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\begin_body

\begin_layout Standard
Derivative of EssentialMatrix epipolar error.
\end_layout

\begin_layout Standard
With respect to orientation:
\begin_inset Formula 
\[
e(\omega)=a^{T}[t]_{\times}Re^{\omega}b=a^{T}Ee^{\omega}b
\]

\end_inset


\begin_inset Formula 
\[
\frac{\partial e(\omega)}{\partial v}=a^{T}E[b]_{\times}
\]

\end_inset


\end_layout

\begin_layout Standard
With respect to tangent to sphere:
\begin_inset Formula 
\[
e(v)=a^{T}(Bv\times Rb)
\]

\end_inset


\begin_inset Formula 
\[
\frac{\partial e(v)}{\partial v}=a^{T}\frac{\partial(Bv\times Rb)}{\partial v}=a^{T}[-Rb]_{\times}B=a^{T}R[-b]_{\times}RB
\]

\end_inset


\begin_inset Formula 
\[
(1*3)(3*3)(3*2)
\]

\end_inset


\end_layout

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