Pose Inversion
![inversion.gif](../../twiki/pub/Chair/PoseInversion/inversion.gif)
Error propagation for the inversion of a transformation with error
Given a transformation
![](../../twiki/pub/Chair/PoseInversion/_MathModePlugin_8a349aecf49149a132eec0a494d51734.png)
with the corresponding covariance matrix
![](../../twiki/pub/Chair/PoseInversion/_MathModePlugin_92d3294bdbf2026f0c27d7a47e7f73cd.png)
, the inverse of the full transformation with error is given by
%$
x^\prime=\left(
\left[\begin{array}{cc}R&t\cr0&1\cr\end{array}\right]
\left[\begin{array}{cc}\Delta_R&\Delta_t\cr0&1\cr\end{array}\right] \right)^{-1}x
=
\left[\begin{array}{cc}\Delta_R&\Delta_t\cr0&1\cr\end{array}\right]^{-1}
\left[\begin{array}{cc}R&t\cr0&1\cr\end{array}\right]^{-1} x
$%