Camera Parameters: Difference between revisions
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It consists of the following: | It consists of the following: | ||
* Focal Length \(f\) | * Focal Length \(f\) - this determines the field of view. | ||
* Image Center \(\mathbf{o} = (o_x, o_y)\) | * Image Center \(\mathbf{o} = (o_x, o_y)\) (also known as principal point) | ||
* Size of pixels \(\mathbf{s} = (s_x, s_y)\) | * Size of pixels \(\mathbf{s} = (s_x, s_y)\) (based on the resolution) | ||
* Axis skew \(s\) typically 0 | * Axis skew \(s\) typically 0 | ||
| Line 15: | Line 15: | ||
M_{int} = | M_{int} = | ||
\begin{bmatrix} | \begin{bmatrix} | ||
f/s_x & s & o_x\\ | |||
0 & | 0 & f/s_x & o_y\\ | ||
0 & 0 & 1 | 0 & 0 & 1 | ||
\end{bmatrix} | \end{bmatrix} | ||
\end{equation} | \end{equation} | ||
\] | \] | ||
E.g. if your camera has a 90 deg FOV on each side and outputs a resolution of <math>256 \times 256</math>, then the intrinsic matrix should project <math>(1,0,1)</math> to <math>(256, 0)</math>: | |||
\[ | |||
\begin{equation} | |||
M_{int} = | |||
\begin{bmatrix} | |||
128/256 & 0 & 128/256\\ | |||
0 & 128/256 & 128/256\\ | |||
0 & 0 & 1 | |||
\end{bmatrix} | |||
\end{equation} | |||
\] | |||
;Note you can also write <math>f/s_x</math> as <math>f_x</math>, and similar for <math>f_y</math>. | |||
==Extrinsics== | ==Extrinsics== | ||
This is the view matrix which encodes the camera's position and rotation. | This is the view matrix which encodes the camera's position and rotation. | ||
Suppose the camera position is \(\mathbf{C}\) and rotation \(\mathbf{R}_c\). | |||
\[ | \[ | ||
\begin{equation} | \begin{equation} | ||
M_{ext}= [\mathbf{R} | \mathbf{t}] | M_{ext}= [\mathbf{R} | \mathbf{t}] = [\mathbf{R}_c^T | -\mathbf{R}_c^T \mathbf{C}] | ||
\end{equation} | \end{equation} | ||
\] | \] | ||
Latest 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: \[ \begin{equation} M_{int} = \begin{bmatrix} f/s_x & s & o_x\\ 0 & f/s_x & o_y\\ 0 & 0 & 1 \end{bmatrix} \end{equation} \]
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 \(\mathbf{R}_c\).
\[ \begin{equation} M_{ext}= [\mathbf{R} | \mathbf{t}] = [\mathbf{R}_c^T | -\mathbf{R}_c^T \mathbf{C}] \end{equation} \]