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diedrim authored Sep 17, 2024
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22 changes: 16 additions & 6 deletions book/mia.tex
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Expand Up @@ -44,6 +44,13 @@
\vspace*{\fill}

\newpage

\vspace*{\fill}
\noindent
\copyright \ This work is licensed under CC BY 4.0
% \vspace*{\fill}


\thispagestyle{empty}


Expand Down Expand Up @@ -683,7 +690,7 @@ \subsection{Exploiting separability}
\fat{C} = \bldgr{\Phi}_1\transp \fat{T} \bldgr{\Phi}_2,
$$
where $\fat{C}$ is a $M_1 \times M_2$ matrix such that $\mathrm{vec}( \fat{C} ) = \fat{c}$.
Similarly, it can be shown that $\bldgr{\Phi} \fat{w}$ can be more efficiently computed as $\bldgr{\Phi}_x \fat{W} \bldgr{\Phi}_y\transp$, with $\mathrm{vec}( \fat{W} ) = \fat{w}$.
Similarly, it can be shown that $\bldgr{\Phi} \fat{w}$ can be more efficiently computed as $\bldgr{\Phi}_1 \fat{W} \bldgr{\Phi}_2\transp$, with $\mathrm{vec}( \fat{W} ) = \fat{w}$.
Therefore, the solution~\eqref{eq:coefficients}, which can be written as
$$
\bldgr{\Phi}\transp
Expand Down Expand Up @@ -1491,7 +1498,7 @@ \section{Landmark-based registration}
However, this solution does not necessarily satisfy the second constraint of rotational matrices that
$\det( \fat{R} ) = 1$. It is also possible\footnote{%
Since $\det(\fat{A} \fat{B}) = \det(\fat{A}) \det(\fat{B})$,
we have that $\det(R) = \det(U) \det(V)$.
we have that $\det(\fat{R}) = \det(\fat{U}) \det(\fat{V})$.
Furthermore,
$\det(\fat{U}) \pm 1$ and $\det(\fat{V}) \pm 1$ since $\fat{U}\transp \fat{U} = \fat{I}$ and $\fat{V}\transp \fat{V} = \fat{I}$.
}
Expand Down Expand Up @@ -3975,12 +3982,15 @@ \section{Estimating the ground truth}


\backmatter
\clearpage

\chaptermark{Bibliography}
\renewcommand{\sectionmark}[1]{\markright{#1}}
\sectionmark{Bibliography}

% \chaptermark{Bibliography}
% \renewcommand{\sectionmark}[1]{\markright{#1}}
% \sectionmark{Bibliography}

\addcontentsline{toc}{chapter}{Bibliography}
% \sectionmark{References}
% \renewcommand{\sectionmark}[1]{\markright{#1}}
\bibliographystyle{ieeetr}
\bibliography{mia}

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