equation} \]