Camera Parameters: Difference between revisions
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M_{int} = | M_{int} = | ||
\begin{bmatrix} | \begin{bmatrix} | ||
f/s_x & s & o_x\\ | |||
0 & | 0 & f/s_y & o_y\\ | ||
0 & 0 & 1 | 0 & 0 & 1 | ||
\end{bmatrix} | \end{bmatrix} | ||
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M_{int} = | M_{int} = | ||
\begin{bmatrix} | \begin{bmatrix} | ||
128/256 & 0 & 128/256\\ | |||
0 & | 0 & 128/256 & 128/256\\ | ||
0 & 0 & 1 | 0 & 0 & 1 | ||
\end{bmatrix} | \end{bmatrix} | ||
Revision as of 13:11, 23 September 2020
Camera Parameters
Intrinsics
The is the projection matrix which turns camera coordinates to image coordinates.
It consists of the following:
- Focal Length \(f\)
- Image Center \(\mathbf{o} = (o_x, o_y)\)
- Size of pixels \(\mathbf{s} = (s_x, s_y)\)
- Axis skew \(s\) typically 0
The formula for this matrix is: \[ \begin{equation} M_{int} = \begin{bmatrix} f/s_x & s & o_x\\ 0 & f/s_y & o_y\\ 0 & 0 & 1 \end{bmatrix} \end{equation} \]
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 \(\displaystyle (256, 0)\): \[ \begin{equation} M_{int} = \begin{bmatrix} 128/256 & 0 & 128/256\\ 0 & 128/256 & 128/256\\ 0 & 0 & 1 \end{bmatrix} \end{equation} \]
Extrinsics
This is the view matrix which encodes the camera's position and rotation.
Suppose the camera position is \(\mathbf{C}\) and rotation \(\mathbf{R}_c\).
\[ \begin{equation} M_{ext}= [\mathbf{R} | \mathbf{t}] = [\mathbf{R}_c^T | -\mathbf{R}_c^T \mathbf{C}] \end{equation} \]