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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:
\[
\begin{equation}
M_{int} =
\begin{bmatrix}
-f/s_x & s & o_x\\
0 & -f/s_y & o_y\\
0 & 0 & 1
\end{bmatrix}
\end{equation}
\]
Extrinsics
This is the view matrix which encodes the camera's position and rotation.
Suppose the camera position is \(\mathbf{C}\) and rotation \(\mathbf{R}_c\).
\[
\begin{equation}
M_{ext}= [\mathbf{R} | \mathbf{t}] = [\mathbf{R}_c^T | -\mathbf{R}_c^TC]
\end{equation}
\]
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